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2
Task/Prime-triangle/00-META.yaml
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2
Task/Prime-triangle/00-META.yaml
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---
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from: http://rosettacode.org/wiki/Prime_triangle
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7
Task/Prime-triangle/00-TASK.txt
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7
Task/Prime-triangle/00-TASK.txt
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You will require a function f which when given an integer S will return a list of the arrangements of the integers 1 to S such that g<sub>1</sub>=1 g<sub>S</sub>=S and generally for n=1 to n=S-1 g<sub>n</sub>+g<sub>n+1</sub> is prime. S=1 is undefined. For S=2 to S=20 print f(S) to form a triangle. Then again for S=2 to S=20 print the number of possible arrangements of 1 to S meeting these requirements.
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;See also
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:* [[oeis:A036440|OEIS:A036440]]
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94
Task/Prime-triangle/ALGOL-68/prime-triangle.alg
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94
Task/Prime-triangle/ALGOL-68/prime-triangle.alg
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BEGIN # find solutions to the "Prime Triangle" - a triangle of numbers that sum to primes #
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INT max number = 18; # largest number we will consider #
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# construct a primesieve and from that a table of pairs of numbers whose sum is prime #
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[ 0 : 2 * max number ]BOOL prime;
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prime[ 0 ] := prime[ 1 ] := FALSE;
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prime[ 2 ] := TRUE;
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FOR i FROM 3 BY 2 TO UPB prime DO prime[ i ] := TRUE OD;
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FOR i FROM 4 BY 2 TO UPB prime DO prime[ i ] := FALSE OD;
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FOR i FROM 3 BY 2 TO ENTIER sqrt( UPB prime ) DO
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IF prime[ i ] THEN
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FOR s FROM i * i BY i + i TO UPB prime DO prime[ s ] := FALSE OD
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FI
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OD;
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# returns the number of possible arrangements of the integers for a row in the prime triangle #
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PROC count arrangements = ( INT n )INT:
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IF n < 2 THEN # no solutions for n < 2 # 0
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ELIF n < 4 THEN
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# for 2 and 3. there is only 1 solution: 1, 2 and 1, 2, 3 #
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FOR i TO n DO print( ( whole( i, -3 ) ) ) OD; print( ( newline ) );
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1
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ELSE
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# 4 or more - must find the solutions #
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BOOL print solution := TRUE;
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[ 0 : n ]BOOL used;
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[ 0 : n ]INT number;
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# the triangle row must have 1 in the leftmost and n in the rightmost elements #
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# the numbers must alternate between even and odd in order for the sum to be prime #
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FOR i FROM 0 TO n DO
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used[ i ] := FALSE;
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number[ i ] := i MOD 2
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OD;
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used[ 1 ] := TRUE;
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number[ n ] := n;
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used[ n ] := TRUE;
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# find the intervening numbers and count the solutions #
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INT count := 0;
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INT p := 2;
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WHILE p > 0 DO
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INT p1 = number[ p - 1 ];
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INT current = number[ p ];
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INT next := current + 2;
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WHILE IF next >= n THEN FALSE ELSE NOT prime[ p1 + next ] OR used[ next ] FI DO
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next +:= 2
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OD;
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IF next >= n THEN next := 0 FI;
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IF p = n - 1 THEN
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# we are at the final number before n #
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# it must be the final even/odd number preceded by the final odd/even number #
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IF next /= 0 THEN
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# possible solution #
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IF prime[ next + n ] THEN
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# found a solution #
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count +:= 1;
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IF print solution THEN
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FOR i TO n - 2 DO
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print( ( whole( number[ i ], -3 ) ) )
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OD;
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print( ( whole( next, -3 ), whole( n, - 3 ), newline ) );
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print solution := FALSE
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FI
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FI;
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next := 0
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FI;
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# backtrack for more solutions #
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p -:= 1
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# here will be a further backtrack as next is 0 ( there could only be one possible number at p - 1 ) #
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FI;
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IF next /= 0 THEN
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# have a/another number that can appear at p #
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used[ current ] := FALSE;
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used[ next ] := TRUE;
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number[ p ] := next;
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p +:= 1
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ELIF p <= 2 THEN
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# no more solutions #
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p := 0
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ELSE
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# can't find a number for this position, backtrack #
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used[ number[ p ] ] := FALSE;
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number[ p ] := p MOD 2;
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p -:= 1
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FI
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OD;
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count
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FI # count arrangements # ;
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[ 2 : max number ]INT arrangements;
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FOR n FROM LWB arrangements TO UPB arrangements DO
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arrangements[ n ] := count arrangements( n )
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OD;
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FOR n FROM LWB arrangements TO UPB arrangements DO
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print( ( " ", whole( arrangements[ n ], 0 ) ) )
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OD;
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print( ( newline ) )
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END
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77
Task/Prime-triangle/C++/prime-triangle.cpp
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77
Task/Prime-triangle/C++/prime-triangle.cpp
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@ -0,0 +1,77 @@
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#include <cassert>
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#include <chrono>
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#include <iomanip>
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#include <iostream>
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#include <numeric>
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#include <vector>
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bool is_prime(unsigned int n) {
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assert(n > 0 && n < 64);
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return (1ULL << n) & 0x28208a20a08a28ac;
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}
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template <typename Iterator>
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bool prime_triangle_row(Iterator begin, Iterator end) {
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if (std::distance(begin, end) == 2)
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return is_prime(*begin + *(begin + 1));
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for (auto i = begin + 1; i + 1 != end; ++i) {
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if (is_prime(*begin + *i)) {
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std::iter_swap(i, begin + 1);
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if (prime_triangle_row(begin + 1, end))
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return true;
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std::iter_swap(i, begin + 1);
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}
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}
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return false;
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}
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template <typename Iterator>
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void prime_triangle_count(Iterator begin, Iterator end, int& count) {
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if (std::distance(begin, end) == 2) {
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if (is_prime(*begin + *(begin + 1)))
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++count;
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return;
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}
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for (auto i = begin + 1; i + 1 != end; ++i) {
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if (is_prime(*begin + *i)) {
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std::iter_swap(i, begin + 1);
