110 · 最小路径和Minimum Path Sum

原创于 2021-06-08 16:36:58 发布 · 95 阅读

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#动态规划 #算法 #java

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该博客介绍了如何解决给定网格中找到从左上角到右下角的最小路径和问题。提供了一个Java代码示例，通过动态规划计算最小路径。算法遍历网格，更新每个位置的最小路径和。

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110 · 最小路径和Minimum Path Sum

描述
Given a m * nm∗n grid filled with non-negative numbers, find a path from top left to bottom right which minimizes the sum of all numbers along its path.
Example 1:

Input:

grid = [[1,3,1],[1,5,1],[4,2,1]]
Output:

7
Explanation:

Path is: 1 -> 3 -> 1 -> 1 -> 1

public class Solution {
    /**
     * @param grid: a list of lists of integers
     * @return: An integer, minimizes the sum of all numbers along its path
     */
    public int minPathSum(int[][] grid) {
        // write your code here
        int m = grid.length , n = grid[0].length ; 
        int[][] f = new int[m][n] ;
        f[0][0] = grid[0][0] ;
        for(int i = 1 ; i < m ; i++){
            f[i][0] = f[i-1][0] + grid[i][0] ;
        }
        for(int i = 1 ; i < n ; i++){
            f[0][i] = f[0][i-1] + grid[0][i] ;
        }
        for(int i = 1 ; i < m ; i++){
            for(int j = 1 ; j < n ; j++){
                f[i][j] = Math.min(f[i-1][j] , f[i][j-1]) + grid[i][j] ;
            }
        }
        return f[m-1][n-1] ;
    }
}