027_最小路径和

知识点：动态规划、状态压缩、利用原有数组

LeetCode第六十四题：https://leetcode-cn.com/problems/minimum-path-sum/solution/

语言：GoLang

// 利用原有的grid，空间复杂度O(1)
func minPathSum(grid [][]int) int {
    rowLen := len(grid)
    colLen := len(grid[0])

    // init
    for i := 1;i < rowLen; i++ {
        grid[i][0] += grid[i - 1][0]
    }
    for j := 1; j < colLen; j++ {
        grid[0][j] += grid[0][j - 1]
    }

    // process
    for i := 1; i < rowLen; i++ {
        for j := 1; j < colLen; j++ {
            grid[i][j] += min(grid[i - 1][j], grid[i][j - 1])
        }
    }

    return grid[rowLen - 1][colLen - 1]
}


// 二维dp
func minPathSum_(grid [][]int) int {
    rowLen := len(grid)
    colLen := len(grid[0])

    // init
    dp := make([][]int, rowLen)
    for i := 0; i < rowLen; i++ {
        dp[i] = make([]int, colLen)
    }
    dp[0][0] = grid[0][0]
    for i := 1;i < rowLen; i++ {
        dp[i][0] = dp[i - 1][0] + grid[i][0]
    }
    for j := 1; j < colLen; j++ {
        dp[0][j] = dp[0][j - 1] + grid[0][j]
    }

    // process
    for i := 1; i < rowLen; i++ {
        for j := 1; j < colLen; j++ {
            dp[i][j] = min(dp[i - 1][j], dp[i][j - 1]) + grid[i][j]
        }
    }

    return dp[rowLen - 1][colLen - 1]
}

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