Problem Description

There are n jobs that can be executed in parallel on a processor, where the execution time of the i-th job is executionTime[i]. To speed up execution, the following strategy is used:

• In one operation, a job is chosen as the major job, and it is executed for x seconds.
• All other jobs are executed for y seconds, where y < x.

A job is complete when it has been executed for at least executionTime[i] seconds. Once a job is complete, it exits the pool.

Find the minimum number of operations required for the processor to completely execute all the jobs if run optimally.

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Function Description

Complete the function citadelGetMinOperations in the editor.

int citadelGetMinOperations(int executionTime[n], int x, int y)

Parameters:

• int executionTime[n]: An array representing the execution times of the jobs.
• int x: The time for which the major job is executed in each operation.
• int y: The time for which all other jobs are executed in each operation.

Returns:

• int: The minimum number of operations required to complete all jobs.

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Examples

Example 1:

Input:
executionTime = [3, 4, 1, 7, 6], x = 4, y = 2
Output:
3

Explanation:

• Operation 1: Choose job 4 as the major job. Execution times:
  [1, 2, -1, 3, 4]. Job 3 is complete.
• Operation 2: Choose job 4 again. Execution times:
  [-1, 0, -, -1, 2]. Jobs 1, 2, and 4 are complete.
• Operation 3: Choose job 5. Execution times:
  [-, -, -, -, -2]. Job 5 is complete.

It takes 3 operations to execute all the jobs.

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Example 2:

Input:
executionTime = [3, 3, 6, 3, 9], x = 3, y = 2
Output:
3

Explanation:

• Operation 1: Choose job 5. Execution times:
  [1, 1, 4, 1, 6].
• Operation 2: Choose job 5 again. Execution times:
  [-1, -1, 2, -1, 3]. Jobs 1, 2, and 4 are complete.
• Operation 3: Choose job 5 again. Execution times:
  [-, -, 0, -, 0]. Jobs 3 and 5 are complete.

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Example 3:

Input:
executionTime = [2, 3, 5], x = 3, y = 1
Output:
3

Explanation:

• Operation 1: Choose job 3. Execution times:
  [1, 2, 2].
• Operation 2: Choose job 3 again. Execution times:
  [0, 1, -1]. Jobs 1 and 3 are complete.
• Operation 3: Choose job 2. Execution times:
  [-, -2, -]. Job 2 is complete.

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Constraints:

• 1 <= n <= 3 × 10^5
• 1 <= executionTime[i] <= 10^9
• 1 <= y < x <= 10^9

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Key Insight:

• The problem revolves around optimization: finding the best strategy to minimize the number of operations while ensuring that all jobs meet their required execution times.

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