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6. Search Insert Position

easyAsked at Coursera

Find the insert index in a sorted array — Coursera tests binary-search invariants for ordered course-catalog inserts.

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

Problem

Given a sorted array of distinct integers and a target, return the index if found. If not, return the index where it would be inserted to keep the array sorted.

Constraints

  • 1 <= nums.length <= 10^4
  • -10^4 <= nums[i], target <= 10^4
  • nums is sorted ascending with no duplicates

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 nums[i] >= 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 lower bound

Standard half-open lo/hi loop; return lo at end.

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:

Coursera-specific tips

Coursera asks you to defend your binary-search invariants out loud — they have been burned by off-by-one bugs in the course-catalog insertion path before.

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Output

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