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6. Search Insert Position

easyAsked at Chegg

Find the index where a target would be inserted in a sorted array — Chegg uses this to test binary-search rigor on textbook-page indexing.

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.

Constraints

  • 1 <= nums.length <= 10^4
  • -10^4 <= nums[i] <= 10^4
  • 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 a value >= 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

Classic lower-bound binary search. lo ends up at the insertion point.

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:

Chegg-specific tips

Chegg wants candidates to nail the half-open interval invariant since their textbook-page index uses lower-bound search to jump straight to chapter starts in O(log n).

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Output

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