64. Minimum Path Sum.go

package leetcode

// 解法一 原地 DP，无辅助空间
func minPathSum(grid [][]int) int {
	m, n := len(grid), len(grid[0])
	for i := 1; i < m; i++ {
		grid[i][0] += grid[i-1][0]
	}
	for j := 1; j < n; j++ {
		grid[0][j] += grid[0][j-1]
	}
	for i := 1; i < m; i++ {
		for j := 1; j < n; j++ {
			grid[i][j] += min(grid[i-1][j], grid[i][j-1])
		}
	}
	return grid[m-1][n-1]

}

// 解法二 最原始的方法，辅助空间 O(n^2)
func minPathSum1(grid [][]int) int {
	if len(grid) == 0 {
		return 0
	}
	m, n := len(grid), len(grid[0])
	if m == 0 || n == 0 {
		return 0
	}

	dp := make([][]int, m)
	for i := 0; i < m; i++ {
		dp[i] = make([]int, n)
	}
	// initFirstCol
	for i := 0; i < len(dp); i++ {
		if i == 0 {
			dp[i][0] = grid[i][0]
		} else {
			dp[i][0] = grid[i][0] + dp[i-1][0]
		}
	}
	// initFirstRow
	for i := 0; i < len(dp[0]); i++ {
		if i == 0 {
			dp[0][i] = grid[0][i]
		} else {
			dp[0][i] = grid[0][i] + dp[0][i-1]
		}
	}
	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 int, b int) int {
	if a > b {
		return b
	}
	return a
}