4-median-of-two-sorted-array

[lkhanna1505]

This the best hard problem on leetcode for begineers.

I have solved it in Java and have got the runtime success rate of 100.0%.
Below is my thought process while solving it:-

Intuition

The problem asks for the median of two sorted arrays. My first thought is that since both arrays are sorted, we can merge them into a single sorted array and then directly find the median. This is similar to the merge step in merge sort.

Approach

1. Merge the Arrays:
   Use two pointers to traverse both arrays and merge them into a new sorted array.
2. Find the Median:
   • If the total number of elements is odd, the median is the middle element.
   • If it's even, the median is the average of the two middle elements.

This approach is straightforward and leverages the sorted property of the input arrays.

Complexity

• Time complexity:
  $$O(m + n)$$
  where (m) and (n) are the lengths of the two input arrays. We have to process every element once to merge them.

• Space complexity:
  $$O(m + n)$$
  because we create a new array to store the merged result.

Code

class Solution {
    public double findMedianSortedArrays(int[] nums1, int[] nums2) {
        int m = nums1.length;
        int n = nums2.length;
        int[] merged = new int[m + n];
        
        int i = 0, j = 0, k = 0;
        
        // Merge the two sorted arrays
        while(i < m && j < n) {
            if(nums1[i] < nums2[j]) {
                merged[k++] = nums1[i++];
            } else {
                merged[k++] = nums2[j++];
            }
        }
        
        // Copy remaining elements
        while(i < m) merged[k++] = nums1[i++];
        while(j < n) merged[k++] = nums2[j++];
        
        // Find the median
        int total = m + n;
        if(total % 2 == 1) {
            return merged[total / 2];
        } else {
            return (merged[total / 2 - 1] + merged[total / 2]) / 2.0;
        }
    }
}