[Swift]LeetCode62. 不同路径 | Unique Paths

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A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).

The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below).

How many possible unique paths are there?

Above is a 7 x 3 grid. How many possible unique paths are there?

Note: m and n will be at most 100.

Example 1:

Input: m = 3, n = 2
Output: 3
Explanation:
From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:
1. Right -> Right -> Down
2. Right -> Down -> Right
3. Down -> Right -> Right

Example 2:

Input: m = 7, n = 3
Output: 28

---

一个机器人位于一个 m x n 网格的左上角 （起始点在下图中标记为“Start” ）。

机器人每次只能向下或者向右移动一步。机器人试图达到网格的右下角（在下图中标记为“Finish”）。

问总共有多少条不同的路径？

例如，上图是一个7 x 3 的网格。有多少可能的路径？

说明：m 和 n 的值均不超过 100。

示例 1:

输入: m = 3, n = 2
输出: 3
解释:
从左上角开始，总共有 3 条路径可以到达右下角。
1. 向右 -> 向右 -> 向下
2. 向右 -> 向下 -> 向右
3. 向下 -> 向右 -> 向右

示例 2:

输入: m = 7, n = 3
输出: 28

---

8ms

class Solution {
    func uniquePaths(_ m: Int, _ n: Int) -> Int {
        if m == 0 || n == 0 {
            return 0
        }
        var columns: [Int] = Array(repeating: 1, count: m)
        for _ in 1..<n { // 逐行遍历
            for i in 1..<m { // 第一位, 始终只有1种(+0)
                columns[i] += columns[i-1]
            }
        }
        return columns.last!
    }
}

---

8ms

class Solution {
    func uniquePaths(_ m: Int, _ n: Int) -> Int {
        var pathNums = Array(repeating: Array(repeating:0,count: n),count: m)
        return _helper(&pathNums, m - 1, n - 1)
    }
    private func _helper(_ pathNums: inout [[Int]], _ m: Int, _ n: Int) -> Int {
        if m < 0 || n < 0 {
            return 0
        }
        if m == 0 || n == 0 {
            return 1
        }
        
        if pathNums[m][n] != 0 {
            return pathNums[m][n]
        }
        pathNums[m][n] = _helper(&pathNums, m - 1, n) + _helper(&pathNums, m, n - 1)
        
        return pathNums[m][n]
    }
}

---

12ms

class Solution {
    func uniquePaths(_ m: Int, _ n: Int) -> Int {
        if m == 0 || n == 0 { return 0 }
        var count = Array(repeating: Array(repeating: 0, count: n), count: m)
        var col = n-1
        while col >= 0 {
            var row = m-1
            while row >= 0 {
                if row == m-1 && col == n-1 {
                    count[row][col] = 1
                } else {
                    count[row][col] = (col < n-1 ? count[row][col+1] : 0) + (row < m-1 ? count[row+1][col] : 0)                   
                }
                row -= 1
            }
            col -= 1
        }
        return count[0][0]
    }
}

---

16ms

class Solution {
    
    func uniquePaths(_ m: Int, _ n: Int) -> Int {
        guard m > 0 else {
            return 0
        }
        
        var steps = Array(repeating: Array(repeating: 1, count: n), count: m)
        for row in 1..<m {
            for column in 1..<n {
                steps[row][column] = steps[row - 1][column] + steps[row][column - 1]
            }
        }
        
        return steps[m - 1][n - 1]
    }
    
}

---

20ms

class Solution {
    func uniquePaths(_ m: Int, _ n: Int) -> Int {
        if m == 0 || n == 0 {
            return 0
        }
        var map = Array(repeating: Array(repeating:0,count: n),count: m)
        for i in 1 ..< m {
            for j in 1 ..< n {
                var num1 = map[i - 1][j]
                var num2 = map[i][j - 1]
                 if i - 1 == 0 || j == 0 {
                    num1 = 1
                }
                if i == 0 || j - 1 == 0 {
                    num2 = 1
                }
                map[i][j] = num1 + num2
            }
        }
         if m - 1 == 0 || n - 1 == 0 {
            return 1
        } else {
            let result = map[m - 1][n - 1]
            return result
        }
    }
}

---

24ms

class Solution {
    
    func uniquePaths(_ m: Int, _ n: Int) -> Int {
        var arrs: [[Int]] = Array(repeating: Array(repeating: 0, count: n), count: m)
        for i in 0..<m{
            for j in 0..<n{
                if i == 0 && j == 0{
                    arrs[i][j] = 1
                }else if i == 0 {
                    arrs[i][j] = arrs[i][j-1]
                }else if j == 0{
                    arrs[i][j] = arrs[i-1][j]
                }else{
                    arrs[i][j] = arrs[i-1][j] + arrs[i][j-1]
                }
            }
        }
        return arrs[m-1][n-1]
    }
}

---

32ms

class Solution {
    func uniquePaths(_ m: Int, _ n: Int) -> Int {
        guard m > 1 else {
            return m == 0 ? 0 : 1
        }
        guard n > 1 else {
            return n == 0 ? 0 : 1
        }
        
        var path = [Int].init(repeating: 1, count: m+1)
        path[0] = 0
        for _ in 2...n {
            for j in 1...m {
                path[j] = path[j] + path[j-1]
            }
        }
        print(path)
        return path[m]
    }
}

---

40ms

class Solution {
    func uniquePaths(_ m: Int, _ n: Int) -> Int {
        let l = max(m,n)
        let s = min(m,n)
        if s==1 {
            return 1
        }
        // c l,s 组合
        var ji1 = 1
        var ji2 = 1
        for i in 1...s-1 {
            ji1*=i
            ji2*=l+s-i-1
        }
        return ji2/ji1
    }
}