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 1:
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[[1,3,1],
[1,5,1],
[4,2,1]]
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Given the above grid map, return
. Because the path 1→3→1→1→1 minimizes the sum.
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class {
public int minPathSum(int[][] grid) {
if(grid == null || grid.length == 0) return 0;
int m = grid.length;
int n = grid[0].length;
int sum = 0;
int[][] dp = new int[m][n];
for(int i=0; i<m; i++){
for(int j=0; j<n; j++){
if(i==0 && j==0)
dp[i][j] =grid[0][0];
else if(i == 0){
dp[i][j] = dp[i][j-1] + grid[i][j];
}
else if(j==0){
dp[i][j] = dp[i-1][j] + grid[i][j];
}
else{
dp[i][j] = Math.min(dp[i-1][j], dp[i][j-1]) + grid[i][j];
}
}
}
return dp[m-1][n-1];
}
}
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- 这种情况下，不需要使用DP数组。使用DP数组的好处就是能够不改变Grid中的内容。
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