Minimum sum of two numbers formed from digits of an array

2.1

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.

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 C++ implementation of above idea.

// 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;
}

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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