# Find the Side of the smallest Square that can contain given 4 Big Squares

Given sides of four small squares. You have to find the side of the smallest square such that it can contain all given 4 squares without overlapping. The side of a square can be up to 10^16.
Examples:

```Input: side1 = 2, side2 = 2, side3 = 2, side4 = 2
Output: 4

Input: side1 = 100000000000000, side2 = 123450000000000,
side3 = 987650000000000, side4 = 987654321000000
Output: 1975304321000000```

Approach:
It is given that no two squares will overlap. Therefore to find the side of the smallest suitable square, we will find all four sides, when squares will be put in 2 x 2 manner. That is 2 squares will be side by side and rest 2 will be put together.
So we calculate all four side and select one that will be maximum.
Example: When all small squares are of same side. 1. 1. 1.

Example: When all small squares are of different side.

1. 1. 1.

Below is the implementation of the above approach:

## C++

 `// C++ program to Find the Side` `// of the smallest Square` `// that can contain given 4 Big Squares`   `#include ` `using` `namespace` `std;`   `// Function to find the maximum of two values` `long` `long` `int` `max(``long` `long` `a, ``long` `long` `b)` `{` `    ``if` `(a > b)` `        ``return` `a;` `    ``else` `        ``return` `b;` `}`   `// Function to find the smallest side` `// of the suitable suitcase` `long` `long` `int` `smallestSide(``long` `long` `int` `a[])` `{` `    ``// sort array to find the smallest` `    ``// and largest side of suitcases` `    ``sort(a, a + 4);`   `    ``long` `long` `side1, side2, side3, side4,` `        ``side11, side12, sideOfSquare;`   `    ``// side of the suitcase will be smallest` `    ``// if they arranged in 2 x 2 way` `    ``// so find all possible sides of that arrangement` `    ``side1 = a + a;` `    ``side2 = a + a;` `    ``side3 = a + a;` `    ``side4 = a + a;`   `    ``// since suitcase should be square` `    ``// so find maximum of all four side` `    ``side11 = max(side1, side2);` `    ``side12 = max(side3, side4);`   `    ``// now find greatest side and` `    ``// that will be the smallest square` `    ``sideOfSquare = max(side11, side12);`   `    ``// return the result` `    ``return` `sideOfSquare;` `}`   `// Driver program` `int` `main()` `{` `    ``long` `long` `int` `side;`   `    ``cout << ``"Test Case 1\n"``;`   `    ``// Get the side of the 4 small squares` `    ``side = 2;` `    ``side = 2;` `    ``side = 2;` `    ``side = 2;`   `    ``// Find the smallest side` `    ``cout << smallestSide(side) << endl;`   `    ``cout << ``"\nTest Case 2\n"``;`   `    ``// Get the side of the 4 small squares` `    ``side = 100000000000000;` `    ``side = 123450000000000;` `    ``side = 987650000000000;` `    ``side = 987654321000000;`   `    ``// Find the smallest side` `    ``cout << smallestSide(side) << endl;`   `    ``return` `0;` `}`

## Java

 `// Java program to Find the Side` `// of the smallest Square that ` `// can contain given 4 Big Squares` `// Java implementation of the approach` `import` `java.util.Arrays;`   `class` `GFG ` `{`   `// Function to find the maximum of two values` `static` `long` `max(``long` `a, ``long` `b)` `{` `    ``if` `(a > b)` `        ``return` `a;` `    ``else` `        ``return` `b;` `}`   `// Function to find the smallest side` `// of the suitable suitcase` `static` `long` `smallestSide(``long` `a[])` `{` `    ``// sort array to find the smallest` `    ``// and largest side of suitcases` `    ``Arrays.sort(a);`   `    ``long` `side1, side2, side3, side4,` `        ``side11, side12, sideOfSquare;`   `    ``// side of the