AtCoder Beginner Contest 089 D

Problem Statement

We have a grid with H rows and W columns. The square at the i-th row and the j-th column will be called Square (i,j).

The integers from 1 through H×W are written throughout the grid, and the integer written in Square (i,j) is A_i,j.

You, a magical girl, can teleport a piece placed on Square (i,j) to Square (x,y) by consuming |x−i|+|y−j| magic points.

You now have to take Q practical tests of your ability as a magical girl.

The i-th test will be conducted as follows:

• Initially, a piece is placed on the square where the integer L_i is written.

• Let x be the integer written in the square occupied by the piece. Repeatedly move the piece to the square where the integer x+D is written, as long as x is not R_i. The test ends when x=R_i.

• Here, it is guaranteed that R_i−L_i is a multiple of D.

For each test, find the sum of magic points consumed during that test.

Constraints

• 1≤H,W≤300
• 1≤D≤H×W
• 1≤A_i,j≤H×W
• A_i,j≠A_x,y((i,j)≠(x,y))
• 1≤Q≤10⁵
• 1≤L_i≤R_i≤H×W
• (R_i−L_i) is a multiple of D.

Input

Input is given from Standard Input in the following format:

H W D
A1,1 A1,2 … A1,W
:
AH,1 AH,2 … AH,W
Q
L1 R1
:
LQ RQ

Output

For each test, print the sum of magic points consumed during that test.

Output should be in the order the tests are conducted.

Sample Input 1

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

Sample Output 1

5

• 4 is written in Square (1,2).

• 6 is written in Square (3,3).

• 8 is written in Square (3,1).

Thus, the sum of magic points consumed during the first test is (|3−1|+|3−2|)+(|3−3|+|1−3|)=5.

Sample Input 2

4 2 3
3 7
1 4
5 2
6 8
2
2 2
2 2

Sample Output 2

0
0

Note that there may be a test where the piece is not moved at all, and there may be multiple identical tests.

Sample Input 3

5 5 4
13 25 7 15 17
16 22 20 2 9
14 11 12 1 19
10 6 23 8 18
3 21 5 24 4
3
13 13
2 10
13 13

Sample Output 3

0
5
0

Q最高100000，如果每次都要计算，会超时，先记录前缀和，直接用前缀和相减就好了。
代码：

#include <bits/stdc++.h>///int * int = int
using namespace std;
int h,w,d,s[300][300],q,a,b;
int x[90001],y[90001];
int dp[90001];
int main()
{
    scanf("%d%d%d",&h,&w,&d);
    for(int i = 0;i < h;i ++)
    {
        for(int j = 0;j < w;j ++)
        {
            scanf("%d",&s[i][j]);
            x[s[i][j]] = i;
            y[s[i][j]] = j;
        }
    }
    for(int i = 1 + d;i <= h * w;i ++)
    {
        dp[i] = dp[i - d] + abs(x[i] - x[i - d]) + abs(y[i] - y[i - d]);
    }
    scanf("%d",&q);
    for(int i = 0;i < q;i ++)
    {
        scanf("%d%d",&a,&b);
        printf("%lld
",abs(dp[a] - dp[b]));
    }
}