/*
space complexity: O(n)
[
[1,3,1],
[1,5,1],
[4,2,1]
]
dp[n]代表ith row的各种最短路径
*/
class Solution {
public int minPathSum(int[][] grid) {
int m = grid.length;
int n = grid[0].length;
int[] dp = new int[n];
dp[0] = grid[0][0];
for(int i = 1; i < n; i++)
dp[i] = dp[i - 1] + grid[0][i];
for(int i = 1; i < m; i++) {
for(int j = 0; j < n; j++) {
if(j == 0) {
dp[j] = dp[j] + grid[i][j];
} else {
dp[j] = Math.min(dp[j - 1], dp[j]) + grid[i][j];
}
}
}
return dp[n - 1];
}
}
class Solution {
public int minPathSum(int[][] grid) {
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 i = 1; i < n; i++) {
dp[0][i] = dp[0][i - 1] + grid[0][i];
}
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];
}
}