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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
Updated on: 16-Jun-2020
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