64. Minimum Path Sum

Medium

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:

Input: grid = [[1,3,1],[1,5,1],[4,2,1]]
Output:
 7
Explanation:
 Because the path 1 → 3 → 1 → 1 → 1 minimizes the sum.

Example 2:

Input: grid = [[1,2,3],[4,5,6]]
Output:
 12

Constraints:

• m == grid.length

• n == grid[i].length

• 1 <= m, n <= 200

• 0 <= grid[i][j] <= 100

解題

func minPathSum(grid [][]int) int {
    m, n := len(grid), len(grid[0])
    dp := grid

    for i := 1; i < m; i++ {
        dp[i][0] = dp[i - 1][0] + grid[i][0]
    }

    for i := 1; i < n; i++ {
        dp[0][i] = dp[0][i - 1] + grid[0][i]
    }

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

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

func min(a, b int) int {
    if a < b {
        return a
    }
    return b
}