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飞过闲红千叶，夕岸在哪
类目归类
[LeetCode 64] Minimum Path Sum [Java]
02/10
1. Description
Given a m x 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.
Note: You can only move either down or right at any point in time.
2. Example
[[1,3,1],
[1,5,1],
[4,2,1]]
Given the above grid map, return 7. Because the path 1→3→1→1→1 minimizes the sum.
3. Explanation
[tabby title="DP"]
Let dp[i][j] stands for the minimum sum of all numbers along its path when arrive grid (i,j)
(1). $$dp[0][0] = grid[0][0]; $$
(2). init first column
$$for(i : 1 \rightarrow M)$$
$$dp[i][0] = dp[i - 1][0] + grid[i][0];$$
(3). init first row
$$for(j : 1 \rightarrow N)$$
$$dp[0][j] = dp[0][j - 1] + grid[0][j];$$
(4). $$for(i : 1 \rightarrow M; j : 1 \rightarrow N)$$
$$dp[i][j] = max { dp[i-1][j], dp[i][j-1] } + grid[i][j]$$
[tabbyending]
4.Code
public class LeetCode0064 {
public int minPathSum(int[][] grid) {
if (grid == null || grid.length == 0 || grid[0].length == 0) {
return 0;
}
int m = grid.length;
int n = grid[0].length;
int[][] dp = new int[m][n];
dp[0][0] = grid[0][0];
for (int i = 1; i < m; i++) {
dp[i][0] = dp[i - 1][0] + grid[i][0];
}
for (int j = 1; j < n; j++) {
dp[0][j] = dp[0][j - 1] + grid[0][j];
}
for (int i = 1; i < m; i++) {
for (int j = 1; j < n; j++) {
dp[i][j] = Math.min(dp[i - 1][j], dp[i][j - 1]) + grid[i][j];
}
}
return dp[m - 1][n - 1];
}
public static void main(String[] args) {
LeetCode0064 leetcode = new LeetCode0064();
int[][] grid = new int[][] { { 1, 3, 1 }, { 1, 5, 1 }, { 4, 2, 1 } };
System.out.println(leetcode.minPathSum(grid));
}
}
