Recursive Sums

Little Bear has received a home assignment to find the sum of all digits in a number N. Following his affinity towards single digit number, he intends to repeatedly compute the sum of all digits until the sum itself becomes a single digit number.

Can you write a program to compute the final single-digit sum?

As the number N is very big, it is given in the following run length encoded format - N is represented as a sequence of M blocks, where each block i (0 ≤ i < M) is represented by two integers - (len[i], d[i]). This implies that the digit d[i] occurs len[i] number of times.

For example, {(2,1), (1,2), (2,9)} represents the number 11299.

Example:

Input: m = 3, arr = {{2, 1}, {1, 2}, {2, 9}}
Output: 4

Approach

C++

#include <bits/stdc++.h>
using namespace std;
#define MOD 1000000007

long long recursiveSum(long long m,
                       vector<vector<long long>> &arr)
{
    long long ans = 0;
    long long x = 0;
    for (long long i = 0; i < m; i++)
    {
        long long len = arr[i][0], d = arr[i][1];

        ans = len * d;
        while (ans)
        {
            x += ans % 10;
            ans = ans / 10;
        }
    }
    ans = x;
    while (ans >= 10)
    {
        long long res = 0;
        while (ans)
        {
            res += ans % 10;
            ans = ans / 10;
        }
        ans = res;
    }
    return ans;
}
int main()
{

    long long m = 3;

    vector<vector<long long>> arr = {{2, 1}, {1, 2}, {2, 9}};

    cout << recursiveSum(m, arr) << "\n";

    return 0;
}