Create 312-Burst-Balloons.cpp

cpp/312-Burst-Balloons.cpp

@@ -0,0 +1,27 @@
+class Solution {
+public:
+    int solve(const vector<int> &nums, vector<vector<int>> &dp, int l, int r) {
+        if (l > r)
+            return 0;
+        if (dp[l][r] > 0)
+            return dp[l][r];
+        for (int i = l; i <= r; ++i) {
+            // burst nums[i] the last
+            // score from current coin: nums[i] * excluded left * excluded right
+            int coins = nums[i] * nums[l - 1] * nums[r + 1];
+            // score from remainders: recursive maximum for range [l ~ i-1] and [i+1 ~ r]
+            coins += solve(nums, dp, l, i - 1) + solve(nums, dp, i + 1, r);
+            dp[l][r] = max(dp[l][r], coins);
+        }
+        return dp[l][r];
+    }
+
+    int maxCoins(vector<int>& nums) {
+        // to simplify the solution, add 1 to both end to process out-of-bound *1 condition
+        nums.insert(nums.begin(), 1);
+        nums.push_back(1);
+        vector<vector<int>> dp(nums.size(), vector<int>(nums.size(), 0));
+        // exclude virtual left end and right end
+        return solve(nums, dp, 1, nums.size() - 2);
+    }
+};