【DP】64.最小路径和

题目

Python

class Solution:
    def minPathSum(self, grid: List[List[int]]) -> int:
        m = len(grid)    # m行
        n = len(grid[0]) # n列
        matrix = [[0 for _ in range(n)] for _ in range(m)]
        matrix[0][0] = grid[0][0]
        for i in range(1, m):
            matrix[i][0] = grid[i][0] + matrix[i-1][0]
        for j in range(1, n):
            matrix[0][j] = grid[0][j] + matrix[0][j-1]
        
        for i in range(1, m):
            for j in range(1, n):
                matrix[i][j] = grid[i][j] + min(matrix[i-1][j], matrix[i][j-1])

        return matrix[m-1][n-1]

Java

法1：二维DP

必须掌握！

class Solution {
    public int minPathSum(int[][] grid) {
        int m = grid.length, n = grid[0].length;
        int[][] matrix = new int[m][n];
        matrix[0][0] = grid[0][0];
        for (int i = 1; i < n; ++i) {
            matrix[0][i] = matrix[0][i - 1] + grid[0][i];
        }
        for (int i = 1; i < m; ++i) {
            matrix[i][0] = matrix[i - 1][0] + grid[i][0];
        }
        for (int i = 1; i < m; ++i) {
            for (int j = 1; j < n; ++j) {
                matrix[i][j] = Math.min(matrix[i - 1][j], matrix[i][j - 1]) + grid[i][j];
            }
        }

        return matrix[m - 1][n - 1];
    }
}