剑指 47. 礼物的最大价值

剑指 Offer 47. 礼物的最大价值

//压缩数组，滚动优化，空间On
func maxValue(grid [][]int) int {
    if len(grid) == 0 || len(grid[0]) == 0 {
        return 0
    }
    n := len(grid[0])
    dp := make([]int, n)
    for i := range grid {
        dp[0] = dp[0] + grid[i][0]          //走一个横排
        for j := 1; j < n; j++ {
            if i == 0 {
                dp[j] = dp[j-1] + grid[0][j]
            } else {
                dp[j] = max(dp[j], dp[j-1]) + grid[i][j]
            }
        }
    }
    return dp[n-1]
}
func max(x, y int) int {
    if x > y {
        return x
    }
    return y
}

//二维dp，时空都为Omn
func maxValue(grid [][]int) int {
    if len(grid) == 0 || len(grid[0]) == 0 {
        return 0
    }

    m, n := len(grid), len(grid[0])
    dp := make([][]int, m)

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

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

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

func max(x, y int) int {
    if x > y {
        return x
    }
    return y
}