added 5kyu - Simple Fun #339 - Maximum Product 2

Author: gideo

Diff for: 5kyu_SimpleFun#339_MaximumProduct2.js

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+// 5kyu - Simple Fun #339: Maximum Product 2 
+
+// Task
+// Given an positive integer n(5 <= n <= 100). Your task is to divide n into some different integers, maximize the product of these integers.
+
+// Example
+// For n = 5, the output should be 6.
+
+// 5 can divide into 2 and 3, 2 x 3 = 6
+
+// For n = 8, the output should be 15.
+
+// 8 can divide into 3 and 5, 3 x 5 = 15
+
+// For n = 10, the output should be 30.
+
+// 10 can divide into 2, 3 and 5, 2 x 3 x 5 = 30
+
+// For n = 15, the output should be 144.
+
+// 15 can divide into 2, 3, 4 and 6, 2 x 3 x 4 x 6 = 144
+
+function maximumProduct(n) {
+  function fn(m, i, a) {
+    if (m === 0) return a;
+    if (m < 0 || i > m) return 0;
+    return Math.max(fn(m-i, i+1, a*i), fn(m, i+1, a));
+  }
+  return fn(n, 2, 1);
+}