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prime_triangle_count(begin + 1, end, count);
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std::iter_swap(i, begin + 1);
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}
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}
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}
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template <typename Iterator>
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void print(Iterator begin, Iterator end) {
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if (begin == end)
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return;
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auto i = begin;
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std::cout << std::setw(2) << *i++;
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for (; i != end; ++i)
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std::cout << ' ' << std::setw(2) << *i;
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std::cout << '\n';
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}
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int main() {
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auto start = std::chrono::high_resolution_clock::now();
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for (unsigned int n = 2; n < 21; ++n) {
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std::vector<unsigned int> v(n);
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std::iota(v.begin(), v.end(), 1);
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if (prime_triangle_row(v.begin(), v.end()))
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print(v.begin(), v.end());
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}
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std::cout << '\n';
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for (unsigned int n = 2; n < 21; ++n) {
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std::vector<unsigned int> v(n);
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std::iota(v.begin(), v.end(), 1);
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int count = 0;
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prime_triangle_count(v.begin(), v.end(), count);
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if (n > 2)
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std::cout << ' ';
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std::cout << count;
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}
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std::cout << '\n';
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auto end = std::chrono::high_resolution_clock::now();
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std::chrono::duration<double> duration(end - start);
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std::cout << "\nElapsed time: " << duration.count() << " seconds\n";
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}
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84
Task/Prime-triangle/C/prime-triangle-1.c
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84
Task/Prime-triangle/C/prime-triangle-1.c
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@ -0,0 +1,84 @@
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#include <assert.h>
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#include <stdbool.h>
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#include <stdio.h>
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#include <time.h>
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bool is_prime(unsigned int n) {
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assert(n < 64);
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static bool isprime[] = {0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0,
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0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1,
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0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1,
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0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0};
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return isprime[n];
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}
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void swap(unsigned int* a, size_t i, size_t j) {
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unsigned int tmp = a[i];
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a[i] = a[j];
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a[j] = tmp;
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}
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bool prime_triangle_row(unsigned int* a, size_t length) {
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if (length == 2)
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return is_prime(a[0] + a[1]);
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for (size_t i = 1; i + 1 < length; i += 2) {
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if (is_prime(a[0] + a[i])) {
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swap(a, i, 1);
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if (prime_triangle_row(a + 1, length - 1))
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return true;
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swap(a, i, 1);
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}
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}
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return false;
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}
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int prime_triangle_count(unsigned int* a, size_t length) {
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int count = 0;
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if (length == 2) {
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if (is_prime(a[0] + a[1]))
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++count;
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} else {
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for (size_t i = 1; i + 1 < length; i += 2) {
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if (is_prime(a[0] + a[i])) {
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swap(a, i, 1);
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count += prime_triangle_count(a + 1, length - 1);
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swap(a, i, 1);
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}
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}
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}
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return count;
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}
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void print(unsigned int* a, size_t length) {
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if (length == 0)
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return;
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printf("%2u", a[0]);
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for (size_t i = 1; i < length; ++i)
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printf(" %2u", a[i]);
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printf("\n");
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}
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int main() {
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clock_t start = clock();
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for (unsigned int n = 2; n < 21; ++n) {
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unsigned int a[n];
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for (unsigned int i = 0; i < n; ++i)
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a[i] = i + 1;
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if (prime_triangle_row(a, n))
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print(a, n);
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}
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printf("\n");
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for (unsigned int n = 2; n < 21; ++n) {
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unsigned int a[n];
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for (unsigned int i = 0; i < n; ++i)
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a[i] = i + 1;
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if (n > 2)
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printf(" ");
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printf("%d", prime_triangle_count(a, n));
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}
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printf("\n");
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clock_t end = clock();
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double duration = (end - start + 0.0) / CLOCKS_PER_SEC;
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printf("\nElapsed time: %f seconds\n", duration);
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return 0;
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}
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92
Task/Prime-triangle/C/prime-triangle-2.c
Normal file
92
Task/Prime-triangle/C/prime-triangle-2.c
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@ -0,0 +1,92 @@
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#include <stdio.h>
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#include <stdint.h>
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#define GCC_ASM // use GCC's asm for i386. If it does not work, #undef it to use alternative func
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typedef uint32_t uint;
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typedef uint64_t ulong;
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#define MASK 0xa08228828228a2bULL
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#ifdef GCC_ASM
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static inline uint
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bpos(uint x)
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{
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uint b;
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asm("bsf %0, %0" : "=r" (b): "0" (x));
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return b;
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}
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#else
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static inline uint
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bpos(uint x)
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{
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static const uint bruijin[32] = {
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0, 1, 28, 2, 29, 14, 24, 3, 30, 22, 20, 15, 25, 17, 4, 8,
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31, 27, 13, 23, 21, 19, 16, 7, 26, 12, 18, 6, 11, 5, 10, 9
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};
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return bruijin[((uint)((x & -x) * 0x077CB531U)) >> 27];
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}
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#endif // GCC_ASM
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int count(uint n, const uint s, uint avail)
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{
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int cnt = 0;
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avail ^= s;
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if (--n)
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for (uint b = (uint)(MASK>>bpos(s)) & avail; b; b &= b-1)
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cnt += count(n, b&-b, avail);
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else
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return (MASK & s) != 0;
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return cnt;
