# Smallest of three integers without comparison operators

Write a program to find the smallest of three integers, without using any of the comparison operators.
Let 3 input numbers be x, y and z.
Method 1 (Repeated Subtraction)
Take a counter variable c and initialize it with 0. In a loop, repeatedly subtract x, y and z by 1 and increment c. The number which becomes 0 first is the smallest. After the loop terminates, c will hold the minimum of 3.

## C++

 `// C++ program to find Smallest` `// of three integers without` `// comparison operators` `#include ` `using` `namespace` `std;` `int` `smallest(``int` `x, ``int` `y, ``int` `z)` `{` `    ``int` `c = 0;` `    ``while` `(x && y && z) {` `        ``x--;` `        ``y--;` `        ``z--;` `        ``c++;` `    ``}` `    ``return` `c;` `}`   `// Driver Code` `int` `main()` `{` `    ``int` `x = 12, y = 15, z = 5;` `    ``cout << ``"Minimum of 3 numbers is "` `         ``<< smallest(x, y, z);` `    ``return` `0;` `}`   `// This code is contributed` `// by Akanksha Rai`

## C

 `// C program to find Smallest` `// of three integers without` `// comparison operators` `#include `   `int` `smallest(``int` `x, ``int` `y, ``int` `z)` `{` `    ``int` `c = 0;` `    ``while` `(x && y && z) {` `        ``x--;` `        ``y--;` `        ``z--;` `        ``c++;` `    ``}` `    ``return` `c;` `}`   `int` `main()` `{` `    ``int` `x = 12, y = 15, z = 5;` `    ``printf``(``"Minimum of 3 numbers is %d"``, smallest(x, y, z));` `    ``return` `0;` `}`

## Java

 `// Java program to find Smallest` `// of three integers without` `// comparison operators` `class` `GFG {`   `    ``static` `int` `smallest(``int` `x, ``int` `y, ``int` `z)` `    ``{` `        ``int` `c = ``0``;`   `        ``while` `(x != ``0` `&& y != ``0` `&& z != ``0``) {` `            ``x--;` `            ``y--;` `            ``z--;` `            ``c++;` `        ``}`   `        ``return` `c;` `    ``}`   `    ``public` `static` `void` `main(String[] args)` `    ``{` `        ``int` `x = ``12``, y = ``15``, z = ``5``;`   `        ``System.out.printf(``"Minimum of 3"` `                              ``+ ``" numbers is %d"``,` `                          ``smallest(x, y, z));` `    ``}` `}`   `// This code is contributed by  Smitha Dinesh Semwal.`

## Python3

 `# Python3 program to find Smallest` `# of three integers without ` `# comparison operators`   `def` `smallest(x, y, z):` `    ``c ``=` `0` `    `  `    ``while` `( x ``and` `y ``and` `z ):` `        ``x ``=` `x``-``1` `        ``y ``=` `y``-``1` `        ``z ``=` `z``-``1` `        ``c ``=` `c ``+` `1`   `    ``return` `c`   `# Driver Code` `x ``=` `12` `y ``=` `15` `z ``=` `5` `print``(``"Minimum of 3 numbers is"``,` `       ``smallest(x, y, z))`   `# This code is contributed by Anshika Goyal`

## C#

 `// C# program to find Smallest of three` `// integers without comparison operators` `using` `System;`   `class` `GFG {` `    ``static` `int` `smallest(``int` `x, ``int` `y, ``int` `z)` `    ``{` `        ``int` `c = 0;`   `        ``while` `(x != 0 && y != 0 && z != 0) {` `            ``x--;` `            ``y--;` `            ``z--;` `            ``c++;` `        ``}`   `        ``return` `c;` `    ``}`   `    ``// Driver Code` `    ``public` `static` `void` `Main()` `    ``{` `        ``int` `x = 12, y = 15, z = 5;`   `        ``Console.Write(``"Minimum of 3"` `                      ``+ ``" numbers is "` `+ smallest(x, y, z));` `    ``}` `}`   `// This code is contributed by Sam007`

## PHP

 ``

## Javascript

 ``

Output:

`Minimum of 3 numbers is 5`

Time Complexity: O(min(x, y, z))

Auxiliary Space: O(1)

This method doesn’t work for negative numbers. Method 2 works for negative numbers also.
Method 2 (Use Bit Operations)
Use method 2 of this post to find minimum of two numbers (We can’t use Method 1 as Method 1 uses comparison operator). Once we have functionality to find minimum of 2 numbers, we can use this to find minimum of 3 numbers.

