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6. Search Insert Position

easyAsked at Zoom

Find the index where a target is or where it should be inserted.

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

Problem

Given a sorted array of distinct integers and a target, return the index if the target is found. If not, return the index where it would be inserted in order. Must run in O(log n).

Constraints

  • 1 <= nums.length <= 10^4
  • Sorted distinct integers
  • -10^4 <= target <= 10^4

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 target <= 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

Track lo/hi and converge until lo > hi; lo lands at the insertion point.

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

Tradeoff:

Zoom-specific tips

Zoom phone-screens this to validate binary-search instincts since their meeting-scheduling and bandwidth-tier lookup tables are sorted intervals where log-n insertion matters.

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