# Check if a number is a perfect square having all its digits as a perfect square

Given an integer N, the task is to check if the given number is a perfect square having all its digits as a perfect square or not. If found to be true, then print “Yes”. Otherwise, print “No”.
Examples:

Input: N = 144
Output: Yes
Explanation:
The number 144 is a perfect square and also the digits of the number {1(= 12, 4(= 22} is also a perfect squares.
Input: N = 81
Output: No

Approach: The idea is to check if the given number N is a perfect square or not. If found to be true, check if all its digits are either 0, 1, 4, or 9. If found to be true, print “Yes”. Otherwise, print “No”.
Below is the implementation of the above approach:

 `// C++ program for the above approach`   `#include ` `using` `namespace` `std;`   `// Function to check if digits of` `// N is a perfect square or not` `bool` `check_digits(``long` `N)` `{`   `    ``// Iterate over the digits` `    ``while` `(N > 0) {`   `        ``// Extract the digit` `        ``int` `n = N % 10;`   `        ``// Check if digit is a` `        ``// perfect square or not` `        ``if` `((n != 0) && (n != 1)` `            ``&& (n != 4) && (n != 9)) {` `            ``return` `0;` `        ``}`   `        ``// Divide N by 10` `        ``N = N / 10;` `    ``}`   `    ``// Return true` `    ``return` `1;` `}`   `// Function to check if N is` `// a perfect square or not` `bool` `is_perfect(``long` `N)` `{` `    ``long` `double` `n = ``sqrt``(N);`   `    ``// If floor and ceil of n` `    ``// is not same` `    ``if` `(``floor``(n) != ``ceil``(n)) {` `        ``return` `0;` `    ``}` `    ``return` `1;` `}`   `// Function to check if N satisfies` `// the required conditions or not` `void` `isFullSquare(``long` `N)` `{` `    ``// If both the conditions` `    ``// are satisfied` `    ``if` `(is_perfect(N)` `        ``&& check_digits(N)) {` `        ``cout << ``"Yes"``;` `    ``}` `    ``else` `{` `        ``cout << ``"No"``;` `    ``}` `}`   `// Driver Code` `int` `main()` `{` `    ``long` `N = 144;`   `    ``// Function Call` `    ``isFullSquare(N);`   `    ``return` `0;` `}`

 `// Java program for ` `// the above approach` `import` `java.util.*;` `class` `GFG{`   `// Function to check if digits of` `// N is a perfect square or not` `static` `boolean` `check_digits(``long` `N)` `{` `  ``// Iterate over the digits` `  ``while` `(N > ``0``) ` `  ``{` `    ``// Extract the digit` `    ``int` `n = (``int``) (N % ``10``);`   `    ``// Check if digit is a` `    ``// perfect square or not` `    ``if` `((n != ``0``) && (n != ``1``) && ` `        ``(n != ``4``) && (n != ``9``)) ` `    ``{` `      ``return` `false``;` `    ``}`   `    ``// Divide N by 10` `    ``N = N / ``10``;` `  ``}`   `  ``// Return true` `  ``return` `true``;` `}`   `// Function to check if N is` `// a perfect square or not` `static` `boolean` `is_perfect(``long` `N)` `{` `  ``double` `n = Math.sqrt(N);`   `  ``// If floor and ceil of n` `  ``// is not same` `  ``if` `(Math.floor(n) != Math.ceil(n)) ` `  ``{` `    ``return` `false``;` `  ``}` `  ``return` `true``;` `}`   `// Function to check if N satisfies` `// the required conditions or not` `static` `void` `isFullSquare(``long` `N)` `{` `  ``// If both the conditions` `  ``// are satisfied` `  ``if` `(is_perfect(N) && ` `      ``check_digits(N)) ` `  ``{` `    ``System.out.print(``"Yes"``);` `  ``}` `  ``else` `  ``{` `    ``System.out.print(``"No"``);` `  ``}` `}`   `// Driver Code` `public` `static` `void` `main(String[] args)` `{` `  ``long` `N = ``144``;`   `  ``// Function Call` `  ``isFullSquare(N);` `}` `}`   `// This code is contributed by Rajput-Ji`

 `# Python3 program for the above approach ` `import` `math`   `# Function to check if digits of` `# N is a perfect square or not` `def` `check_digits(N):`   `    ``# Iterate over the digits` `    ``while` `(N > ``0``):`   `        ``# Extract the digit` `        ``n ``=` `N ``%` `10`   `        ``# Check if digit is a` `        ``# perfect square or not` `        ``if` `((n !``=` `0``) ``and` `(n !``=` `1``) ``and` `            ``(n !``=` `4``) ``and` `(n !``=` `9``)):` `            ``return` `0` `    `  `        ``# Divide N by 10` `        ``N ``=` `N ``/``/` `10` `    `  `    ``# Return true` `    ``return` `1`   `# Function to check if N is` `# a perfect square or not` `def` `is_perfect(N):` `    `  `    ``n ``=` `math.sqrt(N)`   `    ``# If floor and ceil of n` `    ``# is not same` `    ``if` `(math.floor(n) !``=` `math.ceil(n)):` `        ``return` `0` `    `  `    ``return` `1`   `# Function to check if N satisfies` `# the required conditions or not` `def` `isFullSquare(N):` `    `  `    ``# If both the conditions` `    ``# are satisfied` `    ``if` `(is_perfect(N) ``and` `      ``check_digits(N)):` `        ``print``(``"Yes"``)` `    ``else``:` `        ``print``(``"No"``)` `    `  `# Driver Code` `N ``=` `144`   `# Function call` `isFullSquare(N)`   `# This code is contributed by sanjoy_62`

 `// C# program for ` `// the above approach` `using` `System;` `class` `GFG{`   `// Function to check if digits of` `// N is a perfect square or not` `static` `bool` `check_digits(``long` `N)` `{` `  ``// Iterate over the digits` `  ``while` `(N > 0) ` `  ``{` `    ``// Extract the digit` `    ``int` `n = (``int``) (N % 10);`   `    ``// Check if digit is a` `    ``// perfect square or not` `    ``if` `((n != 0) && (n != 1) && ` `        ``(n != 4) && (n != 9)) ` `    ``{` `      ``return` `false``;` `    ``}`   `    ``// Divide N by 10` `    ``N = N / 10;` `  ``}`   `  ``// Return true` `  ``return` `true``;` `}`   `// Function to check if N is` `// a perfect square or not` `static` `bool` `is_perfect(``long` `N)` `{` `  ``double` `n = Math.Sqrt(N);`   `  ``// If floor and ceil of n` `  ``// is not same` `  ``if` `(Math.Floor(n) != Math.Ceiling(n)) ` `  ``{` `    ``return` `false``;` `  ``}` `  ``return` `true``;` `}`   `// Function to check if N satisfies` `// the required conditions or not` `static` `void` `isFullSquare(``long` `N)` `{` `  ``// If both the conditions` `  ``// are satisfied` `  ``if` `(is_perfect(N) && ` `      ``check_digits(N)) ` `  ``{` `    ``Console.Write(``"Yes"``);` `  ``}` `  ``else` `  ``{` `    ``Console.Write(``"No"``);` `  ``}` `}`   `// Driver Code` `public` `static` `void` `Main()` `{` `  ``long` `N = 144;`   `  ``// Function Call` `  ``isFullSquare(N);` `}` `}`   `// This code is contributed by Chitranayal`

Output:
```Yes

```

Time Complexity: O(log10N)
Auxiliary Space: O(1)

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Improved By : sanjoy_62, Rajput-Ji, chitranayal

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