Add Burst Baloons DP problem solution

Author: Alex Syrotenko

Dynamic Programming/Burst_Baloons/burst_baloons.cpp

@@ -0,0 +1,39 @@
+// Problem statement :
+// Given n balloons, indexed from 0 to n-1.
+// Each balloon is painted with a number on it represented by array nums.
+// You are asked to burst all the balloons.
+// If the you burst balloon i you will get nums[left] * nums[i] * nums[right] coins.
+// Here left and right are adjacent indices of i.
+// After the burst, the left and right then becomes adjacent.
+#include <vector>
+#include <assert.h>
+
+int burst_baloons(const std::vector<int> baloons) {
+    int *nums = new int[baloons.size() + 2];
+    int n = 1;
+    for (int x : baloons)
+        if (x > 0)
+            nums[n++] = x;
+    nums[0] = nums[n++] = 1;
+
+    int **dp = new int*[n];
+    for(int i = 0; i < n; ++i)
+        dp[i] = new int[n];
+    for (int k = 2; k < n; ++k)
+        for (int left = 0; left < n - k; ++left) {
+            int right = left + k;
+            for (int i = left + 1; i < right; ++i) {
+                int challenger = nums[left] * nums[i] * nums[right] + dp[left][i] + dp[i][right];
+                dp[left][right] = std::max(dp[left][right], challenger);
+            }
+        }
+
+    return dp[0][n - 1];
+}
+
+int main() {
+    const std::vector<int> input {3, 1, 5, 8};
+    int result = burst_baloons(input);
+    assert(result == 167);
+    return 0;
+}