## C++

 `// C++ implementation of above approach` `#include ` `using` `namespace` `std;` `#define CHAR_BIT 8`   `/*Function to find minimum of x and y*/` `int` `min(``int` `x, ``int` `y)` `{` `    ``return` `y + ((x - y) & ((x - y) >> (``sizeof``(``int``) * CHAR_BIT - 1)));` `}`   `/* Function to find minimum of 3 numbers x, y and z*/` `int` `smallest(``int` `x, ``int` `y, ``int` `z)` `{` `    ``return` `min(x, min(y, z));` `}`   `// Driver code` `int` `main()` `{` `    ``int` `x = 12, y = 15, z = 5;` `    ``cout << ``"Minimum of 3 numbers is "`  `<< smallest(x, y, z);` `    ``return` `0;` `}`   `// This code is contributed by Code_Mech.`

## C

 `// C implementation of above approach` `#include ` `#define CHAR_BIT 8`   `/*Function to find minimum of x and y*/` `int` `min(``int` `x, ``int` `y)` `{` `    ``return` `y + ((x - y) & ((x - y) >> (``sizeof``(``int``) * CHAR_BIT - 1)));` `}`   `/* Function to find minimum of 3 numbers x, y and z*/` `int` `smallest(``int` `x, ``int` `y, ``int` `z)` `{` `    ``return` `min(x, min(y, z));` `}`   `int` `main()` `{` `    ``int` `x = 12, y = 15, z = 5;` `    ``printf``(``"Minimum of 3 numbers is %d"``, smallest(x, y, z));` `    ``return` `0;` `}`

## Java

 `// Java implementation of above approach` `class` `GFG` `{` `    `  `static` `int` `CHAR_BIT = ``8``;`   `// Function to find minimum of x and y` `static` `int` `min(``int` `x, ``int` `y)` `{` `    ``return` `y + ((x - y) & ((x - y) >> ` `               ``((Integer.SIZE/``8``) * CHAR_BIT - ``1``)));` `}`   `// Function to find minimum of 3 numbers x, y and z` `static` `int` `smallest(``int` `x, ``int` `y, ``int` `z)` `{` `    ``return` `Math.min(x, Math.min(y, z));` `}`   `// Driver code` `public` `static` `void` `main (String[] args) ` `{` `    ``int` `x = ``12``, y = ``15``, z = ``5``;` `    ``System.out.println(``"Minimum of 3 numbers is "` `+ ` `                                ``smallest(x, y, z));` `}` `}`   `// This code is contributed by mits`

## Python3

 `# Python3 implementation of above approach` `CHAR_BIT ``=` `8`   `# Function to find minimum of x and y` `def` `min``(x, y):` `    ``return` `y ``+` `((x ``-` `y) & \` `               ``((x ``-` `y) >> (``32` `*` `CHAR_BIT ``-` `1``)))`   `# Function to find minimum ` `# of 3 numbers x, y and z` `def` `smallest(x, y, z):` `    ``return` `min``(x, ``min``(y, z))`   `# Driver code` `x ``=` `12` `y ``=` `15` `z ``=` `5` `print``(``"Minimum of 3 numbers is "``, ` `               ``smallest(x, y, z))`   `# This code is contributed` `# by Mohit Kumar`

## C#

 `// C# implementation of above approach` `using` `System;`   `class` `GFG` `{` `    `  `static` `int` `CHAR_BIT=8;`   `/*Function to find minimum of x and y*/` `static` `int` `min(``int` `x, ``int` `y)` `{` `    ``return` `y + ((x - y) & ((x - y) >> (``sizeof``(``int``) * CHAR_BIT - 1)));` `}`   `/* Function to find minimum of 3 numbers x, y and z*/` `static` `int` `smallest(``int` `x, ``int` `y, ``int` `z)` `{` `    ``return` `Math.Min(x, Math.Min(y, z));` `}`   `// Driver code` `static` `void` `Main()` `{` `    ``int` `x = 12, y = 15, z = 5;` `    ``Console.WriteLine(``"Minimum of 3 numbers is "``+smallest(x, y, z));` `}` `}`   `// This code is contributed by mits`

## Javascript

 ``

Output:

`Minimum of 3 numbers is 5`

Time Complexity: O(1)

Auxiliary Space: O(1)

Method 3 (Use Division operator)
We can also use division operator to find minimum of two numbers. If value of (a/b) is zero, then b is greater than a, else a is greater. Thanks to gopinath and Vignesh for suggesting this method.

