# Program to count number of permutations where sum of adjacent pairs are perfect square in Python

PythonServer Side ProgrammingProgramming

Suppose we have a list of numbers called nums. We have to find the number of permutations of nums such that sum of every pair of adjacent values is a perfect square. Two permutations A and B are unique when there is some index i where A[i] is not same as B[i].

So, if the input is like nums = [2, 9, 7], then the output will be 2, as we have [2, 7, 9] and [9, 7, 2]

To solve this, we will follow these steps −

• res := 0

• Define a function util() . This will take i

• if i + 1 is same as size of nums , then

• res := res + 1

• return

• visited := a new empty set

• for j in range i + 1 to size of nums, do

• s := nums[i] + nums[j]

• if s is not visited and (square root of s)^2 is s, then

• mark s as visited

• swap nums[i + 1] and nums[j]

• util(i + 1)

• swap nums[i + 1] and nums[j]

• From the main method do the following −

• visited := a new set

• for i in range 0 to size of nums, do

• swap nums[i] and nums

• if nums is not visited, then

• util(0)

• mark nums as visited

• swap nums[i] and nums

• return res

Let us see the following implementation to get better understanding −

## Example

Live Demo

from math import sqrt
class Solution:
def solve(self, nums):
self.res = 0
def util(i):
if i + 1 == len(nums):
self.res += 1
return
visited = set()
for j in range(i + 1, len(nums)):
s = nums[i] + nums[j]
if s not in visited and int(sqrt(s)) ** 2 == s:
nums[i + 1], nums[j] = nums[j], nums[i + 1]
util(i + 1)
nums[i + 1], nums[j] = nums[j], nums[i + 1]
visited = set()
for i in range(len(nums)):
nums[i], nums = nums, nums[i]
if nums not in visited:
util(0)
nums[i], nums = nums, nums[i]
return self.res
ob = Solution()
nums = [2, 9, 7]
print(ob.solve(nums))

## Input

[2, 9, 7]

## Output

2