suitcase will be smallest` `    ``// if they arranged in 2 x 2 way` `    ``// so find all possible sides of that arrangement` `    ``side1 = a[``0``] + a[``3``];` `    ``side2 = a[``1``] + a[``2``];` `    ``side3 = a[``0``] + a[``1``];` `    ``side4 = a[``2``] + a[``3``];`   `    ``// since suitcase should be square` `    ``// so find maximum of all four side` `    ``side11 = max(side1, side2);` `    ``side12 = max(side3, side4);`   `    ``// now find greatest side and` `    ``// that will be the smallest square` `    ``sideOfSquare = max(side11, side12);`   `    ``// return the result` `    ``return` `sideOfSquare;` `}`   `// Driver program` `public` `static` `void` `main(String[] args) ` `{` `    ``long` `side[] = ``new` `long``[``4``];`   `    ``System.out.println(``"Test Case 1"``);`   `    ``// Get the side of the 4 small squares` `    ``side[``0``] = ``2``;` `    ``side[``1``] = ``2``;` `    ``side[``2``] = ``2``;` `    ``side[``3``] = ``2``;`   `    ``// Find the smallest side` `    ``System.out.println(smallestSide(side));`   `    ``System.out.println(``"\nTest Case 2"``);`   `    ``// Get the side of the 4 small squares` `    ``side[``0``] = 100000000000000L;` `    ``side[``1``] = 123450000000000L;` `    ``side[``2``] = 987650000000000L;` `    ``side[``3``] = 987654321000000L;`   `    ``// Find the smallest side` `    ``System.out.println(smallestSide(side));`   `    ``}` `}`   `/* This code contributed by PrinciRaj1992 */`

## Python3

 `# Python 3 program to Find the Side` `# of the smallest Square that  ` `# can contain given 4 Big Squares`   `# Function to find the maximum ` `# of two values` `def` `max``(a, b):` `    ``if` `(a > b):` `        ``return` `a` `    ``else``:` `        ``return` `b`   `# Function to find the smallest side` `# of the suitable suitcase` `def` `smallestSide(a):` `    `  `    ``# sort array to find the smallest` `    ``# and largest side of suitcases` `    ``a.sort(reverse ``=` `False``)`   `    ``# side of the suitcase will be ` `    ``# smallest if they arranged in ` `    ``# 2 x 2 way so find all possible` `    ``# sides of that arrangement` `    ``side1 ``=` `a[``0``] ``+` `a[``3``]` `    ``side2 ``=` `a[``1``] ``+` `a[``2``]` `    ``side3 ``=` `a[``0``] ``+` `a[``1``]` `    ``side4 ``=` `a[``2``] ``+` `a[``3``]`   `    ``# since suitcase should be square` `    ``# so find maximum of all four side` `    ``side11 ``=` `max``(side1, side2)` `    ``side12 ``=` `max``(side3, side4)`   `    ``# now find greatest side and` `    ``# that will be the smallest square` `    ``sideOfSquare ``=` `max``(side11, side12)`   `    ``# return the result` `    ``return` `sideOfSquare`   `# Driver Code` `if` `__name__ ``=``=` `'__main__'``:` `    ``side ``=` `[``0` `for` `i ``in` `range``(``4``)]`   `    ``print``(``"Test Case 1"``)`   `    ``# Get the side of the 4` `    ``# small squares` `    ``side[``0``] ``=` `2` `    ``side[``1``] ``=` `2` `    ``side[``2``] ``=` `2` `    ``side[``3``] ``=` `2`   `    ``# Find the smallest side` `    ``print``(smallestSide(side))`   `    ``print``(``"\n"``, end ``=` `"")` `    ``print``(``"Test Case 2"``)`   `    ``# Get the side of the 4 small squares` `    ``side[``0``] ``=` `100000000000000` `    ``side[``1``] ``=` `123450000000000` `    ``side[``2``] ``=` `987650000000000` `    ``side[``3``] ``=` `987654321000000`   `    ``# Find the smallest side` `    ``print``(smallestSide(side))`   `# This code is contributed by` `# Surendra_Gangwar`

