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95. Median of Two Sorted Arrays

hardAsked at Ola

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

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

Problem

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)).

Constraints

  • nums1.length == m
  • nums2.length == n
  • 0 <= m, n <= 1000
  • 1 <= m + n <= 2000

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 pick mid

Merge the two arrays and return the middle.

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

Tradeoff:

2. Binary search on shorter array

Binary search the partition of the smaller array such that left halves combined contain (m+n+1)/2 elements; verify left-max <= right-min.

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;
  let lo = 0, hi = m;
  while (lo <= hi) {
    const i = (lo + hi) >> 1;
    const j = ((m + n + 1) >> 1) - i;
    const aL = i === 0 ? -Infinity : a[i-1];
    const aR = i === m ? Infinity : a[i];
    const bL = j === 0 ? -Infinity : b[j-1];
    const bR = j === n ? Infinity : b[j];
    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:

Ola-specific tips

Ola asks this rarely but uses it for senior IC screens; tie the partition trick to merging two sorted ETA buffers from different region brokers.

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