0120.triangle.md

0120.Triangle

Description

Given a triangle, find the minimum path sum from top to bottom. Each step you may move to adjacent numbers on the row below.

For example, given the following triangle

[ [2], [3,4], [6,5,7], [4,1,8,3] ] The minimum path sum from top to bottom is 11 (i.e., 2 + 3 + 5 + 1 = 11). Example 1:

[
     [2],
    [3,4],
   [6,5,7],
  [4,1,8,3]
]

The minimum path sum from top to bottom is 11 (i.e., 2 + 3 + 5 + 1 = 11).

Tags: Math, String

题意

求三角形的最短路径.

题解

思路1

DFS

//    dfs solution
func minimumTotal(triangle [][]int) int {
    if len(triangle) == 0 || len(triangle[0]) == 0 {
        return 0
    }
    _dfs(triangle, 0, 0, "", 0)

    return minSum
}

func _dfs(triangle [][]int, i, j int, path string, sum int) int {
    //    terminator
    if i == len(triangle)-1 {
        sum += triangle[i][j]
        path += strconv.Itoa(triangle[i][j]) + " #"
        fmt.Println(path + "with sum: " + strconv.Itoa(sum))

        if sum < minSum {
            minSum = sum
            fmt.Println(minSum)
        }
        return sum
    }

    //    process
    sum += triangle[i][j]
    path += strconv.Itoa(triangle[i][j]) + " -> "

    //    drill down
    _dfs(triangle, i+1, j, path, sum)
    _dfs(triangle, i+1, j+1, path, sum)

    //    clear states
    return 0
}

思路2

DP

```go // dp solution func minimumTotal(triangle [][]int) int { if len(triangle) == 0 || len(triangle[0]) == 0 { return 0 } for i := len(triangle) - 2; i >= 0; i-- { for j := len(triangle[i]) - 1; j >= 0; j-- { minSum := min(triangle[i+1][j],triangle[i+1][j+1]) minSum += triangle[i][j] triangle[i][j] = minSum } } return triangle[0][0] } func min(x, y int) int { if x > y { return y } return x }

```

结语

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