Program to check we can reach at position n by jumping or not in Python

Suppose there is a number line from 1 to n. At first we are at position 0, jump one step to go 1, then jump two place to reach at position 3, then jump three position to reach at 6 and so on. We have to check whether maintaining this, we can reach at position n or not.

So, if the input is like n = 21, then the output will be True, because 1+2+3+4+5+6 = 21

To solve this, we will follow these steps −

• j:= (1 + square root of (1+8*n)) / 2
• if |j - int part of j| <= 0, then
  • return True
• otherwise return False

Example

Let us see the following implementation to get better understanding −

from math import sqrt
def solve(n):
   j=(1+sqrt(1+8*n))/2
   if abs(j-int(j))<=0:
      return True
   else:
      return False

n = 21
print(solve(n))

Input

21

Output

True