Wednesday, February 1, 2017

Break an array into maximum number of sub-arrays such that their averages are same - GeeksforGeeks


Break an array into maximum number of sub-arrays such that their averages are same - GeeksforGeeks
Given an integer array, the task is to divide the array into maximum number of sub-arrays such that averages of all subarrays is same. If it is not possible to divide, then print "Not possible".

The idea is based on the fact that if an array can be divided in subarrays of same average, then anerage of all these subarrays must be same as overall average.
1) Find average of whole array.
2) Traverse array again and keep track of average of current subarray. As soon as the average becomes same as overall overall average, print current subarray and begin new subarray.
This solution divides to maximum number of subarrays because we begin a new subarray as soon as we find average same as overall average.

// C++ prpgram to break given array into maximum
// number of subarrays with equal average.
#include<bits/stdc++.h>
using namespace std;
void findSubarrays(int arr[], int n)
{
    // To store all points where we can break
    // given array into equal average subarrays.
    vector<int> result;
    // Compute total array sum
    int sum = 0;
    for (int i = 0; i < n; i++)
        sum += arr[i];
    int curr_sum = 0;     // Current Sum
    int prev_index = -1;  // Index of previous subarray
    for (int i = 0; i < n ; i++)
    {
        curr_sum += arr[i];
        // If current point is a break point. Note that
        // we don't compare actual averages to avoid
        // floating point errors.
        if (sum *(i - prev_index) == curr_sum*n)
        {
            // Update current sum and previous index
            curr_sum = 0;
            prev_index = i;
            // Add current break point
            result.push_back(i);
        }
    }
    // If last break point was not end of array, we
    // cannot break the whole array.
    if (prev_index != n-1)
    {
        cout << "Not Possible";
        return;
    }
    // Printing the result in required format
    cout << "(0, " << result[0] << ")\n";
    for (int i=1; i<result.size(); i++)
        cout << "(" << result[i-1] + 1 << ", "
             << result[i] << ")\n";
}

http://www.geeksforgeeks.org/divide-array-two-sub-arrays-averages-equal/
Given an integer array, the task is to divide an integer array into two sub-arrays to make their averages equal if possible.
An Efficient solution is to find sum of array elements. Initialize leftsum as zero. Run a loop and find leftsum by adding elements of array. For rightsum, we substract leftsum from total sum then we find rightsum and find average of leftsum and rightsum as according to their index.
void findSubarrays(int arr[], int n)
{
    // Find array sum
    int sum = 0;
    for (int i=0; i<n; i++)
        sum += arr[i];
 
    bool found = false;
    int lsum = 0;
    for (int i=0; i<n-1; i++)
    {
        lsum += arr[i];
        int rsum = sum - lsum;
 
        // If averages of arr[0...i] and arr[i+1..n-1]
        // are same. To avoid floating point problems
        // we compare "lsum*(n-i+1)" and "rsum*(i+1)"
        // instead of "lsum/(i+1)" and "rsum/(n-i+1)"
        if (lsum*(n-i-1) == rsum*(i+1))
        {
            printf("From (%d  %d) to (%d  %d)\n", 0, i,
                                            i+1, n-1);
            found = true;
        }
    }
 
    // If no subarrays found
    if (found == false)
        cout << "Subarrays not found" << endl;
}
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