[Swift]LeetCode62. 不一樣路徑 | 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

---

一個機器人位於一個 m x n 網格的左上角 （起始點在下圖中標記爲「Start」 ）。

機器人每次只能向下或者向右移動一步。機器人試圖達到網格的右下角（在下圖中標記爲「Finish」）。

問總共有多少條不一樣的路徑？

例如，上圖是一個7 x 3 的網格。有多少可能的路徑？

說明：m 和 n 的值均不超過 100。

示例 1:

輸入: m = 3, n = 2
輸出: 3
解釋:
從左上角開始，總共有 3 條路徑能夠到達右下角。
1. 向右 -> 向右 -> 向下
2. 向右 -> 向下 -> 向右
3. 向下 -> 向右 -> 向右

示例 2:

輸入: m = 7, n = 3
輸出: 28

---

8ms

 1 class Solution {
 2     func uniquePaths(_ m: Int, _ n: Int) -> Int {
 3         if m == 0 || n == 0 {
 4             return 0
 5         }
 6         var columns: [Int] = Array(repeating: 1, count: m)
 7         for _ in 1..<n { // 逐行遍歷
 8             for i in 1..<m { // 第一位, 始終只有1種(+0)
 9                 columns[i] += columns[i-1]
10             }
11         }
12         return columns.last!
13     }
14 }

---

8ms

 1 class Solution {
 2     func uniquePaths(_ m: Int, _ n: Int) -> Int {
 3         var pathNums = Array(repeating: Array(repeating:0,count: n),count: m)
 4         return _helper(&pathNums, m - 1, n - 1)
 5     }
 6     private func _helper(_ pathNums: inout [[Int]], _ m: Int, _ n: Int) -> Int {
 7         if m < 0 || n < 0 {
 8             return 0
 9         }
10         if m == 0 || n == 0 {
11             return 1
12         }
13         
14         if pathNums[m][n] != 0 {
15             return pathNums[m][n]
16         }
17         pathNums[m][n] = _helper(&pathNums, m - 1, n) + _helper(&pathNums, m, n - 1)
18         
19         return pathNums[m][n]
20     }
21 }

---

12ms

 1 class Solution {
 2     func uniquePaths(_ m: Int, _ n: Int) -> Int {
 3         if m == 0 || n == 0 { return 0 }
 4         var count = Array(repeating: Array(repeating: 0, count: n), count: m)
 5         var col = n-1
 6         while col >= 0 {
 7             var row = m-1
 8             while row >= 0 {
 9                 if row == m-1 && col == n-1 {
10                     count[row][col] = 1
11                 } else {
12                     count[row][col] = (col < n-1 ? count[row][col+1] : 0) + (row < m-1 ? count[row+1][col] : 0)                   
13                 }
14                 row -= 1
15             }
16             col -= 1
17         }
18         return count[0][0]
19     }
20 }

---

16ms

 1 class Solution {
 2     
 3     func uniquePaths(_ m: Int, _ n: Int) -> Int {
 4         guard m > 0 else {
 5             return 0
 6         }
 7         
 8         var steps = Array(repeating: Array(repeating: 1, count: n), count: m)
 9         for row in 1..<m {
10             for column in 1..<n {
11                 steps[row][column] = steps[row - 1][column] + steps[row][column - 1]
12             }
13         }
14         
15         return steps[m - 1][n - 1]
16     }
17     
18 }

---

20ms

 1 class Solution {
 2     func uniquePaths(_ m: Int, _ n: Int) -> Int {
 3         if m == 0 || n == 0 {
 4             return 0
 5         }
 6         var map = Array(repeating: Array(repeating:0,count: n),count: m)
 7         for i in 1 ..< m {
 8             for j in 1 ..< n {
 9                 var num1 = map[i - 1][j]
10                 var num2 = map[i][j - 1]
11                  if i - 1 == 0 || j == 0 {
12                     num1 = 1
13                 }
14                 if i == 0 || j - 1 == 0 {
15                     num2 = 1
16                 }
17                 map[i][j] = num1 + num2
18             }
19         }
20          if m - 1 == 0 || n - 1 == 0 {
21             return 1
22         } else {
23             let result = map[m - 1][n - 1]
24             return result
25         }
26     }
27 }

---

24ms

 1 class Solution {
 2     
 3     func uniquePaths(_ m: Int, _ n: Int) -> Int {
 4         var arrs: [[Int]] = Array(repeating: Array(repeating: 0, count: n), count: m)
 5         for i in 0..<m{
 6             for j in 0..<n{
 7                 if i == 0 && j == 0{
 8                     arrs[i][j] = 1
 9                 }else if i == 0 {
10                     arrs[i][j] = arrs[i][j-1]
11                 }else if j == 0{
12                     arrs[i][j] = arrs[i-1][j]
13                 }else{
14                     arrs[i][j] = arrs[i-1][j] + arrs[i][j-1]
15                 }
16             }
17         }
18         return arrs[m-1][n-1]
19     }
20 }

---

32ms

 1 class Solution {
 2     func uniquePaths(_ m: Int, _ n: Int) -> Int {
 3         guard m > 1 else {
 4             return m == 0 ? 0 : 1
 5         }
 6         guard n > 1 else {
 7             return n == 0 ? 0 : 1
 8         }
 9         
10         var path = [Int].init(repeating: 1, count: m+1)
11         path[0] = 0
12         for _ in 2...n {
13             for j in 1...m {
14                 path[j] = path[j] + path[j-1]
15             }
16         }
17         print(path)
18         return path[m]
19     }
20 }

---

40ms

 1 class Solution {
 2     func uniquePaths(_ m: Int, _ n: Int) -> Int {
 3         let l = max(m,n)
 4         let s = min(m,n)
 5         if s==1 {
 6             return 1
 7         }
 8         // c l,s 組合
 9         var ji1 = 1
10         var ji2 = 1
11         for i in 1...s-1 {
12             ji1*=i
13             ji2*=l+s-i-1
14         }
15         return ji2/ji1
16     }
17 }