Strong Laser

This is a function-based interactive problem.

There is a hidden $N \times N$ grid. Each cell either contains one block or is empty. You cannot see the hidden grid directly.

You may use the following two types of lasers.

• For each row, a laser fired from left to right.
• For each column, a laser fired from top to bottom.

Each laser has an integer strength $k$. A laser of strength $k$ penetrates the first $k$ blocks it meets in its direction, and stops at the next block. If there are at most $k$ blocks in its direction, the laser exits the grid.

You may perform at most $10$ experiments. In one experiment, you choose the strengths of all row lasers and all column lasers, and fire them simultaneously. After the experiment, you receive the stopping position of each laser, or the information that it exited the grid.

Using only the results of these experiments, find the total number of blocks in the entire grid.

#include "plast.h"

int count_blocks(int n);

std::vector<int> experiment(
    const std::vector<int>& row_strength,
    const std::vector<int>& col_strength
);

This is a function-based interactive problem, so the contestant program must not read from standard input directly.

The grader passes the size $n$ of the hidden grid as the argument of count\_blocks(n).

The contestant program must not print the answer to standard output directly.

The function count\_blocks(n) must return the total number of blocks in the grid.

• $1 \le n \le 100$.
• Each cell either contains one block or is empty.
• The function experiment may be called at most $10$ times.
• In each experiment, every laser strength must be an integer between $0$ and $n$, inclusive.