Final Array State After K Multiplication Operations I

class Solution {
public:
    vector<int> updateNumbers(vector<int>& data, int iterations, int factor) {
        vector<pair<int, int>> minHeap;
        for (int idx = 0; idx < data.size(); ++idx) {
            minHeap.emplace_back(data[idx], idx);
        }

        make_heap(minHeap.begin(), minHeap.end(), greater<>());

        while (iterations--) {
            pop_heap(minHeap.begin(), minHeap.end(), greater<>());
            auto [val, pos] = minHeap.back();
            minHeap.pop_back();

            data[pos] *= factor;
            minHeap.push_back({data[pos], pos});
            push_heap(minHeap.begin(), minHeap.end(), greater<>());
        }

        return data;
    }
};

This solution implements a function to transform the state of an array following a defined number of multiplication operations. It uses a minimum heap to optimize the process of identifying the smallest elements in the array, which are then multiplied by a specified factor.

• The function updateNumbers takes three parameters:

  • data - the array of integers,
  • iterations - the number of multiplication operations to perform,
  • factor - the factor by which the selected array element is multiplied.

• Here's how the algorithm unfolds:

1. Initialize a minimum heap to prioritize the elements with the smallest values for multiplication. The elements of the heap are pairs consisting of the value from the array and its corresponding index.

2. Convert the vector of pairs into a heap structure using the make_heap function with a custom comparison to maintain it as a minimum heap.

3. Proceed with the prescribed number of iterations:

   • Remove the smallest element from the heap using pop_heap.
   • Multiply the selected element of the array by the given factor.
   • Insert the updated value back into the heap, maintaining the heap structure with push_heap.

4. Following all iterations, return the updated array.

This approach ensures that the least element of the array, at each step, gets multiplied, leveraging the efficiency of the heap for both accessing and updating the minimum element. The use of a heap is optimal in scenarios where continual access to the smallest/largest item is needed, making this algorithm efficient particularly when iteration values are significant relative to the size of the data.

class Solution {

    public int[] updateArray(int[] data, int iterations, int factor) {
        PriorityQueue<int[]> minHeap = new PriorityQueue<>((x, y) -> {
            int comparison = Integer.compare(x[0], y[0]);
            if (comparison == 0) {
                return Integer.compare(x[1], y[1]);
            }
            return comparison;
        });

        for (int i = 0; i < data.length; i++) {
            minHeap.offer(new int[] { data[i], i });
        }

        while (iterations-- > 0) {
            int[] minimum = minHeap.poll();
            int idx = minimum[1];

            data[idx] *= factor;
            minHeap.offer(new int[] { data[idx], idx });
        }

        return data;
    }
}

The given Java code defines a method to update an array using a multiplication operation applied multiple times. The solution leverages a priority queue to efficiently manage which element to update in each iteration. The method modifies the input array in-place and returns it after performing all operations. Follow the explanation below to understand the working model of the function:

1. Create a PriorityQueue that organizes array elements based on their value. If two elements have the same value, they are further ordered based on their index.

2. Insert each element of the input array data into the priority queue. Each element is stored as an array where the first value is the element value and the second value is its index in the original array.

3. Perform the update operation iterations times. Each operation consists of the following steps:

   • Extract the smallest element from the priority queue.
   • Multiply this element by a given factor.
   • Update the value in the original array.
   • Re-insert the updated element and its index back into the priority queue to maintain the correct order for subsequent operations.

4. Once all iterations are complete, the method returns the modified array data.

This approach, using a minimum priority queue, allows the function to always modify the smallest current element, thus efficiently applying the specified multiplication operations across the array elements.

class Solution:
    def calculateResult(self, values: List[int], iterations: int, factor: int):
        min_heap = [(value, idx) for idx, value in enumerate(values)]
        heapify(min_heap)

        for _ in range(iterations):
            _, index = heappop(min_heap)
            values[index] *= factor
            heappush(min_heap, (values[index], index))

        return values

The provided Python solution efficiently calculates the final state of an array after performing a specified number of multiplication operations using a minimum heap. Here is a concise overview of how the code achieves this:

• First, it initializes a minimum heap to keep track of the smallest elements in the input list, values. Each element in the heap is a tuple consisting of the value and its index from the original list.
• The code utilizes Python's heapq library to manage the heap operations. It iterates through the number of specified iterations (denoted as k in the problem statement).
• In each iteration, the smallest element is removed from the heap (heappop()), its corresponding value in the original values list is multiplied by the given factor, and the updated value is then pushed back into the heap (heappush()).
• This iterative updating and pushing into the heap ensures that at every step, the next smallest element of the array is multiplied, adhering to the conditions set by the problem.
• Finally, after all iterations are completed, the modified list values is returned as the final state of the array.

This process ensures efficient handling of the multiplication operations, even for larger lists, as the heap operations allow for quick access and modification of the smallest elements.