Watch 8 video solutions for Final Array State After K Multiplication Operations II, a hard level problem involving Array, Heap (Priority Queue), Simulation. This walkthrough by codingMohan has 1,672 views views. Want to try solving it yourself? Practice on FleetCode or read the detailed text solution.
You are given an integer array nums, an integer k, and an integer multiplier.
You need to perform k operations on nums. In each operation:
x in nums. If there are multiple occurrences of the minimum value, select the one that appears first.x with x * multiplier.After the k operations, apply modulo 109 + 7 to every value in nums.
Return an integer array denoting the final state of nums after performing all k operations and then applying the modulo.
Example 1:
Input: nums = [2,1,3,5,6], k = 5, multiplier = 2
Output: [8,4,6,5,6]
Explanation:
| Operation | Result |
|---|---|
| After operation 1 | [2, 2, 3, 5, 6] |
| After operation 2 | [4, 2, 3, 5, 6] |
| After operation 3 | [4, 4, 3, 5, 6] |
| After operation 4 | [4, 4, 6, 5, 6] |
| After operation 5 | [8, 4, 6, 5, 6] |
| After applying modulo | [8, 4, 6, 5, 6] |
Example 2:
Input: nums = [100000,2000], k = 2, multiplier = 1000000
Output: [999999307,999999993]
Explanation:
| Operation | Result |
|---|---|
| After operation 1 | [100000, 2000000000] |
| After operation 2 | [100000000000, 2000000000] |
| After applying modulo | [999999307, 999999993] |
Constraints:
1 <= nums.length <= 1041 <= nums[i] <= 1091 <= k <= 1091 <= multiplier <= 106Problem Overview: You are given an array and must perform k operations. In each operation, select the smallest element in the array (ties resolved by index), multiply it by a given multiplier, and place it back in the array. After performing all operations, return the final state of the array.
Approach 1: Direct Array Manipulation (O(k * n) time, O(1) space)
The straightforward simulation scans the array during every operation to locate the smallest value. Once found, multiply that element by the given multiplier and update it in place. This approach uses only the original array, so the space complexity stays O(1). However, each operation requires a full O(n) scan, making the total runtime O(k * n). This works when k and n are relatively small, but it becomes slow when the number of operations grows large.
Approach 2: Min-Heap Method (O(k log n) time, O(n) space)
A more efficient solution keeps track of the smallest element using a min-heap (priority queue). Push pairs of (value, index) into the heap so ties are naturally resolved by index. For each operation, pop the smallest element from the heap, multiply its value by the multiplier, and push the updated pair back. The heap guarantees that retrieving the minimum takes O(log n) time instead of scanning the entire array. After completing all k operations, the array reflects the correct final state.
This approach models the process exactly while improving performance significantly. Each operation involves one pop and one push, both O(log n), leading to a total runtime of O(k log n). The heap stores all elements, so the extra memory required is O(n). Priority queues are a natural fit for problems where repeated minimum extraction is required.
Problems like this commonly appear when practicing Array manipulation combined with Heap (Priority Queue) data structures and Simulation techniques.
Recommended for interviews: Start by explaining the direct simulation to show you understand the rules of the process. Then move to the min-heap optimization. Interviewers usually expect the heap-based solution because it reduces repeated scans and demonstrates familiarity with priority queues and efficient state simulation.
| Approach | Time | Space | When to Use |
|---|---|---|---|
| Direct Array Manipulation | O(k * n) | O(1) | Small arrays or small k where a simple simulation is sufficient |
| Min-Heap (Priority Queue) | O(k log n) | O(n) | General case where frequent minimum selection must be efficient |