leetcode_c++:Divide and Conquer：Burst Balloons（312）

https://leetcode.com/problems/burst-balloons/

---

class Solution {public:    int maxCoins(vector<int>& nums) {        //remove all of zero item        nums.erase(remove_if(nums.begin(), nums.end(), [](int n){return n==0;}), nums.end());        //add 1 for head and tail        nums.insert(nums.begin(),1);        nums.push_back(1);        int n = nums.size();        vector< vector<int> > matrix(n, vector<int>(n,0));        return maxCoins_DP(nums, matrix);        return maxCoins_DC(nums, matrix, 0, n-1);    }    //Divide and Conquer    //    //  If we seprate the array to two part, left part and right part.    //    //  Then, we will find in this problem the left and right become adjacent     //  and have effects on the maxCoins in the future.    //    //  So, if we think reversely, if the balloon i is the last balloon of all to burst,     //  the left and right section now has well defined boundary and do not affect each other!     //  Therefore we can do either recursive method with memoization    //    int maxCoins_DC(vector<int>& nums, vector<vector<int>>& matrix, int low, int high) {        if (low + 1 == high) return 0;        if (matrix[low][high] > 0) return matrix[low][high];        int result = 0;        for (int i = low + 1; i < high; ++i){            result = max(result,  nums[low] * nums[i] * nums[high]                                     + maxCoins_DC(nums, matrix, low, i)                                     + maxCoins_DC(nums, matrix, i, high));        }        matrix[low][high] = result;        return result;    }    //Dynamic Programming    //     //  using the same idea of above     //    int maxCoins_DP(vector<int>& nums, vector<vector<int>>& dp) {        int n = nums.size();        for (int k = 2; k < n; ++k) {            for (int low = 0; low < n - k; low++){                int high = low + k;                for (int i = low + 1; i < high; ++i)                    dp[low][high] = max( dp[low][high],                         nums[low] * nums[i] * nums[high] + dp[low][i] + dp[i][high]);            }        }        return dp[0][n - 1];    }private:    void printVector(vector<int>& nums) {        cout << "nums: ";        for (auto n: nums) {            cout << n << ' ';        }        cout << '\n';    }};