# Number of Squareful Arrays in C++

C++Server Side ProgrammingProgramming

Suppose we have an array A of positive integers, we can say that array is squareful if for every pair of adjacent elements, their sum is a perfect square. We have to find the number of permutations of A that are squareful. Two permutations A1 and A2 will not be same if and only if there is some index i such that A1[i] not same as A2[i].

So, if the input is like [3,30,6], then the output will be 2, as we have two permutations like [3,6,30], [30,6,3].

To solve this, we will follow these steps −

• Define a function isSqr(), this will take n,

• x := square root of n

• return true when (x * x) is same as n

• Define a function solve(), this will take an array a, idx,

• if idx is same as size of a, then −

• (increase count by 1)

• return

• Define one set visited

• for initialize i := idx, when i < size of a, update (increase i by 1), do −

• if (idx is same as 0 or isSqr(a[idx - 1] + a[i])) and a[i] is not in visited then −

• swap(a[idx], a[i])

• solve(a, idx + 1)

• swap(a[idx], a[i])

• insert a[i] into visited

• From the main method, do the following −

• count := 0

• solve(a, 0)

• return count

Let us see the following implementation to get better understanding −

## Example

Live Demo

#include <bits/stdc++.h>
using namespace std;
typedef long long int lli;
class Solution {
public:
int count;
bool isSqr(lli n){
lli x = sqrt(n);
return x * x == n;
}
void solve(vector<int>& a, int idx){
if (idx == a.size()) {
count++;
return;
}
set<int> visited;
for (int i = idx; i < a.size(); i++) {
if ((idx == 0 || isSqr(a[idx - 1] + a[i])) &&
!visited.count(a[i])) {
swap(a[idx], a[i]);
solve(a, idx + 1);
swap(a[idx], a[i]);
visited.insert(a[i]);
}
}
}
int numSquarefulPerms(vector<int>& a){
count = 0;
solve(a, 0);
return count;
}
};
main(){
Solution ob;
vector<int> v = {3,30,6};
cout << (ob.numSquarefulPerms(v));
}

## Input

{3,30,6}

## Output

2