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22. Median of Two Sorted Arrays

hardAsked at Swiggy

Find the median of two sorted arrays in logarithmic time.

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

Problem

Given two sorted arrays nums1 and nums2 of size m and n, return the median of the combined array. Aim for O(log(min(m, n))) time.

Constraints

  • 0 <= m, n <= 1000
  • 1 <= m + n <= 2000
  • -10^6 <= nums[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 the two sorted arrays then read median position.

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

Tradeoff:

2. Binary search partition

Binary search on the smaller array to choose a partition so left halves combine to floor((m+n+1)/2) elements with max(left) <= min(right). The median falls at the boundary.

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;
  const half = Math.floor((m + n + 1) / 2);
  let lo = 0, hi = m;
  while (lo <= hi) {
    const i = (lo + hi) >> 1;
    const 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:

Swiggy-specific tips

Swiggy poses this in late-loop senior rounds; talking through the partition invariant out loud before any code is the bar-raiser signal.

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Output

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