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2718. Sum of Matrix After Queries

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You are given an integer n and a 0-indexed 2D array queries where queries[i] = [typei, indexi, vali].

Initially, there is a 0-indexed n x n matrix filled with 0's. For each query, you must apply one of the following changes:

  • if typei == 0, set the values in the row with indexi to vali, overwriting any previous values.
  • if typei == 1, set the values in the column with indexi to vali, overwriting any previous values.

Return the sum of integers in the matrix after all queries are applied.

 

Example 1:

Input: n = 3, queries = [[0,0,1],[1,2,2],[0,2,3],[1,0,4]]
Output: 23
Explanation: The image above describes the matrix after each query. The sum of the matrix after all queries are applied is 23.

Example 2:

Input: n = 3, queries = [[0,0,4],[0,1,2],[1,0,1],[0,2,3],[1,2,1]]
Output: 17
Explanation: The image above describes the matrix after each query. The sum of the matrix after all queries are applied is 17.

 

Constraints:

  • 1 <= n <= 104
  • 1 <= queries.length <= 5 * 104
  • queries[i].length == 3
  • 0 <= typei <= 1
  • 0 <= indexi < n
  • 0 <= vali <= 105
ArrayHash Table

Hints

Hint 1
Process queries in reversed order, as the latest queries represent the most recent changes in the matrix.
Hint 2
Once you encounter an operation on some row/column, no further operations will affect the values in this row/column. Keep track of seen rows and columns with a set.
Hint 3
When operating on an unseen row/column, the number of affected cells is the number of columns/rows you haven’t previously seen.