Median of 2 Sorted Arrays of Equal Size

Understanding the Problem

The goal is to find the median of two sorted arrays of equal size.

Method 1: Simple Merge

This method merges the two arrays and finds the median.

#include <iostream>
using namespace std;

double findMedianSortedArrays(int arr1[], int arr2[], int n) {
    int merged[2 * n];
    int i = 0, j = 0, k = 0;

    while (i < n && j < n) {
        if (arr1[i] < arr2[j]) {
            merged[k++] = arr1[i++];
        } else {
            merged[k++] = arr2[j++];
        }
    }
    while (i < n) merged[k++] = arr1[i++];
    while (j < n) merged[k++] = arr2[j++];

    return (merged[n - 1] + merged[n]) / 2.0;
}

int main() {
    int arr1[] = {1, 3};
    int arr2[] = {2, 4};
    int n = sizeof(arr1) / sizeof(arr1[0]);
    cout << "Median: " << findMedianSortedArrays(arr1, arr2, n) << endl;
    return 0;
}
            

Output:

Median: 2.5

Method 2: Binary Search

This method uses binary search to find the median efficiently.

#include <iostream>
#include <climits>
using namespace std;

double findMedianSortedArrays(int arr1[], int arr2[], int n) {
    int low = 0, high = n;
    while (low <= high) {
        int partition1 = (low + high) / 2;
        int partition2 = n - partition1;

        int maxLeft1 = (partition1 == 0) ? INT_MIN : arr1[partition1 - 1];
        int minRight1 = (partition1 == n) ? INT_MAX : arr1[partition1];

        int maxLeft2 = (partition2 == 0) ? INT_MIN : arr2[partition2 - 1];
        int minRight2 = (partition2 == n) ? INT_MAX : arr2[partition2];

        if (maxLeft1 <= minRight2 && maxLeft2 <= minRight1) {
            return (max(maxLeft1, maxLeft2) + min(minRight1, minRight2)) / 2.0;
        } else if (maxLeft1 > minRight2) {
            high = partition1 - 1;
        } else {
            low = partition1 + 1;
        }
    }
    throw invalid_argument("Input arrays are not sorted.");
}

int main() {
    int arr1[] = {1, 3};
    int arr2[] = {2, 4};
    int n = sizeof(arr1) / sizeof(arr1[0]);
    cout << "Median: " << findMedianSortedArrays(arr1, arr2, n) << endl;
    return 0;
}
            

Output:

Median: 2.5

Method 3: Using a Combined Array

This method combines the arrays and finds the median directly.

#include <iostream>
#include <algorithm>
using namespace std;

double findMedianSortedArrays(int arr1[], int arr2[], int n) {
    int combined[2 * n];
    for (int i = 0; i < n; i++) {
        combined[i] = arr1[i];
        combined[i + n] = arr2[i];
    }
    sort(combined, combined + 2 * n);
    return (combined[n - 1] + combined[n]) / 2.0;
}

int main() {
    int arr1[] = {1, 3};
    int arr2[] = {2, 4};
    int n = sizeof(arr1) / sizeof(arr1[0]);
    cout << "Median: " << findMedianSortedArrays(arr1, arr2, n) << endl;
    return 0;
}