Triangle

[leetcode]Triangle

链接：https://leetcode.com/problems/triangle/description/

Question

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

class Solution {
public:
  int minimumTotal(vector<vector<int>>& triangle) {
    int size = triangle.size();
    std::vector<int > dp;
    dp.resize(size);

    for (int j = 0; j < size; j++) dp[j] = triangle[size-1][j];
    // 自底向上
    for (int i = size-2; i >= 0; i--) {
      for (int j = 0; j <= i; j++) {
        dp[j] = min(dp[j], dp[j+1])+triangle[i][j];
      }
    }
    return dp[0];
  }
};

思路：这道题的动态规划思想是自底向上的。之前用了自顶向下的方法来解，但是实在不好做。以后思考这类问题要学会换角度进行思考。