I can't think of a good algorithm [closed] - c++

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Closed 10 years ago.
There is a magic board. The magic board has N*N cells: N rows and N columns. Every cell contains one integer, which is 0 initially. Let the rows and the columns be numbered from 1 to N.
There are 2 types of operations can be applied to the magic board:
•RowSet i x: it means that all integers in the cells on row i have been changed to x after this operation.
•ColSet i x: it means that all integers in the cells on column i have been changed to x after this operation.
And your friend sometimes has an interest in the total number of the integers 0s on some row or column:
•RowQuery i: it means that you should answer the total number of 0s on row i.
•ColQuery i: it means that you should answer the total number of 0s on column i.
Input
The first line of input contains 2 space-separated integers N and Q. They indicate the size of the magic board, and the total number of operations and queries from the friend.
Then each of the next Q lines contains an operation or a query by the format mentioned above.
Output
For each query, output the answer of the query.
Constraints
1 ≤ N, Q ≤ 500000 (5 * 105)
1 ≤ i ≤ N
x ∈ {0, 1} (That is, x = 0 or 1)
Sample Input:
3 6
RowQuery 1
ColSet 1 1
RowQuery 1
ColQuery 1
RowSet 1 0
ColQuery 1
Output:
3
2
0
1
How to go about it? The time constraint is 0.6 seconds and therefore the naïve algorithm of marking out the operations on a 2D array, wont work.

Answer 1

If you can't think of a good algorithm, try this technique:
Run an example using pencil and graph paper.
Run an example again, this time write down each detailed step you
perform.
Run an example again, using your steps. Adjust as necessary.
Convert your steps into code.
Using this technique, you can come up with more appropriate questions to search on Stackoverflow, such as "How do I implement a square area of memory / matrix?"
Or "How do I use a debugger?"
Or "Here is the smallest program that recreates my issue of ...., what am I doing wrong?"
Edit 1: (to advance my S.O. reputation)
Looks like, from the requirements, that you will need at least two functions: Set a row to the given value or set a column to the given value.
Let us start with something small like a 4x4 matrix.
And use the command: Set Row 1 0 // Set Row 1 to all zeros.
Remember that C++ indexes from 0 to N-1 not 1 to N as the requirements are, so we'll have to subtract one from our row number.
Let us use the notation: board[row][column] to represent a cell on the board.
By hand:
board[0][0] = 0;
board[0][1] = 0; // Note the incrementing column numbers.
board[0][2] = 0;
board[0][3] = 0; // Note the last column index is 3 not 4.
Looking at the above code, we can note a pattern, namely, the column index is changing each time, by 1. So we can put this into a loop:
Set column to zero.
While column is less than 4 do:
board[0][column] = 0;
column = column + 1;
end-while
The next step is to turn this into some code:
unsigned int column;
unsigned int board[4][4];
for (column = 0; column < 4; ++column)
{
board[0][column] = 0;
}
Since the the Set Row command allows for a variable row index and a variable row value, we make those variables and insert them into our code:
unsigned int row = 0;
unsigned int value = 0;
unsigned int column;
unsigned int board[4][4];
for (column = 1; column < 4; ++column)
{
board[row][column] = value;
}
We could make this into an free standing function by providing a function signature:
void Set_Row(unsigned int& array[4][4],
unsigned int row,
unsigned int value)
{
// Insert above code fragment here.
}
Next, make functions for the other commands.
Create a main function to read the commands.
Run the program, notice where any issues are, such as being able to declare a matrix of any size at run-time.
Add in code to resolve the issues.
Repeat.