Solve four OA coding problems

1. Sorted Frequency

Given a sorted array arr and a target value k, return the count of occurrences of k in arr. Optimize for O(log n) time. Example: arr = [1, 2, 2, 2, 3], k = 2 -> Output: 3

2. Minimum Recharges

You have a distance D to travel and a vehicle with battery capacity C. You start with a full battery. There are recharge stations at positions stations = [s1, s2, ..., sn]. Return the minimum number of recharges needed to reach D, or -1 if impossible. Example: D = 10, C = 6, stations = [3, 6, 8] -> Output: 2 (Charge at 3 and 8).

3. Island Count

Given a 2D binary grid of '1's (land) and '0's (water), count the number of islands. An island is surrounded by water and formed by connecting adjacent lands horizontally or vertically. Example: grid = [['1','1','0'], ['1','0','0'], ['0','0','1']] -> Output: 2

4. Longest Consecutive Sequence

Given an unsorted array of integers, find the length of the longest consecutive elements sequence. The algorithm must run in O(n) time. Example: nums = [100, 4, 200, 1, 3, 2] -> Output: 4 (Sequence: [1, 2, 3, 4])

Constraints

• For problems 1, 3, and 4: n up to 10^5.
• For problem 2: Distance and capacity are positive integers up to 10^9.