# Minimum sum of two numbers formed from digits of an array

Given an array of digits (values are from 0 to 9), find the minimum possible sum of two numbers formed from digits of the array. All digits of given array must be used to form the two numbers.

**Examples :**

Input: [6, 8, 4, 5, 2, 3] Output: 604 The minimum sum is formed by numbers 358 and 246 Input: [5, 3, 0, 7, 4] Output: 82 The minimum sum is formed by numbers 35 and 047

A minimum number will be formed from set of digits when smallest digit appears at most significant position and next smallest digit appears at next most significant position ans so on..

The idea is to sort the array in increasing order and build two numbers by alternating picking digits from the array. So first number is formed by digits present in odd positions in the array and second number is formed by digits from even positions in the array. Finally, we return the sum of first and second number.

Below is the implementation of above idea.

## C/C++

`// C++ program to find minimum sum of two numbers ` `// formed from digits of the array. ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Function to find and return minimum sum of ` `// two numbers formed from digits of the array. ` `int` `solve(` `int` `arr[], ` `int` `n) ` `{ ` ` ` `// sort the array ` ` ` `sort(arr, arr + n); ` ` ` ` ` `// let two numbers be a and b ` ` ` `int` `a = 0, b = 0; ` ` ` `for` `(` `int` `i = 0; i < n; i++) ` ` ` `{ ` ` ` `// fill a and b with every alternate digit ` ` ` `// of input array ` ` ` `if` `(i & 1) ` ` ` `a = a*10 + arr[i]; ` ` ` `else` ` ` `b = b*10 + arr[i]; ` ` ` `} ` ` ` ` ` `// return the sum ` ` ` `return` `a + b; ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `int` `arr[] = {6, 8, 4, 5, 2, 3}; ` ` ` `int` `n = ` `sizeof` `(arr)/` `sizeof` `(arr[0]); ` ` ` `cout << ` `"Sum is "` `<< solve(arr, n); ` ` ` `return` `0; ` `} ` |

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## Java

`// Java program to find minimum sum of two numbers ` `// formed from digits of the array. ` `import` `java.util.Arrays; ` ` ` `class` `GFG { ` ` ` ` ` `// Function to find and return minimum sum of ` ` ` `// two numbers formed from digits of the array. ` ` ` `static` `int` `solve(` `int` `arr[], ` `int` `n) ` ` ` `{ ` ` ` ` ` `// sort the array ` ` ` `Arrays.sort(arr); ` ` ` ` ` `// let two numbers be a and b ` ` ` `int` `a = ` `0` `, b = ` `0` `; ` ` ` `for` `(` `int` `i = ` `0` `; i < n; i++) ` ` ` `{ ` ` ` ` ` `// fill a and b with every alternate ` ` ` `// digit of input array ` ` ` `if` `(i % ` `2` `!= ` `0` `) ` ` ` `a = a * ` `10` `+ arr[i]; ` ` ` `else` ` ` `b = b * ` `10` `+ arr[i]; ` ` ` `} ` ` ` ` ` `// return the sum ` ` ` `return` `a + b; ` ` ` `} ` ` ` ` ` `//driver code ` ` ` `public` `static` `void` `main (String[] args) ` ` ` `{ ` ` ` `int` `arr[] = {` `6` `, ` `8` `, ` `4` `, ` `5` `, ` `2` `, ` `3` `}; ` ` ` `int` `n = arr.length; ` ` ` ` ` `System.out.print(` `"Sum is "` ` ` `+ solve(arr, n)); ` ` ` `} ` `} ` ` ` `//This code is contributed by Anant Agarwal. ` |

