Asked inDeutsche Bank,Technical Analyst-Intern

Matrix Cell Value Placement

You are provided with an integer N representing the size of an N * N matrix. Initially, each cell of the matrix is empty. You are also given a number K, indicating the number of tasks. Each task involves specifying two integers, I and J, where I represents the ith row and J represents the jth column of the matrix.

Your goal is to perform every task sequentially. In each task, you place 0 in each cell of the ith row and jth column. After all tasks are completed, you need to return an array of size K. The nth element of the array should indicate the number of empty cells in the matrix after executing the nth task.

Input:

The first line contains a single integer T, representing the number of test cases.
For each test case, the first line contains two integers N and K (N is the dimension of the matrix and K is the number of tasks).
Following this, each of the next K lines contains two integers I and J.

Output:

For each test case, output an array indicating the number of empty cells in the matrix after each task, printed on a new line.

Example:

Example with N = 3, K = 2 tasks:
Initial Matrix:
[[ 'NULL', 'NULL', 'NULL']
['NULL', 'NULL', 'NULL']
['NULL', 'NULL', 'NULL'] ]
Task 1: (0, 0)
Matrix after task:
[[0, 0, 0]
[0, 'NULL', 'NULL']
[0, 'NULL', 'NULL'] ]
Empty cells: 4
Task 2: (1, 0)
Matrix after task:
[[0, 0, 0]
[0, 0, 0]
[0, 'NULL', 'NULL'] ]
Empty cells: 2
Return the array [4, 2]

Constraints:

  • 1 <= T <= 5
  • 1 <= N <= 105
  • 0 <= K <= 105
  • 0 <= I, J < N

Note:

Cells are considered empty if they do not contain any value. Indexing is 0-based.
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Deutsche Bank Technical Analyst-Intern Interview Questions
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