【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).

0、题目分析

这是一道动态规划题目，不同于一般做法，一般第一反应可能是想办法找出自上而下的递归表达式，不过这道题需要自下而上，从下往上计算每个位置和它左右脚的较小值的和。最顶端即解答，即，

[
      [11],
    [9, 10],
   [7, 6, 10],
  [4, 1, 8, 3]
]
从倒数第二行开始递推
triangle[i][j] += min(triangle[i+1][j+1],triangle[i+1]

11为最小路径和

1、代码实现

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