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6. Search Insert Position

easyAsked at Expedia

Find target index in sorted array, or where it would be inserted to keep order.

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 if it were inserted in order. You must write an algorithm with O(log n) runtime.

Constraints

  • 1 <= nums.length <= 10^4
  • -10^4 <= nums[i] <= 10^4
  • nums contains distinct values sorted in ascending order

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 first element >= 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. Expedia uses this for price-tier lookups against sorted fare buckets.

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:

Expedia-specific tips

Expedia loves clean lower-bound binary search; nail the loop invariant (lo=hi at termination, hi exclusive) and tie it to price-bucket lookups.

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Output

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