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6. Search Insert Position

easyAsked at Activision

Find the insertion index for a target in a sorted array — Activision uses this to verify binary search fluency on sorted skill-rating tables.

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

Problem

Given a sorted array and a target, return the index if found, or the index where it would be inserted in order. Algorithm must run in O(log n) time.

Constraints

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

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 target or first larger element.

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 lower_bound binary search returns the leftmost 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:

Activision-specific tips

Activision graders care about your invariant on hi — using length (exclusive) avoids the classic off-by-one when target exceeds the array.

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Output

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