Question

There are 100 numbers present in an array and I need to find out the average of top 5 highest numbers among them.

Also in the same way the average of top 5 lowest numbers among them. How could I go about doing it?

Answer 1

Use Hoare’s select algorithm (or the median of medians, if you need to be absolutely certain of the computational complexity), then add the top partition (and divide by its size to get the average).

This is somewhat faster than the obvious method of sorting instead of partitioning — partitioning is (O(N)) where sorting is O(N log(N) ).

Edit: In C++, for real code (i.e., anything except homework where part of the requirement is to do the task entirely on your own) you can use std::nth_element to partition the input into the top 5 and everything else.

Edit2: Here’s another quick demo to complement @Nils’, but this one in full C++11 regalia (so to speak):

#include <numeric>  
#include <algorithm>
#include <iostream>
#include <iterator>
#include <vector>

int main(){
    std::vector<int> x {1, 101, 2, 102, 3, 103, 4, 104, 5, 105, 6};

    auto pos = x.end() - 5;

    std::nth_element(x.begin(), pos, x.end());

    auto sum = std::accumulate(pos, x.end(), 0);
    auto mean = sum / std::distance(pos, x.end());

    std::cout << "sum = " << sum << '\n' << "mean = " << mean << "\n";

    return 0;
}