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6. Search Insert Position

easyAsked at Spotify

Find the index where a target should be inserted in a sorted array.

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

Problem

Given a sorted array of distinct integers and a target value, return the index if the target is found. If not, return the index where it would be inserted in order.

Constraints

  • 1 <= nums.length <= 10^4
  • -10^4 <= nums[i] <= 10^4
  • nums is sorted ascending

Examples

Example 1

Input
nums=[1,3,5,6], target=5
Output
2

Example 2

Input
nums=[1,3,5,6], target=2
Output
1

Approaches

1. Linear scan

Walk until you find an index whose value is >= target

Time
O(n)
Space
O(1)
for (let i=0;i<nums.length;i++)
  if (nums[i] >= target) return i;
return nums.length;

Tradeoff:

2. Binary search

Standard lower-bound binary search. lo collapses to the insert position.

Time
O(log n)
Space
O(1)
function searchInsert(nums, target) {
  let lo = 0, hi = nums.length;
  while (lo < hi) {
    const mid = (lo + hi) >> 1;
    if (nums[mid] < target) lo = mid + 1;
    else hi = mid;
  }
  return lo;
}

Tradeoff:

Spotify-specific tips

Spotify's chart and ranking services rely on lower-bound binary search to slot new tracks into sorted leaderboards, so be explicit about half-open intervals.

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