# Program to print non square numbers

Write a program to print first n non-square number (non perfect square) .

Examples :

```Input : 5
Output : 2 3 5 6 7

Input : 10
Output : 2 3 5 6 7 8 10 11 12 13
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

A naive method is to traverse all numbers from 1 to n. For every number, check if it is perfect square or not. If not a perfect square, print it.

## C++

 `// CPP program to print first n ` `// non-square numbers. ` `#include ` `using` `namespace` `std; ` ` `  `// Function to check perfect square ` `bool` `isPerfectSquare(``int` `n) ` `{ ` `    ``if` `(n < 0) ` `        ``return` `false``; ` ` `  `    ``int` `root = round(``sqrt``(n))); ` `    ``return` `n == root * root; ` `} ` ` `  `// function to print all ` `// non square number ` `void` `printnonsquare(``int` `n) ` `{ ` `    ``// variable which stores the ` `    ``// count ` `    ``int` `count = 0; ` `    ``for` `(``int` `i = 1; count < n; ++i) { ` ` `  `        ``// not perfect square ` `        ``if` `(!isPerfectSquare(i)) { ` `            ``cout << i << ``" "``; ` `            ``count++; ` `        ``} ` `    ``} ` `} ` `int` `main() ` `{ ` `    ``int` `n = 10; ` `    ``printnonsquare(n); ` `    ``return` `0; ` `} `

## Java

 `// Java program to print first n ` `// non-square numbers. ` `import` `java.io.*; ` `import` `java.math.*; ` ` `  `class` `GFG { ` `     `  `    ``// Function to check perfect square ` `    ``static` `boolean` `isPerfectSquare(``int` `n) ` `    ``{ ` `       ``if` `(n < ``0``) ` `          ``return` `false``; ` `     `  `       ``int` `root = Math.round((``int``)(Math.sqrt(n))); ` `       ``return` `n == root * root; ` `    ``} ` `     `  `    ``// function to print all ` `    ``// non square number ` `    ``static` `void` `printnonsquare(``int` `n) ` `    ``{ ` `        ``// variable which stores the ` `        ``// count ` `        ``int` `count = ``0``; ` `        ``for` `(``int` `i = ``1``; count < n; ++i) { ` `     `  `            ``// not perfect square ` `            ``if` `(!isPerfectSquare(i)) { ` `     `  `                ``System.out.print(i + ``" "``); ` `                ``count++; ` `            ``} ` `        ``} ` `    ``} ` `     `  `    ``// Driver code ` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``int` `n = ``10``; ` `        ``printnonsquare(n); ` `    ``} ` `} ` ` `  ` `  `/* This code is contributed by Nikita Tiwari.*/`

## Python3

 `# Python 3 program to print  ` `# first n non-square numbers. ` `import` `math ` ` `  `# Function to check perfect  ` `# square ` `def` `isPerfectSquare(n) : ` `     `  `    ``if` `(n < ``0``) : ` `        ``return` `False` ` `  `    ``root ``=` `round``(math.sqrt(n)) ` `     `  `    ``return` `(n ``=``=` `root ``*` `root) ` ` `  `# function to print all ` `# non square number ` `def` `printnonsquare(n) : ` `     `  `    ``# variable which stores the ` `    ``# count ` `    ``count ``=` `0` `    ``i ``=` `1` `     `  `    ``while``(count < n) : ` `     `  `        ``# Not perfect square ` `        ``if` `(isPerfectSquare(i)``=``=` `False``) : ` `            ``print``(i, end ``=``" "``) ` `            ``count ``=` `count ``+` `1` ` `  `        ``i ``=` `i ``+` `1` ` `  `n ``=` `10` `printnonsquare(n) ` ` `  `# This code is contributed by Nikita Tiwari. `

## C#

 `// C# program to print first n  ` `// non-square numbers.  ` `using` `System; ` ` `  `class` `GFG ` `{ ` `// Function to check perfect square  ` `static` `bool` `isPerfectSquare(``int` `n)  ` `{  ` `if` `(n < 0)  ` `    ``return` `false``;  ` ` `  `double` `root = Math.Round((``double` `)(Math.Sqrt(n)));  ` `return` `n == root * root;  ` `}  ` ` `  `// function to print all  ` `// non square number  ` `static` `void` `printnonsquare(``int` `n)  ` `{  ` `    ``// variable which stores the  ` `    ``// count  ` `    ``int` `count = 0;  ` `    ``for` `(``int` `i = 1; count < n; ++i)  ` `    ``{  ` ` `  `        ``// not perfect square  ` `        ``if` `(!isPerfectSquare(i))  ` `        ``{  ` `            ``Console.Write(i + ``" "``);  ` `            ``count++;  ` `        ``}  ` `    ``}  ` `}  ` ` `  `// Driver code  ` ` `  `static` `public` `void` `Main () ` `{ ` `    ``int` `n = 10;  ` `    ``printnonsquare(n); ` `} ` `} ` ` `  `// This code is contributed by jit_t `

## PHP

 ` `

Output :

