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preface

[C] LeetCode 100

Our community will continue to include Yi Gu (Netflix growth hacker, author of The Way to Interview for iOS, ACE professional fitness coach). Swift algorithm problem solving sorted into text version to facilitate everyone to learn and read.

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Difficulty level: Medium

1. Describe

A robot is located in the upper left corner of an M x N grid (the starting point is marked “Start” in the figure below).

The robot can only move one step to the right or down at a time. The robot attempts to reach the lower right corner of the grid (marked “Finish” in the image below).

How many different paths are there?

Example 2.

Example 1

Input: m = 3, n = 7 Output: 28Copy the code

Example 2

Input: m = 3, n = 2 Output: 3 Description: There are three paths to the lower right corner starting from the upper left corner. Right -> down -> down 2. Down -> Down -> Right 3. Down -> right -> downCopy the code

Example 3

Input: m = 7, n = 3 Output: 28Copy the code

Example 4

Input: m = 3, n = 3 Output: 6Copy the code

Constraints:

  • 1 <= m, n <= 100
  • The problem data guarantees that the answer is less than or equal to2 * 10 ^ 9

3. The answer

class UniquePaths {
    func uniquePaths(m: Int._ n: Int) -> Int {
        var pathNums = Array(count: m, repeatedValue: Array(count: n, repeatedValue: 0))
        return _helper(&pathNums, m - 1, n - 1)}private func _helper(inout pathNums: [[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]
    }
}
Copy the code
  • Main idea: 2D dynamic programming, using 2D array as cache to store computational data.
  • Time complexity: O(Mn)
  • Space complexity: O(Mn)

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