[LeetCode] Problem 64 - Minimum Path Sum

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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:

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[
  [1,3,1],
  [1,5,1],
  [4,2,1]
]

Output: 7

Explanation: Because the path 1→3→1→1→1 minimizes the sum.

Code

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public int minPathSum(int[][] grid) {
    int n = grid.length;
    int m = grid[0].length;
    int[][] dp = new int[n][m];
    dp[0][0] = grid[0][0];

    for (int i = 1; i < m; i++)
        dp[0][i] = grid[0][i] + dp[0][i - 1];

    for (int i = 1; i < n; i++)
        dp[i][0] = grid[i][0] + dp[i - 1][0];

    for (int i = 1; i < n; i++) {
        for (int j = 1; j < m; j++)
            dp[i][j] = grid[i][j] + Math.min(dp[i - 1][j], dp[i][j - 1]);
    }

    return dp[n - 1][m - 1];
}