Score : $500$ points

问题描述

我们有一个包含 $H$ 行（水平方向）和 $W$ 列（垂直方向）的网格。令 $(i, j)$ 表示从上到下的第 $i$ 行以及从左到右的第 $j$ 列的方格。

每个方格内都有一个整数。对于 $i = 1, 2, \ldots, N$，方格 $(r_i, c_i)$ 内含一个正整数 $a_i$。其余方格内则包含一个 $0$。

初始时，棋子位于方格 $(R, C)$ 上。Takahashi 可以将棋子移动到当前位置以外的任何方格上，任意多次。但是，在移动棋子时，必须同时满足以下两个条件：

• 移动至的新方格上的整数严格大于移动自的原方格上的整数。
• 移动过程中涉及的两个方格必须在同一行或同一列上。

对于 $i = 1, 2, \ldots, N$，请打印当 $(R, C) = (r_i, c_i)$ 时，Takahashi 最多可以移动棋子多少次。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

We have a grid with $H$ horizontal rows and $W$ vertical columns. Let $(i, j)$ denote the square at the $i$-th row from the top and $j$-th column from the left.

Each square contains an integer. For each $i = 1, 2, \ldots, N$, the square $(r_i, c_i)$ contains a positive integer $a_i$. The other square contains a $0$.

Initially, there is a piece on the square $(R, C)$. Takahashi can move the piece to a square other than the square it occupies now, any number of times. However, when moving the piece, both of the following conditions must be satisfied.

• The integer written on the square to which the piece is moved is strictly greater than the integer written on the square from which the piece is moved.
• The squares to and from which the piece is moved are in the same row or the same column.

For each $i = 1, 2, \ldots, N$, print the maximum number of times Takahashi can move the piece when $(R, C) = (r_i, c_i)$.

Constraints

• $2 \leq H, W \leq 2 \times 10^5$
• $1 \leq N \leq \min(2 \times 10^5, HW)$
• $1 \leq r_i \leq H$
• $1 \leq c_i \leq W$
• $1 \leq a_i \leq 10^9$
• $i \neq j \Rightarrow (r_i, c_i) \neq (r_j, c_j)$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$H$ $W$ $N$

$r_1$ $c_1$ $a_1$

$r_2$ $c_2$ $a_2$

$\vdots$

$r_N$ $c_N$ $a_N$

Output

Print $N$ lines. For each $i = 1, 2, \ldots, N$, the $i$-th line should contain the maximum number of times Takahashi can move the piece when $(R, C) = (r_i, c_i)$.

Sample Input 1

3 3 7
1 1 4
1 2 7
2 1 3
2 3 5
3 1 2
3 2 5
3 3 5

Sample Output 1

1
0
2
0
3
1
0

The grid contains the following integers.

4 7 0
3 0 5
2 5 5

• When $(R, C) = (r_1, c_1) = (1, 1)$, you can move the piece once by moving it as $(1, 1) \rightarrow (1, 2)$.
• When $(R, C) = (r_2, c_2) = (1, 2)$, you cannot move the piece at all.
• When $(R, C) = (r_3, c_3) = (2, 1)$, you can move the piece twice by moving it as $(2, 1) \rightarrow (1, 1) \rightarrow (1, 2)$.
• When $(R, C) = (r_4, c_4) = (2, 3)$, you cannot move the piece at all.
• When $(R, C) = (r_5, c_5) = (3, 1)$, you can move the piece three times by moving it as $(3, 1) \rightarrow (2, 1) \rightarrow (1, 1) \rightarrow (1, 2)$.
• When $(R, C) = (r_6, c_6) = (3, 2)$, you can move the piece once by moving it as $(3, 2) \rightarrow (1, 2)$.
• When $(R, C) = (r_7, c_7) = (3, 3)$, you cannot move the piece at all.

Sample Input 2

5 7 20
2 7 8
2 6 4
4 1 9
1 5 4
2 2 7
5 5 2
1 7 2
4 6 6
1 4 1
2 1 10
5 6 9
5 3 3
3 7 9
3 6 3
4 3 4
3 3 10
4 2 1
3 5 4
1 2 6
4 7 9

Sample Output 2

2
4
1
5
3
6
6
2
7
0
0
4
1
5
3
0
5
2
4
0

update @ 2024/3/10 09:51:41