MedianOfTwoSortedArray.md

The question

Given two sorted arrays nums1 and nums2 of size m and n respectively, return the median of the two sorted arrays.

The overall run time complexity should be O(log (m+n)).

Example 1:

Input: nums1 = [1,2], nums2 = [3,4]
Output: 2.50000
Explanation: merged array = [1,2,3,4] and median is (2 + 3) / 2 = 2.5.

Approach:-

Lets code:-

public double findMedianSortedArrays(int[] nums1, int[] nums2) {
        if(nums1.length>nums2.length){
              return findMedianSortedArrays(nums2, nums1);
        }
        int x = nums1.length;
        int y = nums2.length;
        
        int low = 0;
        int high = x;
        
        while(low<high){
             int partitionX = (low + high)/2;
             int partitionY = (x+y+1)/2 - partitionX;
             
             int maxLeftX =  partitionX==0?Integer.MIN_VALUE:nums1[partitionX-1];
             int minRightX =  partitionX==x?Integer.MAX_VALUE:nums1[partitionX];
             
             int maxLeftY =  partitionY==0?Integer.MIN_VALUE:nums2[partitionY-1];
             int minRightY =  partitionY==y?Integer.MAX_VALUE:nums2[partitionY];
             
             if(maxLeftX<=minRightY && maxLeftY<=minRightX){
                   if(x+y%2==0){
                       return (double)(Math.max(maxLeftX, maxLeftY) + Math.min(minRightX, minRightY))/2;
                   } else {
                       return (double)(Math.max(maxLeftX, maxLeftY));
                   }
             } else if(maxLeftX>minRightY){
                   high = partitionX - 1;
             } else if(maxLeftY>minRightX){
                   low = partitionX + 1;
             }
       }
       
       throw new Error();
        
}

Time complexity - O(log(min(x, y)) Space complexity - O(1)