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}
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int disp(uint n, const uint s, uint avail, int maxn, uint *seq)
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{
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seq[n--] = s;
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if (!n) {
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if ((MASK & s)) {
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for (int i = 0; i < maxn; i++)
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printf(" %d", bpos(seq[i]) + 1);
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putchar('\n');
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return 1;
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}
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} else {
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for (uint b = (uint)(MASK>>bpos(s)) & (avail ^= s); b; b &= b-1)
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if (disp(n, b&-b, avail, maxn, seq))
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return 1;
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}
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return 0;
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}
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int chain(uint n, int count_only)
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{
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const uint top = 1U<<(n - 1);
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const uint avail = 2*top - 2;
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if (count_only)
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return count(n - 1, top, avail);
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uint seq[32];
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seq[0] = 1;
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disp(n - 1, top, avail, n, seq);
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return 0;
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}
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int main(void)
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{
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for (int n = 2; n < 21; n++)
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chain(n, 0);
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putchar('\n');
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for (int n = 2; n < 21; n++)
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printf("%d ", chain(n, 1));
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putchar('\n');
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return 0;
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}
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8
Task/Prime-triangle/F-Sharp/prime-triangle.fs
Normal file
8
Task/Prime-triangle/F-Sharp/prime-triangle.fs
Normal file
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@ -0,0 +1,8 @@
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// Prime triangle. Nigel Galloway: April 12th., 2022
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let fN i (g,(e,l))=e|>Seq.map(fun n->let n=i n in (n::g,List.partition(i>>(=)n) l))
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let rec fG n g=function 0->n|>Seq.map fst |x->fG(n|>Seq.collect(fN(if g then fst else snd)))(not g)(x-1)
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let primeT row=fG [([1],([for g in {2..2..row-1} do if isPrime(g+1) then yield (1,g)],[for n in {3..2..row-1} do for g in {2..2..row-1} do if isPrime(n+g) then yield (n,g)]))] false (row-2)
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|>Seq.filter(List.head>>(+)row>>isPrime)|>Seq.map(fun n->row::n|>List.rev)
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{2..20}|>Seq.iter(fun n->(primeT>>Seq.head>>List.iter(printf "%3d"))n;printfn "");;
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{2..20}|>Seq.iter(primeT>>Seq.length>>printf "%d "); printfn ""
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116
Task/Prime-triangle/Free-Pascal/prime-triangle.pas
Normal file
116
Task/Prime-triangle/Free-Pascal/prime-triangle.pas
Normal file
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@ -0,0 +1,116 @@
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program PrimePyramid;
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{$IFDEF FPC}
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{$MODE delphi}{$Optimization ON,ALL}{$CodeAlign proc=32}
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{$IFEND}
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const
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MAX = 21;//max 8 different SumToPrime : array[0..MAX,0..7] of byte;
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//MAX = 57;//max 16 different SumToPrime : array[0..MAX,0..15] of byte;
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cMaxAlign32 = (((MAX-1)DIV 32)+1)*32-1;//MAX > 0
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type
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tPrimeRange = set of 0..127;
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var
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SetOfPrimes :tPrimeRange =[2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,
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53,59,61,67,71,73,79,83,89,97,101,103,107,
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109,113,127];
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SumToPrime : array[0..cMaxAlign32,0..7] of byte;
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// SumToPrime : array[0..MAX,0..15] of byte;
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SumToPrimeMaxIdx,
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SumMaxIdx,
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Solution,
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FirstSolution : array[0..cMaxAlign32] of byte;
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free : array[0..cMaxAlign32] of boolean;
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|
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maxused : integer;
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digitcount,SolCount : integer;
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|
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procedure InitSumToPrime;
|
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var
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i,j,idx : integer;
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begin
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For i := 1 to MAX do
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Begin
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idx := 0;
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For j := 1 to MAX do
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If (i+j) in SetOfPrimes then
|
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Begin
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SumToPrime[i,idx] := j;
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inc(idx);
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end;
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SumToPrimeMaxIdx[i] := idx;
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end;
|
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end;
|
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|
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procedure InitFree(maxused : integer);
|
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var
|
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i,j : Integer;
|
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begin
|
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For i := 0 to 1 do
|
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Free[i] := false;
|
||||
For i := 2 to maxused-1 do
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Free[i] := true;
|
||||
For i := maxused to MAX do
|
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Free[i] := false;
|
||||
// search maxidx of max neighour sum to prime
|
||||
For i := 1 to maxused-1 do
|
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begin
|
||||
j := SumToPrimeMaxIdx[i]-1;
|
||||
while SumToPrime[i,j] > maxused-1 do
|
||||
j -= 1;
|
||||
SumMaxIdx[i] := j+1;
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end;
|
||||
end;
|
||||
|
||||
procedure CountSolution(digit:integer);
|
||||
begin
|
||||
// check if maxused can follow
|
||||
if (digit+maxused) in SetOfPrimes then
|
||||
Begin
|
||||
if solcount = 0 then
|
||||
FirstSolution := Solution;
|
||||
inc(solCount);
|
||||
end;
|
||||
end;
|
||||
|
||||
procedure checkDigits(digit:integer);
|
||||
var
|
||||
idx,nextDigit: integer;
|
||||
begin
|
||||
idx := 0;
|
||||
repeat
|
||||
nextDigit := SumToPrime[digit,idx];
|
||||
if Free[nextdigit] then
|
||||
Begin
|
||||
Solution[digitcount] := nextDigit;
|
||||
dec(digitcount);
|
||||
IF digitcount = 0 then
|
||||
CountSolution(nextDigit);
|
||||
free[nextdigit]:= false;
|
||||
checkDigits(nextdigit);
|
||||
inc(digitcount);
|
||||
free[nextdigit]:= true;
|
||||
end;
|
||||
inc(idx);
|
||||
until idx >= SumMaxIdx[digit];
|
||||
end;
|
||||
|
||||
var
|
||||
i,j : integer;
|
||||
Begin
|
||||
InitSumToPrime;
|
||||
writeln('number| count| first solution');
|
||||
writeln(' 2| 1| 1 2');
|
||||
For i := 3 to 20 do
|
||||
Begin
|
||||
maxused := i;
|
||||
InitFree(i);
|
||||
digitcount := i-2;
|
||||
solCount := 0;
|
||||
checkDigits(1);
|
||||
write(i:4,'|',solcount:10,'| 1');
|
||||
For j := i-2 downto 1 do
|
||||
write( FirstSolution[j]:3);
|
||||
writeln(i:3);
|
||||
end;
|
||||
end.
|
||||
71
Task/Prime-triangle/Go/prime-triangle.go
Normal file
71
Task/Prime-triangle/Go/prime-triangle.go
Normal file
|
|
@ -0,0 +1,71 @@
|
|||
package main
|
||||
|
||||
import "fmt"
|
||||
|
||||
var canFollow [][]bool
|
||||
var arrang []int
|
||||
var bFirst = true
|
||||
|
||||
var pmap = make(map[int]bool)
|
||||
|
||||
func init() {
|
||||
for _, i := range []int{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37} {
|
||||
pmap[i] = true
|
||||
}
|
||||
}
|
||||
|
||||
func ptrs(res, n, done int) int {
|
||||
ad := arrang[done-1]
|
||||
if n-done <= 1 {
|
||||
if canFollow[ad-1][n-1] {
|
||||
if bFirst {
|
||||
for _, e := range arrang {
|
||||
fmt.Printf("%2d ", e)
|
||||
}
|
||||
fmt.Println()
|
||||
bFirst = false
|
||||
}
|
||||
res++
|
||||
}
|
||||
} else {
|
||||
done++
|
||||
for i := done - 1; i <= n-2; i += 2 {
|
||||
ai := arrang[i]
|
||||
if canFollow[ad-1][ai-1] {
|
||||
arrang[i], arrang[done-1] = arrang[done-1], arrang[i]
|
||||
res = ptrs(res, n, done)
|
||||
arrang[i], arrang[done-1] = arrang[done-1], arrang[i]
|
||||
}
|
||||
}
|
||||
}
|
||||
return res
|
||||
}
|
||||
|
||||
func primeTriangle(n int) int {
|
||||
canFollow = make([][]bool, n)
|
||||
for i := 0; i < n; i++ {
|
||||
canFollow[i] = make([]bool, n)
|
||||
for j := 0; j < n; j++ {
|
||||
_, ok := pmap[i+j+2]
|
||||
canFollow[i][j] = ok
|
||||
}
|
||||
}
|
||||
bFirst = true
|
||||
arrang = make([]int, n)
|
||||
for i := 0; i < n; i++ {
|
||||
arrang[i] = i + 1
|
||||
}
|
||||
return ptrs(0, n, 1)
|
||||
}
|
||||
|
||||
func main() {
|
||||
counts := make([]int, 19)
|
||||
for i := 2; i <= 20; i++ {
|
||||
counts[i-2] = primeTriangle(i)
|
||||
}
|
||||
fmt.Println()
|
||||
for i := 0; i < 19; i++ {
|
||||
fmt.Printf("%d ", counts[i])
|
||||
}
|
||||
fmt.Println()
|
||||
}
|
||||
2
Task/Prime-triangle/J/prime-triangle-1.j
Normal file
2
Task/Prime-triangle/J/prime-triangle-1.j
Normal file
|
|
@ -0,0 +1,2 @@
|
|||
add_plink=: [:;{{ <y,"1 0 x #~ 1 p:+/|:(x=. x-. y),"0/{: y }}"1
|
||||
prime_pair_seqs=: {{ y add_plink (2}.i.y) add_plink^:(y-2) 1 }}
|
||||
27
Task/Prime-triangle/J/prime-triangle-2.j
Normal file
27
Task/Prime-triangle/J/prime-triangle-2.j
Normal file
|
|
@ -0,0 +1,27 @@
|
|||
task=: {{
|
||||
for_j.2}.i.1+y do.
|
||||
N=. #seqs=. prime_pair_seqs j
|
||||
echo (_8{.":N),' | ',3":{:seqs
|
||||
end.