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## Python3

` ` `# Python3 program to find minimum sum of two ` `# numbers formed from digits of the array. ` ` ` `# Function to find and return minimum sum of ` `# two numbers formed from digits of the array. ` `def` `solve(arr, n): ` ` ` ` ` `# sort the array ` ` ` `arr.sort() ` ` ` ` ` `# let two numbers be a and b ` ` ` `a ` `=` `0` `; b ` `=` `0` ` ` `for` `i ` `in` `range` `(n): ` ` ` ` ` `# Fill a and b with every alternate ` ` ` `# digit of input array ` ` ` `if` `(i ` `%` `2` `!` `=` `0` `): ` ` ` `a ` `=` `a ` `*` `10` `+` `arr[i] ` ` ` `else` `: ` ` ` `b ` `=` `b ` `*` `10` `+` `arr[i] ` ` ` ` ` `# return the sum ` ` ` `return` `a ` `+` `b ` ` ` `# Driver code ` `arr ` `=` `[` `6` `, ` `8` `, ` `4` `, ` `5` `, ` `2` `, ` `3` `] ` `n ` `=` `len` `(arr) ` `print` `(` `"Sum is "` `, solve(arr, n)) ` ` ` `# This code is contributed by Anant Agarwal. ` |

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## C#

`// C# program to find minimum ` `// sum of two numbers formed ` `// from digits of the array. ` `using` `System; ` ` ` `class` `GFG ` `{ ` ` ` `// Function to find and return ` ` ` `// minimum sum of two numbers ` ` ` `// formed from digits of the array. ` ` ` `static` `int` `solve(` `int` `[]arr, ` `int` `n) ` ` ` `{ ` ` ` `// sort the array ` ` ` `Array.Sort(arr); ` ` ` ` ` `// let two numbers be a and b ` ` ` `int` `a = 0, b = 0; ` ` ` `for` `(` `int` `i = 0; i < n; i++) ` ` ` `{ ` ` ` `// fill a and b with every alternate digit ` ` ` `// of input array ` ` ` `if` `(i % 2 != 0) ` ` ` `a = a * 10 + arr[i]; ` ` ` `else` ` ` `b = b * 10 + arr[i]; ` ` ` `} ` ` ` ` ` `// return the sum ` ` ` `return` `a + b; ` ` ` `} ` ` ` ` ` `// Driver code ` ` ` `public` `static` `void` `Main () ` ` ` `{ ` ` ` `int` `[]arr = {6, 8, 4, 5, 2, 3}; ` ` ` `int` `n = arr.Length; ` ` ` `Console.WriteLine(` `"Sum is "` `+ solve(arr, n)); ` ` ` `} ` `} ` ` ` `// This code is contributed by Anant Agarwal. ` |

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## PHP

`<?php ` `// PHP program to find minimum ` `// sum of two numbers formed ` `// from digits of the array. ` ` ` `// Function to find and return ` `// minimum sum of two numbers ` `// formed from digits of the array. ` `function` `solve(` `$arr` `, ` `$n` `) ` `{ ` ` ` `// sort the array ` ` ` `sort(` `$arr` `); sort(` `$arr` `, ` `$n` `); ` ` ` ` ` `// let two numbers be a and b ` ` ` `$a` `= 0; ` `$b` `= 0; ` ` ` `for` `(` `$i` `= 0; ` `$i` `< ` `$n` `; ` `$i` `++) ` ` ` `{ ` ` ` `// fill a and b with every ` ` ` `// alternate digit of input array ` ` ` `if` `(` `$i` `& 1) ` ` ` `$a` `= ` `$a` `* 10 + ` `$arr` `[` `$i` `]; ` ` ` `else` ` ` `$b` `= ` `$b` `* 10 + ` `$arr` `[` `$i` `]; ` ` ` `} ` ` ` ` ` `// return the sum ` ` ` `return` `$a` `+ ` `$b` `; ` `} ` ` ` `// Driver code ` `$arr` `= ` `array` `(6, 8, 4, 5, 2, 3); ` `$n` `= sizeof(` `$arr` `); ` `echo` `"Sum is "` `, solve(` `$arr` `, ` `$n` `); ` ` ` `// This code is contributed by nitin mittal. ` `?> ` |

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**Output :**

Sum is 604

This article is contributed by **Aditya Goel**. If you like GeeksforGeeks and would like to contribute, you can also write an article and mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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