Create maximize-number-of-nice-divisors.cpp

Author: kamyu104

C++/maximize-number-of-nice-divisors.cpp

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+// Time:  O(logn)
+// Space: O(1)
+
+// variant of "343. integer break"
+class Solution {
+public:
+    int maxNiceDivisors(int primeFactors) {
+        static const int mod = 1e9 + 7;
+        
+        // given a1 + a2 + ... + ak <= n, find max of a1 * a2 * ... * ak 
+        // => given a1 + a2 + ... + ak <= n, find max of a1 * a2 * ... * ak 
+        // => ai is either 3 or 2, see proof in "343. integer break"
+        if (primeFactors <= 3) {
+            return primeFactors;
+        }
+        if (primeFactors % 3 == 0) {
+            return powmod(3, primeFactors / 3, mod);  // 6 => 3 * 3
+        }
+        if (primeFactors % 3 == 1) {
+            return 4 * powmod(3, (primeFactors - 4) / 3, mod) % mod;  // 4 => 2 * 2
+        }
+        return 2 * powmod(3, (primeFactors - 2) / 3, mod) % mod;  // 5 => 2 * 3
+    }
+
+private:
+    uint32_t powmod(uint32_t a, uint32_t b, uint32_t mod) {
+        a %= mod;
+        uint64_t result = 1;
+        while (b) {
+            if (b & 1) {
+                result = result * a % mod;
+            }
+            a = uint64_t(a) * a % mod;
+            b >>= 1;
+        }
+        return result;
+    }
+};