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6. Search Insert Position

easyAsked at Chime

Given a sorted array and a target, return the index where the target is or should be inserted.

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

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 the array until the 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

Lower-bound binary search returns first index >= target.

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:

Chime-specific tips

Chime asks binary search when discussing transaction look-up by timestamp or balance sorted state; show comfort with lower-bound semantics over off-by-one bugs.

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