|
||||
}}
|
||||
|
||||
task 20
|
||||
1 | 1 2
|
||||
1 | 1 2 3
|
||||
1 | 1 2 3 4
|
||||
1 | 1 4 3 2 5
|
||||
1 | 1 4 3 2 5 6
|
||||
2 | 1 6 5 2 3 4 7
|
||||
4 | 1 6 7 4 3 2 5 8
|
||||
7 | 1 6 7 4 3 8 5 2 9
|
||||
24 | 1 6 7 4 9 8 5 2 3 10
|
||||
80 | 1 10 9 8 5 6 7 4 3 2 11
|
||||
216 | 1 10 9 8 11 6 7 4 3 2 5 12
|
||||
648 | 1 12 11 8 9 10 7 6 5 2 3 4 13
|
||||
1304 | 1 12 11 8 9 10 13 6 7 4 3 2 5 14
|
||||
3392 | 1 12 11 8 9 14 5 6 13 10 7 4 3 2 15
|
||||
13808 | 1 12 11 8 15 14 9 10 13 6 5 2 3 4 7 16
|
||||
59448 | 1 16 15 14 9 10 13 6 11 12 7 4 3 8 5 2 17
|
||||
155464 | 1 16 15 14 17 12 11 8 9 10 13 6 7 4 3 2 5 18
|
||||
480728 | 1 18 13 16 15 14 17 12 11 8 9 10 7 6 5 2 3 4 19
|
||||
1588162 | 1 18 19 12 17 14 15 16 13 10 9 8 11 2 5 6 7 4 3 20
|
||||
75
Task/Prime-triangle/Java/prime-triangle.java
Normal file
75
Task/Prime-triangle/Java/prime-triangle.java
Normal file
|
|
@ -0,0 +1,75 @@
|
|||
public class PrimeTriangle {
|
||||
public static void main(String[] args) {
|
||||
long start = System.currentTimeMillis();
|
||||
for (int i = 2; i <= 20; ++i) {
|
||||
int[] a = new int[i];
|
||||
for (int j = 0; j < i; ++j)
|
||||
a[j] = j + 1;
|
||||
if (findRow(a, 0, i))
|
||||
printRow(a);
|
||||
}
|
||||
System.out.println();
|
||||
StringBuilder s = new StringBuilder();
|
||||
for (int i = 2; i <= 20; ++i) {
|
||||
int[] a = new int[i];
|
||||
for (int j = 0; j < i; ++j)
|
||||
a[j] = j + 1;
|
||||
if (i > 2)
|
||||
s.append(" ");
|
||||
s.append(countRows(a, 0, i));
|
||||
}
|
||||
System.out.println(s);
|
||||
long finish = System.currentTimeMillis();
|
||||
System.out.printf("\nElapsed time: %d milliseconds\n", finish - start);
|
||||
}
|
||||
|
||||
private static void printRow(int[] a) {
|
||||
for (int i = 0; i < a.length; ++i) {
|
||||
if (i != 0)
|
||||
System.out.print(" ");
|
||||
System.out.printf("%2d", a[i]);
|
||||
}
|
||||
System.out.println();
|
||||
}
|
||||
|
||||
private static boolean findRow(int[] a, int start, int length) {
|
||||
if (length == 2)
|
||||
return isPrime(a[start] + a[start + 1]);
|
||||
for (int i = 1; i + 1 < length; i += 2) {
|
||||
if (isPrime(a[start] + a[start + i])) {
|
||||
swap(a, start + i, start + 1);
|
||||
if (findRow(a, start + 1, length - 1))
|
||||
return true;
|
||||
swap(a, start + i, start + 1);
|
||||
}
|
||||
}
|
||||
return false;
|
||||
}
|
||||
|
||||
private static int countRows(int[] a, int start, int length) {
|
||||
int count = 0;
|
||||
if (length == 2) {
|
||||
if (isPrime(a[start] + a[start + 1]))
|
||||
++count;
|
||||
} else {
|
||||
for (int i = 1; i + 1 < length; i += 2) {
|
||||
if (isPrime(a[start] + a[start + i])) {
|
||||
swap(a, start + i, start + 1);
|
||||
count += countRows(a, start + 1, length - 1);
|
||||
swap(a, start + i, start + 1);
|
||||
}
|
||||
}
|
||||
}
|
||||
return count;
|
||||
}
|
||||
|
||||
private static void swap(int[] a, int i, int j) {
|
||||
int tmp = a[i];
|
||||
a[i] = a[j];
|
||||
a[j] = tmp;
|
||||
}
|
||||
|
||||
private static boolean isPrime(int n) {
|
||||
return ((1L << n) & 0x28208a20a08a28acL) != 0;
|
||||
}
|
||||
}
|
||||
71
Task/Prime-triangle/Jq/prime-triangle.jq
Normal file
71
Task/Prime-triangle/Jq/prime-triangle.jq
Normal file
|
|
@ -0,0 +1,71 @@
|
|||
# $i and $j should be relevant integers (possibly negataive)
|
||||
# Usage with an array-valued key: .key |= array_swap($i; $j)
|
||||
def array_swap($i; $j):
|
||||
if $i == $j then .
|
||||
else .[$i] as $t
|
||||
| .[$i] = .[$j]
|
||||
| .[$j] = $t
|
||||
end;
|
||||
|
||||
# For syntactic convenience
|
||||
def swap($array; $i; $j):
|
||||
$array | array_swap($i; $j);
|
||||
|
||||
def pmap:
|
||||
reduce (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37) as $i ([];
|
||||
.[$i] = true) ;
|
||||
|
||||
# input: {bFirst, arrang, canFollow, emit}
|
||||
# output: same + {res, emit, i, count}
|
||||
def ptrs($res; $n; $done):
|
||||
. + {$res, count: $done}
|
||||
| .arrang[$done-1] as $ad
|
||||
| if ($n - $done <= 1)
|
||||
then if .canFollow[$ad-1][$n-1]
|
||||
then if .bFirst
|
||||
then .emit += [.arrang]
|
||||
| .bFirst = false
|
||||
else .
|
||||
end
|
||||
| .res += 1
|
||||
else .
|
||||
end
|
||||
else .count += 1
|
||||
| .count as $count
|
||||
| reduce range($count - 1; $n - 1; 2) as $i (.;
|
||||
.arrang[$i] as $ai
|
||||
| if .canFollow[$ad-1][$ai-1]
|
||||
then .arrang = swap(.arrang; $i; $count-1)
|
||||
| ptrs(.res; $n; $count)
|
||||
| .arrang = swap(.arrang; $i; $count-1)
|
||||
else .
