AtCoder Beginner Contest 089 D - Practical Skill Test 题解

D - Practical Skill Test

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Time limit : 2sec / Memory limit : 256MB

Score : 400 points

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.

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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.

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Sample Input 1

Copy

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

Sample Output 1

Copy

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.

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Sample Input 2

Copy

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

Sample Output 2

Copy

0
0

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

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Sample Input 3

Copy

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

Copy

0
5
0

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题意：上来一看题目就看错了，还以为是曼哈顿距离的最小生成树，然而，sum是按照顺序进行计算的。也就是在矩阵中找到介于R、L中且是R+kD（0<=k<=(L-R)/D）的坐标，并按照sum的要求进行计算。

思路：理清题意后，思路不是一个大问题，值得注意的是相当于多组数据。所以，每次寻找计算可能会T。但是对于每组值，D的值是确定的，所以可以利用一个数组记忆化这些值，直接相减即可。

代码：

#include<cstdio>
#define abs(x) ((x>0)?x:(-(x)))
int H,W,D,A;
int Q,L,R;
int px[90001] ,py [90001];
int d[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",&A);
            px[A]=i,py[A]=j;
        }
    }
    for(int i=D+1;i<=H*W;i++){ 
        d[i]=d[i-D]+abs(px[i]-px[i-D])+ abs(py[i]-py[i-D]);
    } 
    scanf ("%d",&Q);
    while(Q--){ 
        scanf ("%d%d",&L,&R);
        printf ("%d\n",d[R]-d[L]);
    } 
}