Final Array State After K Multiplication Operations II

Problem Description

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, find the minimum value x in nums and replace it with x * multiplier. After k operations, apply modulo 10^9 + 7 to every value in nums. Return the final state of nums after all operations and the modulo.

Key Insights

• The problem involves repeated modifications to an array based on the minimum value.
• A priority queue (min-heap) can efficiently retrieve and update the minimum value.
• The constraints allow for very large k, suggesting that simulating each operation directly may not be feasible.
• We need to handle large numbers due to multiplication and ensure results fit within standard data types using modulo.

Space and Time Complexity

Time Complexity: O(k log n) if using a priority queue, or O(n + k) if optimized. Space Complexity: O(n) for storing the nums array and priority queue.

Solution

To solve the problem, we will use a priority queue (min-heap) to keep track of the minimum values efficiently. For each of the k operations, we will:

1. Extract the minimum value from the heap.
2. Multiply it by the multiplier.
3. Insert the updated value back into the heap. After performing all operations, we will iterate through the array and apply the modulo 10^9 + 7 to each element to get the final result.

Code Solutions