|
||||
end )
|
||||
end;
|
||||
|
||||
# Emit {emit, res} from the call to ptrs
|
||||
def primeTriangle($n):
|
||||
pmap as $pmap
|
||||
| {}
|
||||
| .canFollow = (reduce range(0;$n) as $i ([];
|
||||
.[$i] = [range(0;$n) | false]
|
||||
| reduce range(0;$n) as $j (.;
|
||||
.[$i][$j] = $pmap[$i+$j+2] )))
|
||||
| .bFirst = true
|
||||
| .arrang = [range(1; 1+$n)]
|
||||
| ptrs(0; $n; 1)
|
||||
| {emit, res} ;
|
||||
|
||||
def task($n):
|
||||
range(2;$n+1) as $i
|
||||
| primeTriangle($i) ;
|
||||
|
||||
def task($n):
|
||||
foreach (range(2;$n+1), null) as $i ({counts: [], emit: null};
|
||||
if $i == null then .emit = "\n\(.counts)"
|
||||
else primeTriangle($i) as $pt
|
||||
| .counts += [$pt|.res]
|
||||
| .emit = $pt.emit
|
||||
end;
|
||||
.emit);
|
||||
|
||||
task(20)[]
|
||||
31
Task/Prime-triangle/Julia/prime-triangle-1.julia
Normal file
31
Task/Prime-triangle/Julia/prime-triangle-1.julia
Normal file
|
|
@ -0,0 +1,31 @@
|
|||
using Combinatorics, Primes
|
||||
|
||||
function primetriangle(nrows::Integer)
|
||||
nrows < 2 && error("number of rows requested must be > 1")
|
||||
pmask, spinlock = primesmask(2 * (nrows + 1)), Threads.SpinLock()
|
||||
counts, rowstrings = [1; zeros(Int, nrows - 1)], ["" for _ in 1:nrows]
|
||||
for r in 2:nrows
|
||||
@Threads.threads for e in collect(permutations(2:2:r))
|
||||
p = zeros(Int, r - 1)
|
||||
for o in permutations(3:2:r)
|
||||
i = 0
|
||||
for (x, y) in zip(e, o)
|
||||
p[i += 1] = x
|
||||
p[i += 1] = y
|
||||
end
|
||||
length(e) > length(o) && (p[i += 1] = e[end])
|
||||
if pmask[p[i] + r + 1] && pmask[p[begin] + 1] && all(j -> pmask[p[j] + p[j + 1]], 1:r-2)
|
||||
lock(spinlock)
|
||||
if counts[r] == 0
|
||||
rowstrings[r] = " 1" * prod([lpad(n, 3) for n in p]) * lpad(r + 1, 3) * "\n"
|
||||
end
|
||||
counts[r] += 1
|
||||
unlock(spinlock)
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
println(" 1 2\n" * prod(rowstrings), "\n", counts)
|
||||
end
|
||||
|
||||
@time primetriangle(16)
|
||||
32
Task/Prime-triangle/Julia/prime-triangle-2.julia
Normal file
32
Task/Prime-triangle/Julia/prime-triangle-2.julia
Normal file
|
|
@ -0,0 +1,32 @@
|
|||
using Primes
|
||||
|
||||
function solverow(row, pos, avail)
|
||||
results, nresults = Int[], 0
|
||||
for (i, tf) in enumerate(avail)
|
||||
if tf && isprime(row[pos - 1] + i + 1)
|
||||
if pos >= length(row) - 1 && isprime(row[end] + i + 1)
|
||||
row[pos] = i + 1
|
||||
return (copy(row), 1)
|
||||
else
|
||||
row[pos] = i + 1
|
||||
newav = copy(avail)
|
||||
newav[i] = false
|
||||
newresults, n = solverow(copy(row), pos + 1, newav)
|
||||
nresults += n
|
||||
results = isempty(results) && !isempty(newresults) ? newresults : results
|
||||
end
|
||||
end
|
||||
end
|
||||
return results, nresults
|
||||
end
|
||||
|
||||
function primetriangle(nrows::Integer)
|
||||
nrows < 2 && error("number of rows requested must be > 1")
|
||||
counts, rowstrings = [1; zeros(Int, nrows - 1)], ["" for _ in 1:nrows]
|
||||
for r in 2:nrows
|
||||
p, n = solverow(collect(1:r+1), 2, trues(r - 1))
|
||||
rowstrings[r] = prod([lpad(n, 3) for n in p]) * "\n"
|
||||
counts[r] = n
|
||||
end
|
||||
println(" 1 2\n" * prod(rowstrings), "\n", counts)
|
||||
end
|
||||
33
Task/Prime-triangle/Mathematica/prime-triangle.math
Normal file
33
Task/Prime-triangle/Mathematica/prime-triangle.math
Normal file
|
|
@ -0,0 +1,33 @@
|
|||
ClearAll[FindPrimeTriangles, FindPrimeTrianglesHelper]
|
||||
FindPrimeTriangles[max_] :=
|
||||
Module[{count = 0, firstsolution, primes, primeQ},
|
||||
primes = PrimeQ[Range[2 max]];
|
||||
primeQ[n_] := primes[[n]];
|
||||
ClearAll[FindPrimeTrianglesHelper];
|
||||
FindPrimeTrianglesHelper[start_, remainder_, mxx_] :=
|
||||
Module[{last, nexts, r, newstart, newremainder},
|
||||
If[Length[remainder] > 0,
|
||||
last = Last[start];
|
||||
Do[
|
||||
r = remainder[[ri]];
|
||||
If[primeQ[last + r],
|
||||
newstart = Append[start, r];
|
||||
newremainder = Delete[remainder, ri];
|
||||
FindPrimeTrianglesHelper[newstart, newremainder, mxx]
|
||||
]
|
||||
,
|
||||
{ri, Length[remainder]}
|
||||
]
|
||||
,
|
||||
If[primeQ[Last[start] + mxx],
|
||||
count++;
|
||||
If[count == 1,
|
||||
Print[Append[start, mxx]]
|
||||
]
|
||||
]
|
||||
]
|
||||
];
|
||||
FindPrimeTrianglesHelper[{1}, Range[2, max - 1], max];
|
||||
count
|
||||
]
|
||||
Table[FindPrimeTriangles[S],{S, 2, 20}]
|
||||
60
Task/Prime-triangle/Nim/prime-triangle.nim
Normal file
60
Task/Prime-triangle/Nim/prime-triangle.nim
Normal file
|
|
@ -0,0 +1,60 @@
|
|||
import std/[monotimes, strutils, times]
|
||||
|
||||
const IsPrime = [false, false, true, true, false, true, false, true,
|
||||
false, false, false, true, false, true, false, false,
|
||||
false, true, false, true, false, false, false, true,
|
||||
false, false, false, false, false, true, false, true,
|
||||
false, false, false, false, false, true, false, false,
|
||||
false, true, false, true, false, false, false, true,
|
||||
false, false, false, false, false, true, false, false,
|
||||
false, false, false, true, false, true, false, false]
|
||||
|
||||
type TriangleRow = openArray[Natural]
|
||||
|
||||
template isPrime(n: Natural): bool = IsPrime[n]
|
||||
|
||||
func primeTriangleRow(a: var TriangleRow): bool =
|
||||
if a.len == 2:
|
||||
return isPrime(a[0] + a[1])
|
||||
for i in countup(1, a.len - 2, 2):
|
||||
if isPrime(a[0] + a[i]):
|
||||
swap a[i], a[1]
|
||||
if primeTriangleRow(a.toOpenArray(1, a.high)):
|
||||
return true
|
||||
swap a[i], a[1]
|
||||
|
||||
func primeTriangleCount(a: var TriangleRow): Natural =
|
||||
if a.len == 2:
|
||||
if isPrime(a[0] + a[1]):
|
||||
inc result
|
||||
else:
|
||||
for i in countup(1, a.len - 2, 2):
|
||||
if isPrime(a[0] + a[i]):
|
||||
swap a[i], a[1]
|
||||
inc result, primeTriangleCount(a.toOpenArray(1, a.high))
|
||||
swap a[i], a[1]
|
||||
|
||||
proc print(a: TriangleRow) =
|
||||
if a.len == 0: return
|
||||
for i, n in a:
|
||||
if n > 0: stdout.write ' '
|
||||
stdout.write align($n, 2)
|
||||
stdout.write '\n'
|
||||
|
||||
let start = getMonoTime()
|
||||
for n in 2..20:
|
||||
var a = newSeq[Natural](n)
|
||||
for i in 0..<n:
|
||||
a[i] = i + 1
|
||||
if a.primeTriangleRow:
|
||||
print a
|
||||
echo()
|
||||
for n in 2..20:
|
||||
var a = newSeq[Natural](n)
|
||||
for i in 0..<n:
|
||||
a[i] = i + 1
|
||||
if n > 2: stdout.write " "
|
||||
stdout.write a.primeTriangleCount
|
||||
echo '\n'
|
||||
|
||||
echo "Elapsed time: ", (getMonoTime() - start).inMilliseconds, " ms"
|
||||
35
Task/Prime-triangle/Perl/prime-triangle.pl
Normal file
35
Task/Prime-triangle/Perl/prime-triangle.pl
Normal file
|
|
@ -0,0 +1,35 @@
|
|||
use strict;
|
||||
use warnings;
