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

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