Median of two sorted array

Medians are the middle numbers, in other words, the median value is the middle observation in an ordered list. It corresponds to the cumulative percentage of 50%.

The size of two arrays must be same, we will find the median of two separate arrays at first, then compare the separate medians to get an actual median of two lists.

Input and Output

Input: Two sorted array are given. Array 1: {1, 2, 3, 6, 7} Array 2: {4, 6, 8, 10, 11} Output: The median from two array. Here the median value is 6. Merge the given lists into one. {1, 2, 3, 4, 6, 6, 7, 8, 10, 11} From the merged list find the average of two middle elements. here (6+6)/2 = 6.

Algorithm

median(list, n)

Input: List of data, and the number of data.

Output: Median of the given list.

Begin    if the list has even number of data, then       return (list[n/2] + list[n/2-1])/2    else       return list[n/2] End

findMedian(list1, list2, n)

Input − Two sorted lists, and the number of lists.

Output − The median from two sorted lists.

Begin    if n <= 0, then       it is invalid, and return invalid number    if n = 1, then       return (list1[0] + list2[0])/2    if n = 2, then       return ((max of list1[0], list2[0]) + (min of list1[1], list2[1]))/2    med1 := median(list1, n)    med2 := median(list2, n)    if med1 = med2, then       return med1    if med1 < med2, then       if item has even number of data, then          subList := data from list2, from 0 to n/2 – 1 data          return findMedian(subList, list1, n – (n/2) + 1)       subList := data from list2, from 0 to n/2 data       return findMedian(subList, list2, n – (n/2)) End

Example

#include<iostream> using namespace std; int median(int list[], int n) {    if (n%2 == 0)     //when array containts even number of data       return (list[n/2] + list[n/2-1])/2;    else        //for odd number of data       return list[n/2]; } intfindMedian(int list1[], int list2[], int n) {    if (n <= 0)       return -1;      //invalid length of lists    if (n == 1)       return (list1[0] + list2[0])/2;    //for single element simply get average from two array    if (n == 2)       return (max(list1[0], list2[0]) + min(list1[1], list2[1])) / 2;    int med1 = median(list1, n);     //Find median from first array    int med2 = median(list2, n);     //Find median from second array    if (med1 == med2)    //when both medians are same, they are the final median        return med1;    if (med1 < med2) {        if (n % 2 == 0)           return findMedian(list1 + n/2 - 1, list2, n - n/2 +1);        return findMedian(list1 + n/2, list2, n - n/2);    }    if (n % 2 == 0)    //when med1 > med2       return findMedian(list2 + n/2 - 1, list1, n - n/2 + 1);    return findMedian(list2 + n/2, list1, n - n/2); } int main() {    int list1[] = {1, 2, 3, 6, 7};    int list2[] = {4, 6, 8, 10, 11};    int n1 = 5;    int n2 = 5;    if (n1 == n2)       cout<< "Median is "<<findMedian(list1, list2, n1);    else       cout<< "Doesn't work for lists of unequal size"; }

Output

Median is 6