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| 1 | +'''Leetcode- https://leetcode.com/problems/climbing-stairs/ ''' |
| 2 | +''' |
| 3 | +You are climbing a staircase. It takes n steps to reach the top. |
| 4 | + |
| 5 | +Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top? |
| 6 | + |
| 7 | + |
| 8 | + |
| 9 | +Example 1: |
| 10 | + |
| 11 | +Input: n = 2 |
| 12 | +Output: 2 |
| 13 | +Explanation: There are two ways to climb to the top. |
| 14 | +1. 1 step + 1 step |
| 15 | +2. 2 steps |
| 16 | +''' |
| 17 | +#Top down TLE #T:O(2^n) |
| 18 | +def climbStairs(n): |
| 19 | + if n==1: |
| 20 | + return 1 |
| 21 | + if n==2: |
| 22 | + return 2 |
| 23 | + |
| 24 | + return climbStairs(n-1)+climbStairs(n-1) |
| 25 | + |
| 26 | +#Top down + memorization (list) |
| 27 | +def climbStairs(self,n): |
| 28 | + if n == 1: |
| 29 | + return 1 |
| 30 | + arr = [-1 for i in range(n)] |
| 31 | + arr[0], arr[1] = 1, 2 |
| 32 | + return self.helper(n-1, arr) |
| 33 | + |
| 34 | +def helper(self, n, arr): |
| 35 | + if arr[n] < 0: |
| 36 | + arr[n] = self.helper(n-1, arr)+self.helper(n-2, arr) |
| 37 | + return arr[n] |
| 38 | + |
| 39 | +# Top down + memorization (dictionary/hashmap) #TLE |
| 40 | +def climbStairs(n): |
| 41 | + dic = {1:1,2:2} |
| 42 | + if n not in dic: |
| 43 | + dic[n] = climbStairs(n-1)+climbStairs(n-2) |
| 44 | + return dic[n] |
| 45 | + |
| 46 | +# Bottom up, O(n) space |
| 47 | +def climbStairs(n): |
| 48 | + if n==1: |
| 49 | + return 1 |
| 50 | + res = [0 for i in range(n)] |
| 51 | + res[0],res[1] = 1,2 |
| 52 | + |
| 53 | + for i in range(2,n): |
| 54 | + res[i] = res[i-1] + res [i-2] |
| 55 | + return res[-1] |
| 56 | + |
| 57 | +# Bottom up, constant space |
| 58 | +def climbStairs(n): |
| 59 | + one,two = 1,1 |
| 60 | + |
| 61 | + for i in range(n-1): |
| 62 | + temp = one |
| 63 | + one = one+two |
| 64 | + two = temp |
| 65 | + return one |
| 66 | + |
| 67 | +#T:O(n) |
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