minPathSum.go

/* https://leetcode.com/problems/minimum-path-sum/description/
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.
*/

package ldp

func minPathSum(grid [][]int) int {
	m, n := len(grid), len(grid[0])
	dp := make([][]int, m)
	dp[0] = make([]int, n, n)
	dp[0][0] = grid[0][0]
	for i := 1; i < m; i++ {
		dp[i] = make([]int, n, n)
		dp[i][0] = grid[i][0] + dp[i-1][0]
	}
	for i := 1; i < n; i++ {
		dp[0][i] = grid[0][i] + dp[0][i-1]
	}

	min := func(a, b int) int {
		if a > b {
			return b
		}
		return a
	}

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