[LeetCode]120. Triangle

[LeetCode]120. Triangle

题目描述

思路

动归，新建一个状态保存数组

原数组	状态数组
2	2
3 4	5 6
6 5 7	11 10 13
4 1 8 3	15 11 18 16

所以结果是11

代码

class Solution {
public:
    int minimumTotal(vector<vector<int>>& triangle) {
        vector<vector<int>> dp;
        dp.push_back(*triangle.begin());
        for (int i = 0; i < triangle.size() - 1; ++i) {
            vector<int> num = {};
            dp.push_back(num);
            for (int j = 0; j < triangle[i].size(); ++j) {
                if (j == 0) {
                    dp[i + 1].push_back(dp[i][j] + triangle[i + 1][j]);
                }
                else {
                    if(dp[i][j] + triangle[i + 1][j] < dp[i + 1][j])
                        dp[i + 1][j] =  dp[i][j] + triangle[i + 1][j];
                }
                dp[i + 1].push_back(dp[i][j] + triangle[i + 1][j + 1]);
            }
        }
        int min = dp[dp.size() - 1][0];
        for (auto &p : dp[dp.size() - 1]) {
            min = p < min ? p : min;
        }
        return min;
    }
};

---

更新

思路update

节省空间考虑
状态数组可以从下往上算

原数组	状态数组
4 1 8 3	4 1 8 3
6 5 7	7 6 10
3 4	9 10
2	11

代码update

class Solution {
public:
    int minimumTotal(vector<vector<int>>& triangle) {
        int len = triangle.size();
        vector<int> dp(triangle[len - 1].begin(), triangle[len - 1].end());
        for (int i = len - 2; i >= 0; --i)
            for (int j = 0; j < i + 1; ++j)
                dp[j] = triangle[i][j] + min(dp[j], dp[j + 1]);

        return dp[0];
    }
};