leetcode 120. Triangle

leetcode 120. Triangle

Given a triangle, find the minimum path sum from top to bottom. Each step you may move to adjacent numbers on the row below.

For example, given the following triangle

[
[2],
[3,4],
[6,5,7],
[4,1,8,3]
]
The minimum path sum from top to bottom is 11 (i.e., 2 + 3 + 5 + 1 = 11).

Note:

Bonus point if you are able to do this using only O(n) extra space, where n is the total number of rows in the triangle.

solution

动态规划
状态转移方程为
位置{i}处的最小值要么是左边来的要么是右边来的
dp[i]=min{dp[left], dp[right]}+nowLocation

class Solution {
public:
    int minimumTotal(vector<vector<int>>& triangle) {
        int n = triangle.size();
        int dp[n+1][n+1];
        for(int i = 1; i <= n ;i++)
            dp[1][i] = triangle[n-1][i-1];
        for(int i = 2; i <= n; i++)
            for(int j = 1; j <= n-i+1; j++)
            {
                dp[i][j] = (dp[i-1][j] < dp[i-1][j+1] ? dp[i-1][j] : dp[i-1][j+1]) + triangle[n-i][j-1];
            }
        return dp[n][1];        
    }