# 47.礼物的最大价值

### 一、 题目

在一个 m\*n 的棋盘的每一格都放有一个礼物，每个礼物都有一定的价值（价值大于 0）。你可以从棋盘的左上角开始拿格子里的礼物，并每次向右或者向下移动一格、直到到达棋盘的右下角。给定一个棋盘及其上面的礼物的价值，请计算你最多能拿到多少价值的礼物？   示例 1:

输入:

```
[
  [1,3,1],
  [1,5,1],
  [4,2,1]
]
```

输出: 12

解释: 路径 1→3→5→2→1 可以拿到最多价值的礼物

提示：

0 < grid.length <= 200

0 < grid\[0].length <= 200

来源：力扣（LeetCode）

链接：<https://leetcode-cn.com/problems/li-wu-de-zui-da-jie-zhi-lcof>

著作权归领扣网络所有。商业转载请联系官方授权，非商业转载请注明出处。

### 二、 图解

![图解](/files/2IPNSYbP9dYmcYQYQMPE)

### 三、 解法

```
func maxValue(_ grid: [[Int]]) -> Int {
    let w = grid[0].count
    let h = grid.count
    var dp: [[Int]] = Array(repeating: Array(repeating: 0, count: w), count: h)
    
    for y in 0..<h {
        for x in 0..<w {
            let value = grid[y][x]
            if x == 0, y == 0 { dp[y][x] = value }
            else if y == 0, x > 0 { dp[y][x] = dp[y][x-1] + value }
            else if y > 0, x == 0 { dp[y][x] = dp[y-1][x] + value }
            else { dp[y][x] = max(dp[y][x-1], dp[y-1][x]) + value }
        }
    }
    
    return dp[h-1][w-1]
}
```


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