Final Array State After K Multiplication Operations I

Final Array State After K Multiplication Operations I

What is this problem about?

The Final Array State After K Multiplication Operations I interview question involves an integer array and two variables: k and multiplier. You need to perform k operations. In each operation, you find the smallest element in the array (if there are ties, pick the one with the smallest index) and multiply it by the multiplier. Your goal is to return the state of the array after all k operations are completed.

Why is this asked in interviews?

Companies like Microsoft and Amazon ask this to test your knowledge of Priority Queues (Heaps) and simulation. Even though it's an "Easy" difficulty problem, it evaluates if you can identify that a simple linear scan for the minimum in every operation (O(K*N)) is less efficient than using a heap (O(K log N)). It's a test of choosing the right tool for dynamic minimum retrieval.

Algorithmic pattern used

The problem uses a Simulation with a Min-Heap.

1. Create a Min-Heap and store pairs of (value, index) for every element in the array.
2. For k times:
   • Extract the minimum (val, idx) from the heap.
   • Multiply val by multiplier.
   • Update the original array at idx with the new value.
   • Push the updated (newVal, idx) back into the heap.
3. Return the modified array.

Example explanation

Array: [2, 1, 3], k=2, multiplier=2.

1. Initial Heap: [(1, 1), (2, 0), (3, 2)].
2. Op 1: Min is (1, 1). 1 * 2 = 2. New element: (2, 1). Array: [2, 2, 3].
3. Op 2: Min is (2, 0) (Tied value with index 1, but index 0 is smaller). 2 * 2 = 4. Array: [4, 2, 3]. Result: [4, 2, 3].

Common mistakes candidates make

• Handling Ties: Forgetting the rule about the smallest index when two values are equal.
• O(K*N) approach: Using a loop to find the minimum every time, which works for small N but fails for larger constraints.
• Data type: Not considering integer overflow if the values grow very large (though for version I, constraints are usually safe).

Interview preparation tip

Always mention the time complexity of the heap operations. O(N + K log N) is much better than O(K * N) when N is large.