Syntax error Program to find number of ways we can reach to the next floor using stairs in Python

Program to find number of ways we can reach to the next floor using stairs in Python

Suppose there is a stair case with N steps. One can either go step by step, or at each step, one can take a jump of at most N steps. We have to find the number of ways in which we can go to the top floor. The N value may be large we are only interested in the first and the last K digits of number of ways.

So, if the input is like N = 10 k = 2, then the output will be 63 because there are 10 steps, if there are S number of ways in which we can go to the top, then consider S be of the form wxyz.So, summing wx + yz is 63.

To solve this, we will follow these steps −

  • N := N - 1
  • c := 2 * ceiling of (k + log(N);base10)
  • e := N, b := 2, s := 1
  • while e > 0, do
    • if e is odd, then
      • s := the first p-c digit numbers of (s*b) where p is number of digits in s*b
    • e := floor of e/2
    • b := the first p-c digit numbers of (b*b) where p is number of digits in b*b
  • s := first p - k digit number of s, where p is number of digits in s
  • r := s + (2^N) mod 10^k
  • return r

Example

Let us see the following implementation to get better understanding −

from math import log10,ceil

def solve(N,k):
   N -= 1
   c = 2*ceil(k + log10(N))
   e = N
   b = 2
   s = 1
   while e > 0:
      if e % 2 == 1:
         s = int(str(s*b)[:c])
      e //=2
      b = int(str(b*b)[:c])
   s = str(s)[:k]
   r = int(s) + pow(2, N, 10**k)
   return r

N = 10
k = 2
print(solve(N,k))

Input

10, 2

Output

63
Updated on: 2021-10-25T06:50:10+05:30

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