q120.md

q120

Idea State dp[i][j]: how much value of shortest path to get position i, j State transfer function: dp[i][j] = min(dp[i-1][j-1], dp[i-1][j]) + triangle[i][j] marginal conditions: first column and last column.

deep copy of list: List<List> newTriangle = new ArrayList<>(triangle);

Code

import java.util.Collections;
class Solution {
    public int minimumTotal(List<List<Integer>> triangle) {
        // state: dp[i][j]: how much value of shortest path to get position i, j
        List<List<Integer>> newTriangle = new ArrayList<>(triangle);
        Integer element = triangle.get(0).get(0);
        Integer sum;
        int col_length = 1;
        newTriangle.get(0).set(0, element);
        for (int i = 1; i < triangle.size(); i++){
            col_length = triangle.get(i).size();
            sum = triangle.get(i).get(0) + triangle.get(i-1).get(0);
            newTriangle.get(i).set(0, sum);
            sum = triangle.get(i).get(col_length-1) + triangle.get(i-1).get(col_length-2);
            newTriangle.get(i).set(col_length-1, sum);
            for (int j = 1; j < col_length-1; j++){
                sum = Math.min(triangle.get(i-1).get(j-1), triangle.get(i-1).get(j)) + triangle.get(i).get(j);
                newTriangle.get(i).set(j,sum);
            }
        }
        
        int min_value = Integer.MAX_VALUE;
        int row_length = triangle.size();
        for (int j = 0; j < col_length; j++){
            if (newTriangle.get(row_length-1).get(j) < min_value){
                min_value = newTriangle.get(row_length-1).get(j);
            }
        }
        return min_value;


    }
}