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64. 最小路径和
给定一个包含非负整数的 m x n 网格 grid，请找出一条从左上角到右下角的路径，使得路径上的数字总和为最小。
说明：每次只能向下或者向右移动一步。
示例 1：
输入：grid = [[1,3,1],[1,5,1],[4,2,1]] 输出：7 解释：因为路径 1→3→1→1→1 的总和最小。
示例 2：
输入：grid = [[1,2,3],[4,5,6]] 输出：12
提示：
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m == grid.length -
n == grid[i].length -
1 <= m, n <= 200 -
0 <= grid[i][j] <= 200
思路分析
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一刷
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二刷
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三刷
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/**
* Runtime: 7 ms, faster than 5.53% of Java online submissions for Minimum Path Sum.
* Memory Usage: 43.5 MB, less than 33.78% of Java online submissions for Minimum Path Sum.
*
* @author D瓜哥 · https://www.diguage.com
* @since 2020-01-27 21:29
*/
public int minPathSum(int[][] grid) {
if (Objects.isNull(grid) || grid.length == 0) {
return 0;
}
int yLength = grid.length;
int xLength = grid[0].length;
for (int y = 0; y < yLength; y++) {
for (int x = 0; x < xLength; x++) {
if (y == 0 && x > 0) {
grid[y][x] = grid[y][x - 1] + grid[y][x];
} else if (y > 0 && x == 0) {
grid[y][x] = grid[y - 1][x] + grid[y][x];
} else if (y > 0 && x > 0) {
grid[y][x] = Math.min(grid[y - 1][x], grid[y][x - 1]) + grid[y][x];
}
}
}
return grid[yLength - 1][xLength - 1];
}
/**
* Runtime: 5 ms, faster than 7.69% of Java online submissions for Minimum Path Sum.
* Memory Usage: 43.2 MB, less than 36.48% of Java online submissions for Minimum Path Sum.
*/
public int minPathSumDp(int[][] grid) {
if (Objects.isNull(grid) || grid.length == 0) {
return 0;
}
int yLength = grid.length;
int xLength = grid[0].length;
int[][] sums = new int[yLength][xLength];
for (int i = 1; i < sums.length; i++) {
Arrays.fill(sums[i], Integer.MAX_VALUE);
}
sums[0][0] = grid[0][0];
for (int x = 1; x < xLength; x++) {
sums[0][x] = sums[0][x - 1] + grid[0][x];
}
for (int y = 1; y < yLength; y++) {
sums[y][0] = sums[y - 1][0] + grid[y][0];
}
for (int y = 1; y < yLength; y++) {
for (int x = 1; x < xLength; x++) {
sums[y][x] = Math.min(sums[y - 1][x], sums[y][x - 1]) + grid[y][x];
}
}
return sums[yLength - 1][xLength - 1];
}
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/**
* @author D瓜哥 · https://www.diguage.com
* @since 2020-01-27 21:29
*/
public int minPathSum(int[][] grid) {
int[][] dp = new int[grid.length][grid[0].length];
dp[0][0] = grid[0][0];
for (int i = 1; i < grid[0].length; i++) {
dp[0][i] = grid[0][i] + dp[0][i - 1];
}
for (int i = 1; i < grid.length; i++) {
dp[i][0] = grid[i][0] + dp[i - 1][0];
}
for (int row = 1; row < grid.length; row++) {
for (int column = 1; column < grid[0].length; column++) {
dp[row][column] = Math.min(dp[row - 1][column], dp[row][column - 1])
+ grid[row][column];
}
}
return dp[grid.length - 1][grid[0].length - 1];
}
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/**
* @author D瓜哥 · https://www.diguage.com
* @since 2025-04-18 21:51:48
*/
public int minPathSum(int[][] grid) {
int row = grid.length;
int col = grid[0].length;
for (int i = 1; i < col; i++) {
grid[0][i] += grid[0][i - 1];
}
for (int i = 1; i < row; i++) {
grid[i][0] += grid[i - 1][0];
}
for (int r = 1; r < row; r++) {
for (int c = 1; c < col; c++) {
grid[r][c] += Math.min(grid[r - 1][c], grid[r][c - 1]);
}
}
return grid[row - 1][col - 1];
}