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Grokking the Coding Interview Patterns

Median of Two Sorted Arrays

Explore methods to find the median of two sorted integer arrays with an efficient logarithmic time complexity. Understand the problem constraints and practice implementing solutions that run in O(log(min(m, n))) time using constant space, enhancing your coding interview skills.

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Statement

You’re given two sorted integer arrays, nums1 and nums2, of size mm and nn, respectively. Your task is to return the median of the two sorted arrays.

The overall run time complexity should be O(log⁡(m,n))O(\log (m, n)).

Constraints:

  • nums1.length ==== mm

  • nums2.length ==== nn

  • 0≤m≤10000 \leq m \leq 1000

  • 0≤n≤10000 \leq n \leq 1000

  • 1≤m+n≤20001 \leq m + n \leq 2000

  • −105≤-10^5 \leq nums1[i], nums2[i] ≤105\leq 10^5

Examples

Understand the problem

Let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

Median of Two Sorted Arrays

1.

What is the output if the following arrays are given as input?

nums1 = [3, 5, 9, 10, 14]

nums2 = [1, 4, 6, 9, 30]

A.

7.0

B.

8.0

C.

7.5

1 / 2

Figure it out!

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Note: As an additional challenge, we have intentionally hidden the solution to this puzzle.

Sequence - Vertical
Drag and drop the cards to rearrange them in the correct sequence.
1
2
3
4
5
6

Try it yourself

Implement your solution in the following coding playground.

We have left the solution to this challenge as an exercise for you. The optimal solution to this problem runs in O(log(min(m, n))) time and takes O(1) space. You may try to translate the logic of the solved puzzle into a coded solution.

Java
usercode > Solution.java
import java.util.Arrays;
public class Solution{
   public static double findMedianSortedArrays(int[] nums1, int[] nums2) {
      
      // Replace this placeholder return statement with your code
      return 0;
   }
}
Median of Two Sorted Arrays