Square pyramidal number (Sum of Squares)

A Square pyramidal number represents sum of squares of first natural numbers. First few Square pyramidal numbers are 1, 5, 14, 30, 55, 91, 140, 204, 285, 385, 506, ...
Geometrically these numbers represent number of spheres to be stacked to form a pyramid with square base. Please see this Wiki image for more clarity.
Given a number s (1 <= s <= 1000000000). If s is sum of the squares of the first n natural numbers then print n, otherwise print -1.
Examples : 
 

Input : 14
Output : 3
Explanation : 1*1 + 2*2 + 3*3 = 14

Input : 26
Output : -1

A simple solution is to run through all numbers starting from 1, compute current sum. If current sum is equal to given sum, then we return true, else false.
 

// C++ program to check if a 
// given number is sum of 
// squares of natural numbers.
#include <iostream>
using namespace std;

// Function to find if the 
// given number is sum of 
// the squares of first n
// natural numbers
int findS(int s)
{
    int sum = 0;

    // Start adding squares of
    // the numbers from 1
    for (int n = 1; sum < s; n++) 
    {
        sum += n * n;

        // If sum becomes equal to s
        // return n
        if (sum == s)
            return n;
    }

    return -1;
}

// Drivers code
int main()
{
    int s = 13;
    int n = findS(s);
    n == -1 ? cout << "-1" : cout << n;

    return 0;
}

// C program to check if a 
// given number is sum of 
// squares of natural numbers.
#include <stdio.h>

// Function to find if the 
// given number is sum of 
// the squares of first n
// natural numbers
int findS(int s)
{
    int sum = 0;

    // Start adding squares of
    // the numbers from 1
    for (int n = 1; sum < s; n++) 
    {
        sum += n * n;

        // If sum becomes equal to s
        // return n
        if (sum == s)
            return n;
    }

    return -1;
}

// Drivers code
int main()
{
    int s = 13;
    int n = findS(s);
    
    n == -1 ? printf("-1") : printf("%d",n);

    return 0;
}

// This code is contributed by kothavvsaakash.

// Java program to check if a 
// given number is sum of 
// squares of natural numbers.
class GFG 
{

    // Function to find if the 
    // given number is sum of 
    // the squares of first 
    // n natural numbers
    static int findS(int s)
    {
        int sum = 0;

        // Start adding squares of 
        // the numbers from 1
        for (int n = 1; sum < s; n++) 
        {
            sum += n * n;

            // If sum becomes equal to s
            // return n
            if (sum == s)
                return n;
        }

        return -1;
    }

    // Drivers code
    public static void main(String[] args)
    {

        int s = 13;
        int n = findS(s);
        if (n == -1)
            System.out.println("-1");
        else
            System.out.println(n);
    }
}

# Python3 program to find if
# the given number is sum of 
# the squares of first 
# n natural numbers

# Function to find if the given 
# number is sum of the squares 
# of first n natural numbers
def findS (s):
    _sum = 0
    n = 1
    
    # Start adding squares of
    # the numbers from 1
    while(_sum < s):
        _sum += n * n
        n+= 1
    n-= 1
    
    # If sum becomes equal to s
    # return n
    if _sum == s:
        return n
    return -1

# Driver code
s = 13
n = findS (s)
if n == -1:
    print("-1")
else:
    print(n)

// C# program to check if a given 
// number is sum of squares of 
// natural numbers.
using System;

class GFG 
{
    
    // Function to find if the given
    // number is sum of the squares 
    // of first n natural numbers
    static int findS(int s)
    {
        int sum = 0;
    
        // Start adding squares of 
        // the numbers from 1
        for (int n = 1; sum < s; n++)
        {
            sum += n * n;
    
            // If sum becomes equal 
            // to s return n
            if (sum == s)
                return n;
        }
    
        return -1;
    }
    
    // Drivers code
    public static void Main()
    {
        int s = 13;
        
        int n = findS(s);
        
        if(n == -1)
            Console.Write("-1") ;
        else
            Console.Write(n);
    }
}
// This code is contribute by
// Smitha Dinesh Semwal

<?php
// PHP program to check if a 
// given number is sum of 
// squares of natural numbers.

// Function to find if the given number
// is sum of the squares of first n
// natural numbers
function findS($s)
{
    $sum = 0;

    // Start adding squares of
    // the numbers from 1
    for ($n = 1; $sum < $s; $n++) 
    {
        $sum += $n * $n;

        // If sum becomes equal to s
        // return n
        if ($sum == $s)
            return $n;
    }

    return -1;
}

// Drivers code
$s = 13;
$n = findS($s);
if($n == -1) 
    echo("-1");
else
    echo($n);

// This code is contributed by Ajit.
?>

<script>

// JavaScript to check if a 
// given number is sum of 
// squares of natural numbers.

    // Function to find if the 
    // given number is sum of 
    // the squares of first 
    // n natural numbers
    function findS(s)
    {
        let sum = 0;
  
        // Start adding squares of 
        // the numbers from 1
        for (let n = 1; sum < s; n++) 
        {
            sum += n * n;
  
            // If sum becomes equal to s
            // return n
            if (sum == s)
                return n;
        }
  
        return -1;
    }

// Driver code
        let s = 13;
        let n = findS(s);
        if (n == -1)
            document.write("-1");
        else
            document.write(n);

// This code is contributed by souravghosh0416.
</script>

OUTPUT : 
 

-1

Time complexity: O(s) for given input s
Space complexity: O(1)

An alternate solution is to use Newton Raphson Method. 
We know sum of squares of first n natural numbers is n * (n + 1) * (2*n + 1) / 6.
We can write solutions as
k * (k + 1) * (2*k + 1) / 6 = s
k * (k + 1) * (2*k + 1) - 6s = 0
We can find roots of above cubic equation using Newton Raphson Method, then check if root is integer or not.