```2 3 5 6 7 8 10 11 12 13
```

We can improve the above algorithm by using below formula
F(n) = n + floor(1/2 + sqrt(n))
By applying this function we get nth non square number.

Source and proof of the formula : Quora

Below is the implementation of above approach .

## C++

 `// CPP program to print first n ` `// non square number ` `#include ` ` `  `// Returns n-th non-square number. ` `int` `nonsquare(``int` `n) ` `{ ` `    ``return` `n + (``int``)(0.5 + ``sqrt``(n)); ` `} ` ` `  `void` `printNonSquare(``int` `n) ` `{ ` `    ``// loop to print non squares ` `    ``// below n ` `    ``for` `(``int` `i = 1; i <= n; i++) ` `        ``printf``(``"%d "``, nonsquare(i)); ` `} ` ` `  `int` `main() ` `{ ` `    ``int` `n = 10; ` `    ``printNonSquare(n); ` `    ``return` `0; ` `} `

## Java

 `// Java program to print first n ` `// non-square numbers. ` `import` `java.io.*; ` `import` `java.math.*; ` ` `  `class` `GFG { ` `     `  `    ``// Returns n-th non-square number. ` `    ``static` `int` `nonsquare(``int` `n) ` `    ``{ ` `        ``return` `n + (``int``)(``0.5` `+ (Math.sqrt(n))); ` `    ``} ` ` `  `    ``static` `void` `printNonSquare(``int` `n) ` `    ``{ ` `        ``// loop to print non squares ` `        ``// below n ` `        ``for` `(``int` `i = ``1``; i <= n; i++) ` `            ``System.out.print(nonsquare(i)+``" "``); ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``int` `n = ``10``; ` `        ``printNonSquare(n); ` `    ``} ` `} ` ` `  ` `  `/* This code is contributed by Nikita Tiwari.*/`

## Python3

 `# Python 3 program to print ` `# first n non-square numbers. ` `import` `math ` ` `  `# Returns n-th non-square  ` `# number. ` `def` `nonsquare(n) : ` `     `  `    ``return` `n ``+` `(``int``)(``0.5` `+` `math.sqrt(n)) ` ` `  `def` `printNonSquare(n) : ` `     `  `    ``# loop to print non ` `    ``# squares below n ` `    ``for` `i ``in` `range``(``1``, n ``+` `1``) : ` `        ``print``(nonsquare(i), end ``=` `" "``) ` ` `  `n ``=` `10` `printNonSquare(n) ` `     `  `# This code is contributed by Nikita Tiwari. `

## C#

 `// C# program to print first n ` `// non-square numbers. ` `using` `System; ` ` `  `class` `GFG ` `{ ` `     `  `    ``// Returns n-th non-square number. ` `    ``static` `int` `nonsquare(``int` `n) ` `    ``{ ` `        ``return` `n + (``int``)(0.5 + (Math.Sqrt(n))); ` `    ``} ` ` `  `    ``static` `void` `printNonSquare(``int` `n) ` `    ``{ ` `        ``// loop to print non squares ` `        ``// below n ` `        ``for` `(``int` `i = 1; i <= n; i++) ` `            ``Console.Write(nonsquare(i)+``" "``); ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``int` `n = 10; ` `        ``printNonSquare(n); ` `    ``} ` `} ` ` `  ` `  `// This code is contributed  ` `// by Akanksha Rai(Abby_akku) `

## PHP

 ` `

Output:

