120. Triangle

• Difficulty: Medium

• Topics: Array, Dynamic Programming

• Similar Questions:

Problem:

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.

Solutions:

class Solution {
public:
    int minimumTotal(vector<vector<int>>& triangle) {
        if (triangle.size() == 0)   return 0;
        int level = triangle.size();
        vector<int> dp (level, INT_MAX);
        dp[0] = 0;
        for (auto& values : triangle) {
            for (int i = values.size() - 1; i >= 1; --i) {
                dp[i] = values[i] + min(dp[i-1], dp[i]);
            }
            dp[0] = values[0] + dp[0];
        }

        int ret = INT_MAX;

        for (auto bottom : dp) {
            ret = min(ret, bottom);
        }

        return ret;

    }
};