## C++

 `// C++ implementation of above approach` `#include ` `using` `namespace` `std;`   `// Using division operator to find` `// minimum of three numbers` `int` `smallest(``int` `x, ``int` `y, ``int` `z)` `{` `    ``if` `(!(y / x)) ``// Same as "if (y < x)"` `        ``return` `(!(y / z)) ? y : z;` `    ``return` `(!(x / z)) ? x : z;` `}`   `int` `main()` `{` `    ``int` `x = 78, y = 88, z = 68;` `    ``cout << ``"Minimum of 3 numbers is "` `<< smallest(x, y, z);` `    ``return` `0;` `}` `// this code is contributed by shivanisinghss2110`

## C

 `#include `   `// Using division operator to find` `// minimum of three numbers` `int` `smallest(``int` `x, ``int` `y, ``int` `z)` `{` `    ``if` `(!(y / x)) ``// Same as "if (y < x)"` `        ``return` `(!(y / z)) ? y : z;` `    ``return` `(!(x / z)) ? x : z;` `}`   `int` `main()` `{` `    ``int` `x = 78, y = 88, z = 68;` `    ``printf``(``"Minimum of 3 numbers is %d"``, smallest(x, y, z));` `    ``return` `0;` `}`

## Java

 `// Java program of above approach` `class` `GfG {`   `    ``// Using division operator to` `    ``// find minimum of three numbers` `    ``static` `int` `smallest(``int` `x, ``int` `y, ``int` `z)` `    ``{` `        ``if` `((y / x) != ``1``) ``// Same as "if (y < x)"` `            ``return` `((y / z) != ``1``) ? y : z;` `        ``return` `((x / z) != ``1``) ? x : z;` `    ``}`   `    ``// Driver code` `    ``public` `static` `void` `main(String[] args)` `    ``{` `        ``int` `x = ``78``, y = ``88``, z = ``68``;` `        ``System.out.printf(``"Minimum of 3 numbers"` `                              ``+ ``" is %d"``,` `                          ``smallest(x, y, z));` `    ``}` `}`   `// This code has been contributed by 29AjayKumar`

## python3

 `# Using division operator to find` `# minimum of three numbers` `def` `smallest(x, y, z):`   `    ``if` `(``not` `(y ``/` `x)): ``# Same as "if (y < x)"` `        ``return` `y ``if` `(``not` `(y ``/` `z)) ``else` `z` `    ``return` `x ``if` `(``not` `(x ``/` `z)) ``else` `z`   `# Driver Code` `if` `__name__``=``=` `"__main__"``:`   `    ``x ``=` `78` `    ``y ``=` `88` `    ``z ``=` `68` `    ``print``(``"Minimum of 3 numbers is"``,` `                  ``smallest(x, y, z))`   `# This code is contributed ` `# by ChitraNayal`

## C#

 `// C# program of above approach` `using` `System;` `public` `class` `GfG {`   `    ``// Using division operator to` `    ``// find minimum of three numbers` `    ``static` `int` `smallest(``int` `x, ``int` `y, ``int` `z)` `    ``{` `        ``if` `((y / x) != 1) ``// Same as "if (y < x)"` `            ``return` `((y / z) != 1) ? y : z;` `        ``return` `((x / z) != 1) ? x : z;` `    ``}`   `    ``// Driver code` `    ``public` `static` `void` `Main()` `    ``{` `        ``int` `x = 78, y = 88, z = 68;` `        ``Console.Write(``"Minimum of 3 numbers"` `                          ``+ ``" is {0}"``,` `                      ``smallest(x, y, z));` `    ``}` `}` `/* This code contributed by PrinciRaj1992 */`

## Javascript

 ``

Output:

`Minimum of 3 numbers is 68`

Time Complexity: O(1)

Auxiliary Space: O(1)

Please write comments if you find the above codes/algorithms incorrect, or find other ways to solve the same problem.

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