# Program to find median of two sorted lists in C++

C++Server Side ProgrammingProgramming

Suppose we have two sorted lists. We have to find the median of these two lists. So if the arrays are like [1,5,8] and [2,3,6,9], then the answer will be 5.

To solve this, we will follow these steps:

• Define a function solve(), this will take an array nums1, an array nums2,
• if size of nums1 > size of nums2, then:
• return solve(nums2, nums1)
• x := size of nums1, y := size of nums2
• low := 0, high := x
• totalLength := x + y
• while low <= high, do:
• partitionX := low + (high - low)
• partitionY := (totalLength + 1) / 2 - partitionX
• maxLeftX := (if partitionX is same as 0, then -inf, otherwise nums1[partitionX - 1])
• minRightX := (if partitionX is same as x, then inf, otherwise nums1[partitionX])
• maxLeftY := (if partitionY is same as 0, then -inf, otherwise nums2[partitionY - 1])
• minRightY := (if partitionY is same as y, then inf, otherwise nums2[partitionY])
• if maxLeftX <= minRightY and maxLeftY <= minRightX, then:
• if totalLength mod 2 is same as 0, then:
• return ((maximum of maxLeftX and maxLeftY) + (minimum of minRightX and minRightY))/ 2
• Otherwise
• return maximum of maxLeftX and maxLeftY
• otherwise when maxLeftX > minRightY, then:
• high := partitionX - 1
• Otherwise
• return 0

Let us see the following implementation to get better understanding:

## Example

Live Demo

#include
using namespace std;

class Solution {
public:
double solve(vector& nums1, vector& nums2) {
if(nums1.size()>nums2.size())
return solve(nums2,nums1);
int x = nums1.size();
int y = nums2.size();
int low = 0;
int high = x;
int totalLength = x+y;
while(low<=high){
int partitionX = low + (high - low)/2;
int partitionY = (totalLength + 1)/2 - partitionX;

int maxLeftX = (partitionX ==0?INT_MIN:nums1[partitionX-1] );
int minRightX = (partitionX == x?INT_MAX : nums1[partitionX]);

int maxLeftY = (partitionY ==0?INT_MIN:nums2[partitionY-1] );
int minRightY = (partitionY == y?INT_MAX : nums2[partitionY]);

if(maxLeftX<=minRightY && maxLeftY <= minRightX){
if(totalLength% 2 == 0){
return ((double)max(maxLeftX,maxLeftY) + (double)min(minRightX,minRightY))/2;
}
else{
return max(maxLeftX, maxLeftY);
}
}
else if(maxLeftX>minRightY)
high = partitionX-1;
else low = partitionX+1;
}
return 0;
}
};
main(){
Solution ob;
vector v1 = {1,5,8}, v2 = {2,3,6,9};
cout << (ob.solve(v1, v2));
}

## Input

[1,5,8], [2,3,6,9]

## Output

5