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Task/Iterated-digits-squaring/Python/iterated-digits-squaring-1.py

@@ -0,0 +1,56 @@
+from math import ceil, log10, factorial
+
+def next_step(x):
+    result = 0
+    while x > 0:
+        result += (x % 10) ** 2
+        x /= 10
+    return result
+
+def check(number):
+    candidate = 0
+    for n in number:
+        candidate = candidate * 10 + n
+
+    while candidate != 89 and candidate != 1:
+        candidate = next_step(candidate)
+
+    if candidate == 89:
+        digits_count = [0] * 10
+        for d in number:
+            digits_count[d] += 1
+
+        result = factorial(len(number))
+        for c in digits_count:
+            result /= factorial(c)
+        return result
+
+    return 0
+
+def main():
+    limit = 100000000
+    cache_size = int(ceil(log10(limit)))
+    assert 10 ** cache_size == limit
+
+    number = [0] * cache_size
+    result = 0
+    i = cache_size - 1
+
+    while True:
+        if i == 0 and number[i] == 9:
+            break
+        if i == cache_size - 1 and number[i] < 9:
+            number[i] += 1
+            result += check(number)
+        elif number[i] == 9:
+            i -= 1
+        else:
+            number[i] += 1
+            for j in xrange(i + 1, cache_size):
+                number[j] = number[i]
+            i = cache_size - 1
+            result += check(number)
+
+    print result
+
+main()

Task/Iterated-digits-squaring/Python/iterated-digits-squaring-2.py

@@ -0,0 +1,42 @@
+from itertools import combinations_with_replacement
+from array import array
+from time import clock
+D = 8
+F = [1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600, 6227020800, 87178291200, 1307674368000, 20922789888000, 355687428096000]
+def b(n):
+    yield 1
+    for g in range(1,n+1):
+        gn = g
+        res = 0
+        while gn > 0:
+            gn,rem = divmod(gn,10)
+            res += rem**2
+        if res==89:
+            yield 0
+        else:
+            yield res
+N = array('I',b(81*D))
+for n in range(2,len(N)):
+    q = N[n]
+    while q>1:
+        q = N[q]
+    N[n] = q
+
+es = clock()
+z = 0
+for n in combinations_with_replacement(range(10),D):
+    t = 0
+    for g in n:
+        t += g*g
+    if N[t] == 0:
+        continue
+    t = [0,0,0,0,0,0,0,0,0,0]
+    for g in n:
+        t[g] += 1
+    t1 = F[D]
+    for g in t:
+        t1 /= F[g]
+    z += t1
+ee = clock() - es
+print "\nD==" + str(D) + "\n  " + str(z) + " numbers produce 1 and " + str(10**D-z) + " numbers produce 89"
+print "Time ~= " + str(ee) + " secs"

Task/Iterated-digits-squaring/Python/iterated-digits-squaring-3.py

@@ -0,0 +1,14 @@
+>>> from functools import lru_cache
+>>> @lru_cache(maxsize=1024)
+def ids(n):
+	if n in {1, 89}: return n
+	else: return ids(sum(int(d) ** 2 for d in str(n)))
+
+	
+>>> ids(15)
+89
+>>> [ids(x) for x in range(1, 21)]
+[1, 89, 89, 89, 89, 89, 1, 89, 89, 1, 89, 89, 1, 89, 89, 89, 89, 89, 1, 89]
+>>> sum(ids(x) == 89 for x in range(1, 100000000))
+85744333
+>>>

Task/Iterated-digits-squaring/Python/iterated-digits-squaring-4.py

@@ -0,0 +1,19 @@
+>>> from functools import lru_cache
+>>> @lru_cache(maxsize=1024)
+def _ids(nt):
+	if nt in {('1',), ('8', '9')}: return nt
+	else: return _ids(tuple(sorted(str(sum(int(d) ** 2 for d in nt)))))
+
+	
+>>> def ids(n):
+	return int(''.join(_ids(tuple(sorted(str(n))))))
+
+>>> ids(1), ids(15)
+(1, 89)
+>>> [ids(x) for x in range(1, 21)]
+[1, 89, 89, 89, 89, 89, 1, 89, 89, 1, 89, 89, 1, 89, 89, 89, 89, 89, 1, 89]
+>>> sum(ids(x) == 89 for x in range(1, 100000000))
+85744333
+>>> _ids.cache_info()
+CacheInfo(hits=99991418, misses=5867462, maxsize=1024, currsize=1024)
+>>>