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64. Minimum Path Sum
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.
Example:
Input:
[
[1,3,1],
[1,5,1],
[4,2,1]
]
Output: 7
Explanation: Because the path 1→3→1→1→1 minimizes the sum.
思考题：尝试使用一维数组做备忘录来实现一下。
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.
Example:
Input: [ [1,3,1], [1,5,1], [4,2,1] ] Output: 7 Explanation: Because the path 1→3→1→1→1 minimizes the sum.
思路分析
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一刷
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二刷
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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];
}