|
||||
use feature 'say';
|
||||
use ntheory 'is_prime';
|
||||
use List::MoreUtils qw(zip slideatatime);
|
||||
use Algorithm::Combinatorics qw(permutations);
|
||||
|
||||
say '1 2';
|
||||
|
||||
my @count = (0, 0, 1);
|
||||
|
||||
for my $n (3..17) {
|
||||
my @even_nums = grep { 0 == $_ % 2 } 2..$n-1;
|
||||
my @odd_nums = grep { 1 == $_ % 2 } 3..$n-1;
|
||||
for my $e (permutations [@even_nums]) {
|
||||
next if $$e[0] == 8 or $$e[0] == 14;
|
||||
my $nope = 0;
|
||||
for my $o (permutations [@odd_nums]) {
|
||||
my @list = (zip(@$e, @$o), $n); # 'zip' makes a list with a gap if more evens than odds
|
||||
splice @list, -2, -1 if not defined $list[-2]; # in which case splice out 'undef' in next-to-last position
|
||||
my $it = slideatatime(1, 2, @list);
|
||||
while ( my @rr = $it->() ) {
|
||||
last unless defined $rr[1];
|
||||
$nope++ and last unless is_prime $rr[0]+$rr[1];
|
||||
}
|
||||
unless ($nope) {
|
||||
say '1 ' . join ' ', @list unless $count[$n];
|
||||
$count[$n]++;
|
||||
}
|
||||
$nope = 0;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
say "\n" . join ' ', @count[2..$#count];
|
||||
54
Task/Prime-triangle/Phix/prime-triangle.phix
Normal file
54
Task/Prime-triangle/Phix/prime-triangle.phix
Normal file
|
|
@ -0,0 +1,54 @@
|
|||
(phixonline)-->
|
||||
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
|
||||
<span style="color: #004080;">atom</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">can_follow</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">arrang</span>
|
||||
<span style="color: #004080;">bool</span> <span style="color: #000000;">bFirst</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">true</span>
|
||||
|
||||
<span style="color: #008080;">function</span> <span style="color: #000000;">ptrs</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">done</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000080;font-style:italic;">-- prime triangle recursive sub-procedure
|
||||
-- on entry, arrang[done] is set and arrang[$]==n.
|
||||
-- find something/everything that fits between them.</span>
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">ad</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">arrang</span><span style="color: #0000FF;">[</span><span style="color: #000000;">done</span><span style="color: #0000FF;">]</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">done</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">can_follow</span><span style="color: #0000FF;">[</span><span style="color: #000000;">ad</span><span style="color: #0000FF;">][</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">bFirst</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%s\n"</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">arrang</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">:=</span><span style="color: #008000;">"%d"</span><span style="color: #0000FF;">))</span>
|
||||
<span style="color: #000000;">bFirst</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">false</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #000000;">res</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">else</span>
|
||||
<span style="color: #000000;">done</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
|
||||
<span style="color: #000080;font-style:italic;">-- as per talk page, we only need to examine odd
|
||||
-- numbers following an even number & vice versa</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">done</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">ai</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">arrang</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">can_follow</span><span style="color: #0000FF;">[</span><span style="color: #000000;">ad</span><span style="color: #0000FF;">][</span><span style="color: #000000;">ai</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">aid</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">arrang</span><span style="color: #0000FF;">[</span><span style="color: #000000;">done</span><span style="color: #0000FF;">]</span>
|
||||
<span style="color: #000000;">arrang</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">aid</span>
|
||||
<span style="color: #000000;">arrang</span><span style="color: #0000FF;">[</span><span style="color: #000000;">done</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ai</span>
|
||||
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ptrs</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">done</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">arrang</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ai</span>
|
||||
<span style="color: #000000;">arrang</span><span style="color: #0000FF;">[</span><span style="color: #000000;">done</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">aid</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
|
||||
<span style="color: #008080;">function</span> <span style="color: #000000;">prime_triangle</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">can_follow</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #004600;">false</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">),</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #000000;">can_follow</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">is_prime</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">j</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #000000;">arrang</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">bFirst</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">true</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #000000;">ptrs</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">20</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">),</span><span style="color: #000000;">prime_triangle</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%s\n"</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">:=</span><span style="color: #008000;">"%d"</span><span style="color: #0000FF;">))</span>
|
||||
<span style="color: #0000FF;">?</span><span style="color: #7060A8;">elapsed</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">)</span>
|
||||
<!--
|
||||
49
Task/Prime-triangle/Python/prime-triangle.py
Normal file
49
Task/Prime-triangle/Python/prime-triangle.py
Normal file
|
|
@ -0,0 +1,49 @@
|
|||
from numpy import array
|
||||
# for Rosetta Code by MG - 20230312
|
||||
def is_prime(n: int) -> bool:
|
||||
assert n < 64
|
||||
return ((1 << n) & 0x28208a20a08a28ac) != 0
|
||||
|
||||
def prime_triangle_row(a: array, start: int, length: int) -> bool:
|
||||
if length == 2:
|
||||
return is_prime(a[0] + a[1])
|
||||
for i in range(1, length - 1, 1):
|
||||
