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0070_Climbing_Stairs.py
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0070_Climbing_Stairs.py
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'''
You are climbing a stair case. It takes n steps to reach to the top.
Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top?
Note: Given n will be a positive integer.
Input: 2
Output: 2
Explanation: There are two ways to climb to the top.
1. 1 step + 1 step
2. 2 steps
Input: 3
Output: 3
Explanation: There are three ways to climb to the top.
1. 1 step + 1 step + 1 step
2. 1 step + 2 steps
3. 2 steps + 1 step
'''
class Solution:
''' Approach #1 (Dynamic Programming) '''
'''
One can Reach ith step by:
- Taking one step from (i-1)th step
- Taking two step from (i-2)th step
So, Total number of ways to reach will be sum of ways to reach (i-1)th step and (i-2)th step
'''
def climbStairs(self, n: int) -> int:
if(n<2):return 1
# Initializing dp list
dp = [0]*(n+1)
# For n=1 total_ways = 1
# For n=2 total_ways = 2
dp[1] = 1
dp[2] = 2
for step in range(3,len(dp)):
dp[step] = dp[step-1] + dp[step-2]
return dp[n]
if __name__ == '__main__':
sol = Solution()
n = 3
print(sol.climbStairs(n))