Skip to main content

23. Median of Two Sorted Arrays

hardAsked at Adyen

Find the median of two sorted arrays in O(log(min(m, n))) time.

By Alex Chen, Founder, InterviewChamp.AI · Last verified

Problem

Given two sorted arrays nums1 and nums2 of sizes m and n, return the median of the combined sorted array. The overall run time complexity should be O(log(min(m, n))).

Constraints

  • 0 <= m, n <= 1000
  • 1 <= m + n <= 2000
  • -10^6 <= nums1[i], nums2[i] <= 10^6

Examples

Example 1

Input
nums1 = [1,3], nums2 = [2]
Output
2.0

Example 2

Input
nums1 = [1,2], nums2 = [3,4]
Output
2.5

Approaches

1. Merge then index

Merge fully, then pick the median.

Time
O(m + n)
Space
O(m + n)
const all = [...nums1, ...nums2].sort((a,b)=>a-b);
const n = all.length;
return n % 2 ? all[(n-1)/2] : (all[n/2 - 1] + all[n/2]) / 2;

Tradeoff:

2. Binary search on partition

Binary-search the smaller array for the partition that splits both arrays into equal-size halves.

Time
O(log(min(m, n)))
Space
O(1)
function findMedianSortedArrays(a, b) {
  if (a.length > b.length) [a, b] = [b, a];
  const m = a.length, n = b.length, half = (m + n + 1) >> 1;
  let lo = 0, hi = m;
  while (lo <= hi) {
    const i = (lo + hi) >> 1, j = half - i;
    const aL = i ? a[i-1] : -Infinity, aR = i < m ? a[i] : Infinity;
    const bL = j ? b[j-1] : -Infinity, bR = j < n ? b[j] : Infinity;
    if (aL <= bR && bL <= aR) {
      if ((m + n) % 2) return Math.max(aL, bL);
      return (Math.max(aL, bL) + Math.min(aR, bR)) / 2;
    } else if (aL > bR) hi = i - 1;
    else lo = i + 1;
  }
}

Tradeoff:

Adyen-specific tips

Adyen interviewers grade this for partition reasoning — they reuse the half-split logic when blending dual fraud-signal score streams and want the log-time discipline.

Solve it now

Free. No sign-up. Python and JavaScript run instantly in your browser.

Output

Press Run or Cmd+Enter to execute

Practice these live with InterviewChamp.AI

Drill Median of Two Sorted Arrays and other Adyen interview questions under real-loop conditions with instant feedback on your reasoning, complexity claims, and code.

Practice these live with InterviewChamp.AI →