if is_prime(a[start] + a[start + i]):
|
||||
a[start + i], a[start + 1] = a[start + 1], a[start + i]
|
||||
if prime_triangle_row(a, start + 1, length - 1):
|
||||
return True
|
||||
a[start + i], a[start + 1] = a[start + 1], a[start + i]
|
||||
return False
|
||||
|
||||
def prime_triangle_count(a: array, start: int, length: int) -> int:
|
||||
count: int = 0
|
||||
if length == 2:
|
||||
if is_prime(a[start] + a[start + 1]):
|
||||
count += 1
|
||||
else:
|
||||
for i in range(1, length - 1, 1):
|
||||
if is_prime(a[start] + a[start + i]):
|
||||
a[start + i], a[start + 1] = a[start + 1], a[start + i]
|
||||
count += prime_triangle_count(a, start + 1, length - 1)
|
||||
a[start + i], a[start + 1] = a[start + 1], a[start + i]
|
||||
return count
|
||||
|
||||
def print_row(a: array):
|
||||
if a == []:
|
||||
return
|
||||
print("%2d"% a[0], end=" ")
|
||||
for x in a[1:]:
|
||||
print("%2d"% x, end=" ")
|
||||
print()
|
||||
|
||||
for n in range(2, 21):
|
||||
tr: array = [_ for _ in range(1, n + 1)]
|
||||
if prime_triangle_row(tr, 0, n):
|
||||
print_row(tr)
|
||||
print()
|
||||
for n in range(2, 21):
|
||||
tr: array = [_ for _ in range(1, n + 1)]
|
||||
if n > 2:
|
||||
print(" ", end="")
|
||||
print(prime_triangle_count(tr, 0, n), end="")
|
||||
print()
|
||||
25
Task/Prime-triangle/Raku/prime-triangle.raku
Normal file
25
Task/Prime-triangle/Raku/prime-triangle.raku
Normal file
|
|
@ -0,0 +1,25 @@
|
|||
my @count = 0, 0, 1;
|
||||
my $lock = Lock.new;
|
||||
put (1,2);
|
||||
|
||||
for 3..17 -> $n {
|
||||
my @even = (2..^$n).grep: * %% 2;
|
||||
my @odd = (3..^$n).grep: so * % 2;
|
||||
@even.permutations.race.map: -> @e {
|
||||
quietly next if @e[0] == 8|14;
|
||||
my $nope = 0;
|
||||
for @odd.permutations -> @o {
|
||||
quietly next unless (@e[0] + @o[0]).is-prime;
|
||||
my @list;
|
||||
for (@list = (flat (roundrobin(@e, @o)), $n)).rotor(2 => -1) {
|
||||
$nope++ and last unless .sum.is-prime;
|
||||
}
|
||||
unless $nope {
|
||||
put '1 ', @list unless @count[$n];
|
||||
$lock.protect({ @count[$n]++ });
|
||||
}
|
||||
$nope = 0;
|
||||
}
|
||||
}
|
||||
}
|
||||
put "\n", @count[2..*];
|
||||
71
Task/Prime-triangle/Rust/prime-triangle.rust
Normal file
71
Task/Prime-triangle/Rust/prime-triangle.rust
Normal file
|
|
@ -0,0 +1,71 @@
|
|||
fn is_prime(n: u32) -> bool {
|
||||
assert!(n < 64);
|
||||
((1u64 << n) & 0x28208a20a08a28ac) != 0
|
||||
}
|
||||
|
||||
fn prime_triangle_row(a: &mut [u32]) -> bool {
|
||||
if a.len() == 2 {
|
||||
return is_prime(a[0] + a[1]);
|
||||
}
|
||||
for i in (1..a.len() - 1).step_by(2) {
|
||||
if is_prime(a[0] + a[i]) {
|
||||
a.swap(i, 1);
|
||||
if prime_triangle_row(&mut a[1..]) {
|
||||
return true;
|
||||
}
|
||||
a.swap(i, 1);
|
||||
}
|
||||
}
|
||||
false
|
||||
}
|
||||
|
||||
fn prime_triangle_count(a: &mut [u32]) -> u32 {
|
||||
let mut count = 0;
|
||||
if a.len() == 2 {
|
||||
if is_prime(a[0] + a[1]) {
|
||||
count += 1;
|
||||
}
|
||||
} else {
|
||||
for i in (1..a.len() - 1).step_by(2) {
|
||||
if is_prime(a[0] + a[i]) {
|
||||
a.swap(i, 1);
|
||||
count += prime_triangle_count(&mut a[1..]);
|
||||
a.swap(i, 1);
|
||||
}
|
||||
}
|
||||
}
|
||||
count
|
||||
}
|
||||
|
||||
fn print(a: &[u32]) {
|
||||
if a.is_empty() {
|
||||
return;
|
||||
}
|
||||
print!("{:2}", a[0]);
|
||||
for x in &a[1..] {
|
||||
print!(" {:2}", x);
|
||||
}
|
||||
println!();
|
||||
}
|
||||
|
||||
fn main() {
|
||||
use std::time::Instant;
|
||||
let start = Instant::now();
|
||||
for n in 2..21 {
|
||||
let mut a: Vec<u32> = (1..=n).collect();
|
||||
if prime_triangle_row(&mut a) {
|
||||
print(&a);
|
||||
}
|
||||
}
|
||||
println!();
|
||||
for n in 2..21 {
|
||||
let mut a: Vec<u32> = (1..=n).collect();
|
||||
if n > 2 {
|
||||
print!(" ");
|
||||
}
|
||||
print!("{}", prime_triangle_count(&mut a));
|
||||
}
|
||||
println!();
|
||||
let time = start.elapsed();
|
||||
println!("\nElapsed time: {} milliseconds", time.as_millis());
|
||||
}
|
||||
77
Task/Prime-triangle/Swift/prime-triangle.swift
Normal file
77
Task/Prime-triangle/Swift/prime-triangle.swift
Normal file
|
|
@ -0,0 +1,77 @@
|
|||
import Foundation
|
||||
|
||||
func isPrime(_ n: Int) -> Bool {
|
||||
guard n > 0 && n < 64 else {
|
||||
return false
|
||||
}
|
||||
return ((UInt64(1) << n) & 0x28208a20a08a28ac) != 0
|
||||
}
|
||||
|
||||
func primeTriangleRow(_ a: inout [Int], start: Int, length: Int) -> Bool {
|
||||
if length == 2 {
|
||||
return isPrime(a[start] + a[start + 1])
|
||||
}
|
||||
for i in stride(from: 1, to: length - 1, by: 2) {
|
||||
let index = start + i
|
||||
if isPrime(a[start] + a[index]) {
|
||||
a.swapAt(index, start + 1)
|
||||
if primeTriangleRow(&a, start: start + 1, length: length - 1) {
|
||||
return true
|
||||
}
|
||||
a.swapAt(index, start + 1)
|
||||
}
|
||||
}
|
||||
return false
|
||||
}
|
||||
|
||||
func primeTriangleCount(_ a: inout [Int], start: Int, length: Int) -> Int {
|
||||
var count = 0
|
||||
if length == 2 {
|
||||
if isPrime(a[start] + a[start + 1]) {
|
||||
count += 1
|
||||
}
|
||||
} else {
|
||||
for i in stride(from: 1, to: length - 1, by: 2) {
|
||||
let index = start + i
|
||||
if isPrime(a[start] + a[index]) {
|
||||
a.swapAt(index, start + 1)
|
||||
count += primeTriangleCount(&a, start: start + 1, length: length - 1)
|
||||
a.swapAt(index, start + 1)
|
||||
}
|
||||
}
|
||||
}
|
||||
return count
|
||||
}
|
||||
|
||||
func printRow(_ a: [Int]) {
|
||||
if a.count == 0 {
|
||||
return
|
||||
}
|
||||
print(String(format: "%2d", a[0]), terminator: "")
|
||||
for x in a[1...] {
|
||||
print(String(format: " %2d", x), terminator: "")
|
||||
}
|
||||
print()
|
||||
}
|
||||
|
||||
let startTime = CFAbsoluteTimeGetCurrent()
|
||||
|
||||
for n in 2...20 {
|
||||
var a = Array(1...n)
|
||||
if primeTriangleRow(&a, start: 0, length: n) {
|
||||
printRow(a)
|
||||
}
|
||||
}
|
||||
print()
|
||||
|
||||
for n in 2...20 {
|
||||
var a = Array(1...n)
|
||||
if n > 2 {
|
||||
print(" ", terminator: "")
|
||||
}
|
||||
print("\(primeTriangleCount(&a, start: 0, length: n))", terminator: "")
|
||||
}
|
||||
print()
|
||||
|
||||
let endTime = CFAbsoluteTimeGetCurrent()
|
||||
print("\nElapsed time: \(endTime - startTime) seconds")
|
||||
116
Task/Prime-triangle/Visual-Basic-.NET/prime-triangle.vb
Normal file
116
Task/Prime-triangle/Visual-Basic-.NET/prime-triangle.vb
Normal file
|
|
@ -0,0 +1,116 @@
|
|||
Option Strict On
|
||||
Option Explicit On
|
||||
|
||||
Imports System.IO
|
||||
|
||||
''' <summary>Find solutions to the "Prime Triangle" - a triangle of numbers that sum to primes.</summary>
|
||||
Module vMain
|
||||
|
||||
Public Const maxNumber As Integer = 20 ' Largest number we will consider.
