J5. Modern Art
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A new and upcoming artist has a unique way to create checkered patterns.
The idea is to use an \(M\)-by-\(N\) canvas which is initially entirely
black. Then the artist repeatedly chooses a row or column and runs their
magic brush along the row or column. The brush changes the colour of
each cell in the row or column from black to gold or gold to black.
Given the artist’s choices, your job is to determine how much gold
appears in the pattern determined by these choices.
Marks
The following table shows how the available 15 marks are
distributed.
| 1 mark | \(M = 1\) | \(N=1\) | \(K \leq 100\) | only one cell, and up to 100 choices by the artist |
|---|---|---|---|---|
| 4 marks | \(M = 1\) | \(N \leq 100\) | \(K \leq 100\) | only one row, and up to 100 choices by the artist |
| 5 marks | \(M \leq 100\) | \(N \leq 100\) | \(K \leq 100\) | up to 100 rows, up to 100 columns, and up to 100 choices by the artist |
| 5 marks | \(MN \leq 5\,000\,000\) | \(K \leq 1\,000\,000\) | up to 5000000 cells, and up to 1000000 choices by the artist |
The first line of input will be a positive integer \(M\). The second line of input will be a
positive integer \(N\). The third line
of input will be a positive integer \(K\). The remaining input will be \(K\) lines giving the choices made by the
artist. Each of these lines will either be R
followed by a single space and then an integer which is a row number, or
C followed by a single space and then an
integer which is a column number. Rows are numbered top down from \(1\) to \(M\). Columns are numbered left to right
from \(1\) to \(N\).
Output one non-negative integer which is equal to the number of cells
that are gold in the pattern determined by the artist’s choices.
3
3
2
R 1
C 14After running the brush along the first row, the canvas looks like
this:
GGG
BBB
BBB
Then after running the brush along the first column, four cells are
gold in the final pattern determined by the artist’s choices:
BGG
GBB
GBB
4
5
7
R 3
C 1
C 2
R 2
R 2
C 1
R 410Ten cells are gold in the final pattern determined by the artist’s
choices:
BGBBB
BGBBB
GBGGG
GBGGG
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