Data commit

Task/N-smooth-numbers/D/n-smooth-numbers.d

@@ -0,0 +1,119 @@
+import std.algorithm;
+import std.bigint;
+import std.exception;
+import std.range;
+import std.stdio;
+
+BigInt[] primes;
+int[] smallPrimes;
+
+bool isPrime(BigInt value) {
+    if (value < 2) return false;
+
+    if (value % 2 == 0) return value == 2;
+    if (value % 3 == 0) return value == 3;
+
+    if (value % 5 == 0) return value == 5;
+    if (value % 7 == 0) return value == 7;
+
+    if (value % 11 == 0) return value == 11;
+    if (value % 13 == 0) return value == 13;
+
+    if (value % 17 == 0) return value == 17;
+    if (value % 19 == 0) return value == 19;
+
+    if (value % 23 == 0) return value == 23;
+
+    BigInt t = 29;
+    while (t * t < value) {
+        if (value % t == 0) return false;
+        value += 2;
+
+        if (value % t == 0) return false;
+        value += 4;
+    }
+
+    return true;
+}
+
+// cache all primes up to 521
+void init() {
+    primes ~= BigInt(2);
+    smallPrimes ~= 2;
+
+    BigInt i = 3;
+    while (i <= 521) {
+        if (isPrime(i)) {
+            primes ~= i;
+            if (i <= 29) {
+                smallPrimes ~= i.toInt;
+            }
+        }
+        i += 2;
+    }
+}
+
+BigInt[] nSmooth(int n, int size)
+in {
+    enforce(n >= 2 && n <= 521, "n must be between 2 and 521");
+    enforce(size > 1, "size must be at least 1");
+}
+do {
+    BigInt bn = n;
+    bool ok = false;
+    foreach (prime; primes) {
+        if (bn == prime) {
+            ok = true;
+            break;
+        }
+    }
+    enforce(ok, "n must be a prime number");
+
+    BigInt[] ns;
+    ns.length = size;
+    ns[] = BigInt(0);
+    ns[0] = 1;
+
+    BigInt[] next;
+    foreach(prime; primes) {
+        if (prime > bn) {
+            break;
+        }
+        next ~= prime;
+    }
+
+    int[] indicies;
+    indicies.length = next.length;
+    indicies[] = 0;
+    foreach (m; 1 .. size) {
+        ns[m] = next.reduce!min;
+        foreach (i,v; indicies) {
+            if (ns[m] == next[i]) {
+                indicies[i]++;
+                next[i] = primes[i] * ns[indicies[i]];
+            }
+        }
+    }
+
+    return ns;
+}
+
+void main() {
+    init();
+
+    foreach (i; smallPrimes) {
+        writeln("The first ", i, "-smooth numbers are:");
+        writeln(nSmooth(i, 25));
+        writeln;
+    }
+    foreach (i; smallPrimes.drop(1)) {
+        writeln("The 3,000th to 3,202 ", i, "-smooth numbers are:");
+        writeln(nSmooth(i, 3_002).drop(2_999));
+        writeln;
+    }
+    foreach (i; [503, 509, 521]) {
+        writeln("The 30,000th to 30,019 ", i, "-smooth numbers are:");
+        writeln(nSmooth(i, 30_019).drop(29_999));
+        writeln;
+    }
+}