Bruteforce solve problem 88

python/e088.py

@@ -0,0 +1,90 @@
+
+def product(numbers):
+    r = 1
+    for n in numbers:
+        r = r * n
+    return r
+
+def _incrementer():
+    """ Generator function that returns natural numbers where the higher
+    digits are smaller or equal than the lower digits. """
+    n_digits = 2
+    r = [1] * n_digits
+    while True:
+        yield r
+        incremented = False
+        for i in range(n_digits - 1):
+            if r[i] < r[i + 1]:
+                r[i] += 1
+                incremented = True
+                for j in range(i):
+                    r[j] = 1
+                break
+        if incremented:
+            continue
+        elif r[-1] < 2000:
+            r[-1] += 1
+            for j in range(n_digits - 1):
+                r[j] = 1
+        else:
+            n_digits += 1
+            r = [1] * n_digits
+
+for k in range(40, 50):
+    s = product_sum_number(k)
+        print("k={}: {} = {}".format(k, product(s), s))
+
+
+def product_sum(k):
+    # Create initial list of canditates
+    canditates = []
+    for n in range(2, k + 1):
+        rest_sum = k - n
+        if rest_sum + n * 2 < 2 ** n:
+            break
+        canditates.append(tuple([2 for _ in range(n)]))
+    processed = set(canditates)
+    solutions = []
+
+    while canditates:
+        numbers = canditates.pop()
+        processed.add(numbers)
+
+        s = k - len(numbers) + sum(numbers)
+        p = product(numbers)
+        if s == p:
+            solutions.append(numbers)
+        elif s > p:
+            for i in range(len(numbers) - 1):
+                if numbers[i] < numbers[i + 1]:
+                    n = list(numbers)
+                    n[i] += 1
+                    t = tuple(n)
+                    if not t in processed:
+                        canditates.append(t)
+
+            n = list(numbers)
+            n[-1] += 1
+            t = tuple(n)
+            if not t in processed:
+                canditates.append(t)
+        else:
+            pass
+    result = min([product(ns) for ns in solutions])
+    return result
+
+
+def euler_088():
+    ns = set()
+    for k in range(2, 12001):
+        r = product_sum_2d(k)
+        print("k={}: {}".format(k, r))
+        ns.add(r)
+    return sum(ns)
+
+
+if __name__ == "__main__":
+    solution = euler_088()
+    print("e088.py: " + str(solution))
+    assert(solution == 7587457)
+