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6. Search Insert Position

easyAsked at Nubank

Find the correct insertion index for a new credit-score tier into a sorted threshold table.

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 run in O(log n).

Constraints

  • 1 <= nums.length <= 10^4
  • Distinct sorted ints

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 an 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

Classic left-bound binary search; lo ends at insertion position.

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:

Nubank-specific tips

Nubank wants you to write the half-open `[lo, hi)` invariant explicitly — sloppy binary search bugs silently misprice risk-tier lookups.

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Output

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