|
||||
Dim prime(2 * maxNumber) As Boolean ' prime sieve.
|
||||
|
||||
''' <returns>The number of possible arrangements of the integers for a row in the prime triangle.</returns>
|
||||
Public Function countArrangements(ByVal n As Integer) As Integer
|
||||
If n < 2 Then ' No solutions for n < 2.
|
||||
Return 0
|
||||
ElseIf n < 4 Then
|
||||
' For 2 and 3. there is only 1 solution: 1, 2 and 1, 2, 3.
|
||||
For i As Integer = 1 To n
|
||||
Console.Out.Write(i.ToString.PadLeft(3))
|
||||
Next i
|
||||
Console.Out.WriteLine()
|
||||
Return 1
|
||||
Else
|
||||
' 4 or more - must find the solutions.
|
||||
Dim printSolution As Boolean = true
|
||||
Dim used(n) As Boolean
|
||||
Dim number(n) As Integer
|
||||
' The triangle row must have 1 in the leftmost and n in the rightmost elements.
|
||||
' The numbers must alternate between even and odd in order for the sums to be prime.
|
||||
For i As Integer = 0 To n - 1
|
||||
number(i) = i Mod 2
|
||||
Next i
|
||||
used(1) = True
|
||||
number(n) = n
|
||||
used(n) = True
|
||||
' Find the intervening numbers and count the solutions.
|
||||
Dim count As Integer = 0
|
||||
Dim p As Integer = 2
|
||||
Do While p > 0
|
||||
Dim p1 As Integer = number(p - 1)
|
||||
Dim current As Integer = number(p)
|
||||
Dim [next] As Integer = current + 2
|
||||
Do While [next] < n AndAlso (Not prime(p1 + [next]) Or used([next]))
|
||||
[next] += 2
|
||||
Loop
|
||||
If [next] >= n Then
|
||||
[next] = 0
|
||||
End If
|
||||
If p = n - 1 Then
|
||||
' We are at the final number before n.
|
||||
' It must be the final even/odd number preceded by the final odd/even number.
|
||||
If [next] <> 0 Then
|
||||
' Possible solution.
|
||||
If prime([next] + n) Then
|
||||
' Found a solution.
|
||||
count += 1
|
||||
If printSolution Then
|
||||
For i As Integer = 1 To n - 2
|
||||
Console.Out.Write(number(i).ToString.PadLeft(3))
|
||||
Next i
|
||||
Console.Out.WriteLine([next].ToString.PadLeft(3) & n.ToString.PadLeft(3))
|
||||
printSolution = False
|
||||
End If
|
||||
End If
|
||||
[next] = 0
|
||||
End If
|
||||
' Backtrack for more solutions.
|
||||
p -= 1
|
||||
' There will be a further backtrack as next is 0 ( there could only be one possible number at p - 1 ).
|
||||
End If
|
||||
If [next] <> 0 Then
|
||||
' have a/another number that can appear at p.
|
||||
used(current) = False
|
||||
used([next]) = True
|
||||
number(p) = [next]
|
||||
' Haven't found all the intervening digits yet.
|
||||
p += 1
|
||||
ElseIf p <= 2 Then
|
||||
' No more solutions.
|
||||
p = 0
|
||||
Else
|
||||
' Can't find a number for this position, backtrack.
|
||||
used(number(p)) = False
|
||||
number(p) = p Mod 2
|
||||
p -= 1
|
||||
End If
|
||||
Loop
|
||||
Return count
|
||||
End If
|
||||
End Function
|
||||
|
||||
Public Sub Main
|
||||
prime(2) = True
|
||||
For i As Integer = 3 To UBound(prime) Step 2
|
||||
prime(i) = True
|
||||
Next i
|
||||
For i As Integer = 3 To Convert.ToInt32(Math.Floor(Math.Sqrt(Ubound(prime)))) Step 2
|
||||
If prime(i) Then
|
||||
For s As Integer = i * i To Ubound(prime) Step i + i
|
||||
prime(s) = False
|
||||
Next s
|
||||
End If
|
||||
Next i
|
||||
|
||||
Dim arrangements(maxNumber) As Integer
|
||||
For n As Integer = 2 To UBound(arrangements)
|
||||
arrangements(n) = countArrangements(n)
|
||||
Next n
|
||||
For n As Integer = 2 To UBound(arrangements)
|
||||
Console.Out.Write(" " & arrangements(n))
|
||||
Next n
|
||||
Console.Out.WriteLine()
|
||||
|
||||
End Sub
|
||||
|
||||
End Module
|
||||
55
Task/Prime-triangle/Wren/prime-triangle.wren
Normal file
55
Task/Prime-triangle/Wren/prime-triangle.wren
Normal file
|
|
@ -0,0 +1,55 @@
|
|||
import "./fmt" for Fmt
|
||||
|
||||
var canFollow = []
|
||||
var arrang = []
|
||||
var bFirst = true
|
||||
|
||||
var pmap = {}
|
||||
for (i in [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37]) {
|
||||
pmap[i] = true
|
||||
}
|
||||
|
||||
var ptrs
|
||||
ptrs = Fn.new { |res, n, done|
|
||||
var ad = arrang[done-1]
|
||||
if (n - done <= 1) {
|
||||
if (canFollow[ad-1][n-1]) {
|
||||
if (bFirst) {
|
||||
Fmt.print("$2d", arrang)
|
||||
bFirst = false
|
||||
}
|
||||
res = res + 1
|
||||
}
|
||||
} else {
|
||||
done = done + 1
|
||||
var i = done - 1
|
||||
while (i <= n-2) {
|
||||
var ai = arrang[i]
|
||||
if (canFollow[ad-1][ai-1]) {
|
||||
arrang.swap(i, done-1)
|
||||
res = ptrs.call(res, n, done)
|
||||
arrang.swap(i, done-1)
|
||||
}
|
||||
i = i + 2
|
||||
}
|
||||
}
|
||||
return res
|
||||
}
|
||||
|
||||
var primeTriangle = Fn.new { |n|
|
||||
canFollow = List.filled(n, null)
|
||||
for (i in 0...n) {
|
||||
canFollow[i] = List.filled(n, false)
|
||||
for (j in 0...n) canFollow[i][j] = pmap.containsKey(i+j+2)
|
||||
}
|
||||
bFirst = true
|
||||
arrang = (1..n).toList
|
||||
return ptrs.call(0, n, 1)
|
||||
}
|
||||
|
||||
var counts = []
|
||||
for (i in 2..20) {
|
||||
counts.add(primeTriangle.call(i))
|
||||
}
|
||||
System.print()
|
||||
System.print(counts.join(" "))
|
||||
Loading…
Add table
Add a link
Reference in a new issue