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23. Median of Two Sorted Arrays

hardAsked at Grab

Find the median of two sorted arrays in O(log) time — Grab uses this as a binary-search-on-answer signal.

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

  • 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 and index

Merge into a single sorted array and pick the middle.

Time
O(m+n)
Space
O(m+n)
const merged = [];
let i = 0, j = 0;
while (i < m && j < n) merged.push(nums1[i] <= nums2[j] ? nums1[i++] : nums2[j++]);
// then append leftovers and pick middle

Tradeoff:

2. Binary search on partition

Binary-search the smaller array for the split point such that left halves combined have (m+n+1)/2 elements and max(leftA, leftB) <= min(rightA, rightB).

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 === 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:

Grab-specific tips

Grab interviewers expect the partition-search invariant stated cleanly — frame as finding the global median fare across two regionally partitioned price streams.

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