```2 3 5 6 7 8 10 11 12 13
```

An alternate solution is based on the fact that number of non-squares between two squares is always an even number.
Count of non-square numbers between two consecutive numbers k and k+1 is
= (k+1)2 – k2 + 1
= 2k

Count of non-squares between 1-4, 4-9, 9-16, … are 2, 4, 6, … respectively. Theses are even numbers.

Below is the implementation of the above approach.

## C++

 `// CPP program to print first n ` `// non square number ` `#include ` `#include ` `#include ` ` `  `void` `printNonSquare(``int` `n) ` `{ ` `    ``int` `curr_count = 2, num = 2, count = 0; ` `    ``while` `(count < n) { ` ` `  `        ``// Print curr_count numbers. curr_count ` `        ``// is current gap between two square numbers. ` `        ``for` `(``int` `i = 0; i < curr_count && ` `                        ``count < n; i++) { ` `            ``printf``(``"%d "``, num); ` `            ``count++; ` `            ``num++; ` `        ``} ` ` `  `        ``// skip a square number. ` `        ``num++; ` ` `  `        ``// Count of next non-square numbers ` `        ``// is next even number. ` `        ``curr_count += 2; ` `    ``} ` `} ` ` `  `int` `main() ` `{ ` `    ``int` `n = 10; ` `    ``printNonSquare(n); ` `    ``return` `0; ` `} `

## Java

 `// Java program to print first n ` `// non-square numbers. ` `import` `java.io.*; ` `import` `java.math.*; ` ` `  `class` `GFG { ` `     `  `    ``static` `void` `printNonSquare(``int` `n) ` `    ``{ ` `        ``int` `curr_count = ``2``, num = ``2``, count = ``0``; ` `        ``while` `(count < n) { ` `     `  `            ``// Print curr_count numbers. curr_count is ` `            ``//  current gap between two square numbers. ` `            ``for` `(``int` `i = ``0``; i < curr_count && ` `                                ``count < n; i++) { ` `                                 `  `                ``System.out.print( num+``" "``); ` `                 `  `                ``count++; ` `                ``num++; ` `            ``} ` `     `  `            ``// skip a square number. ` `            ``num++; ` `     `  `            ``// Count of next non-square  ` `            ``// numbers is next even number. ` `            ``curr_count += ``2``; ` `        ``} ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``int` `n = ``10``; ` `        ``printNonSquare(n); ` `    ``} ` `} ` ` `  ` `  `/* This code is contributed by Nikita Tiwari.*/`

## Python3

 `# Python 3 program to print ` `# first n non-square numbers. ` `import` `math ` ` `  `# Returns n-th non-square  ` `# number. ` `def` `printNonSquare(n) : ` ` `  `    ``curr_count ``=` `2` `    ``num ``=` `2` `    ``count ``=` `0` ` `  `    ``while` `(count < n) : ` `         `  `        ``# Print curr_count numbers.  ` `        ``# curr_count is current gap ` `        ``# between two square numbers. ` `        ``i ``=` `0` `         `  `        ``while``(i < curr_count ``and` `count < n) : ` `             `  `            ``print``(num, end ``=` `" "``) ` `            ``count ``=` `count ``+` `1` `            ``num ``=` `num ``+` `1` `            ``i ``=` `i ``+` `1` `             `  `        ``# skip a square number. ` `        ``num ``=` `num ``+` `1` ` `  `        ``# Count of next non-square  ` `        ``# numbers is next even number. ` `        ``curr_count ``=` `curr_count ``+` `2` ` `  `n ``=` `10` `printNonSquare(n) ` `     `  `# This code is contributed by Nikita Tiwari. `

## C#

 `// C# program to print  ` `// first n non-square  ` `// numbers. ` `using` `System; ` ` `  `class` `GFG ` `{ ` `static` `void` `printNonSquare(``int` `n) ` `{ ` `    ``int` `curr_count = 2,  ` `        ``num = 2, count = 0; ` `    ``while` `(count < n) ` `    ``{ ` ` `  `        ``// Print curr_count  ` `        ``// numbers. curr_count  ` `        ``// is current gap between  ` `        ``// two square numbers. ` `        ``for` `(``int` `i = 0; i < curr_count && ` `                            ``count < n; i++)  ` `        ``{ ` `            ``Console.Write(num + ``" "``); ` `             `  `            ``count++; ` `            ``num++; ` `        ``} ` ` `  `        ``// skip a square number. ` `        ``num++; ` ` `  `        ``// Count of next  ` `        ``// non-square numbers ` `        ``// is next even number. ` `        ``curr_count += 2; ` `    ``} ` `} ` ` `  `// Driver code ` `static` `public` `void` `Main () ` `{ ` `    ``int` `n = 10; ` `    ``printNonSquare(n); ` `} ` `} ` ` `  `// This code is contributed  ` `// by akt_mit `

## PHP

 ` `

Output:

```2 3 5 6 7 8 10 11 12 13
```

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