L120. Triangle

DP

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.

Solution:

• back to the last level

public int minimumTotal(List<List<Integer>> triangle) {
    if(triangle == null) throw new IllegalArgumentException();
    int len = triangle.size();
    int[] dp = new int[len];
    for(int i = 0; i < len; i++){
        dp[i] = triangle.get(len - 1).get(i);
    }
    for(int i = len -2; i >= 0; i--){
        for(int j = 0; j<=i; j++){
            dp[j] = Math.min(dp[j], dp[j+1]) + triangle.get(i).get(j);
        }
        
    }
    return dp[0];
}