## C#

 `// C# program to Find the Side` `// of the smallest Square that ` `// can contain given 4 Big Squares` `// Java implementation of the approach` `using` `System;` `    `  `class` `GFG ` `{`   `// Function to find the maximum of two values` `static` `long` `max(``long` `a, ``long` `b)` `{` `    ``if` `(a > b)` `        ``return` `a;` `    ``else` `        ``return` `b;` `}`   `// Function to find the smallest side` `// of the suitable suitcase` `static` `long` `smallestSide(``long` `[]a)` `{` `    ``// sort array to find the smallest` `    ``// and largest side of suitcases` `    ``Array.Sort(a);`   `    ``long` `side1, side2, side3, side4,` `        ``side11, side12, sideOfSquare;`   `    ``// side of the suitcase will be smallest` `    ``// if they arranged in 2 x 2 way` `    ``// so find all possible sides of that arrangement` `    ``side1 = a + a;` `    ``side2 = a + a;` `    ``side3 = a + a;` `    ``side4 = a + a;`   `    ``// since suitcase should be square` `    ``// so find maximum of all four side` `    ``side11 = max(side1, side2);` `    ``side12 = max(side3, side4);`   `    ``// now find greatest side and` `    ``// that will be the smallest square` `    ``sideOfSquare = max(side11, side12);`   `    ``// return the result` `    ``return` `sideOfSquare;` `}`   `// Driver code` `public` `static` `void` `Main(String[] args) ` `{` `    ``long` `[]side = ``new` `long``;`   `    ``Console.WriteLine(``"Test Case 1"``);`   `    ``// Get the side of the 4 small squares` `    ``side = 2;` `    ``side = 2;` `    ``side = 2;` `    ``side = 2;`   `    ``// Find the smallest side` `    ``Console.WriteLine(smallestSide(side));`   `    ``Console.WriteLine(``"\nTest Case 2"``);`   `    ``// Get the side of the 4 small squares` `    ``side = 100000000000000L;` `    ``side = 123450000000000L;` `    ``side = 987650000000000L;` `    ``side = 987654321000000L;`   `    ``// Find the smallest side` `    ``Console.WriteLine(smallestSide(side));` `}` `}`   `// This code contributed by Rajput-Ji`

## PHP

 ` ``\$b``)` `        ``return` `\$a``;` `    ``else` `        ``return` `\$b``;` `}`   `// Function to find the smallest side` `// of the suitable suitcase` `function` `smallestSide(``\$a``)` `{` `    ``// sort array to find the smallest` `    ``// and largest side of suitcases` `    ``sort(``\$a``, 0);`   `    ``// side of the suitcase will be smallest` `    ``// if they arranged in 2 x 2 way` `    ``// so find all possible sides of that arrangement` `    ``\$side1` `= ``\$a`` + ``\$a``;` `    ``\$side2` `= ``\$a`` + ``\$a``;` `    ``\$side3` `= ``\$a`` + ``\$a``;` `    ``\$side4` `= ``\$a`` + ``\$a``;`   `    ``// since suitcase should be square` `    ``// so find maximum of all four side` `    ``\$side11` `= max1(``\$side1``, ``\$side2``);` `    ``\$side12` `= max1(``\$side3``, ``\$side4``);`   `    ``// now find greatest side and` `    ``// that will be the smallest square` `    ``\$sideOfSquare` `= max1(``\$side11``, ``\$side12``);`   `    ``// return the result` `    ``return` `\$sideOfSquare``;` `}`   `// Driver program` `\$side` `= ``array``();`   `echo` `"Test Case 1\n"``;`   `// Get the side of the 4 small squares` `\$side`` = 2;` `\$side`` = 2;` `\$side`` = 2;` `\$side`` = 2;`   `// Find the smallest side` `echo` `smallestSide(``\$side``) . ``"\n"``;`   `echo` `"\nTest Case 2\n"``;`   `// Get the side of the 4 small squares` `\$side`` = 100000000000000;` `\$side`` = 123450000000000;` `\$side`` = 987650000000000;` `\$side`` = 987654321000000;`   `// Find the smallest side` `echo` `smallestSide(``\$side``) . ``"\n"``;`   `// This code is contributed` `// by Akanksha Rai` `?>`

## Javascript

 ``

Output:

```Test Case 1
4

Test Case 2
1975304321000000```

Time Complelxity: O(n log n)
Space Complexity: O(1)

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