Section1.3-Combination Lock

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最新推荐文章于 2024-02-27 10:57:15 发布

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原文链接：http://www.cnblogs.com/hongyang/articles/4682919.html

本文介绍了一种用于确定组合锁有效解锁设置数量的算法。该锁包含三个编号为1到N的旋转拨盘，并有两个预设的开启组合。锁的设计允许当输入组合与预设组合在每个位置上相差不超过2时，锁也能打开。文章通过一个具体示例说明了如何计算所有可能的有效组合。

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Combination Lock

Farmer John's cows keep escaping from his farm and causing mischief. To try and prevent them from leaving, he purchases a fancy combination lock to keep his cows from opening the pasture gate.

Knowing that his cows are quite clever, Farmer John wants to make sure they cannot easily open the lock by simply trying many different combinations. The lock has three dials, each numbered 1..N (1 <= N <= 100), where 1 and N are adjacent since the dials are circular. There are two combinations that open the lock, one set by Farmer John, and also a "master" combination set by the lock maker.

The lock has a small tolerance for error, however, so it will open even if the numbers on the dials are each within at most 2 positions of a valid combination.

For example, if Farmer John's combination is (1,2,3) and the master combination is (4,5,6), the lock will open if its dials are set to (1,3,5) (since this is close enough to Farmer John's combination) or to (2,4,8) (since this is close enough to the master combination). Note that (1,5,6) would not open the lock, since it is not close enough to any one single combination.

Given Farmer John's combination and the master combination, please determine the number of distinct settings for the dials that will open the lock. Order matters, so the setting (1,2,3) is distinct from (3,2,1).

PROGRAM NAME: combo

INPUT FORMAT:

Line 1:	The integer N.
Line 2:	Three space-separated integers, specifying Farmer John's combination.
Line 3:	Three space-separated integers, specifying the master combination (possibly the same as Farmer John's combination).

SAMPLE INPUT (file combo.in):

50
1 2 3
5 6 7

INPUT DETAILS:

Each dial is numbered 1..50. Farmer John's combination is (1,2,3), and the master combination is (5,6,7).

OUTPUT FORMAT:

Line 1:

The number of distinct dial settings that will open the lock.

SAMPLE OUTPUT (file combo.out):

SAMPLE OUTPUT EXPLANATION

Here's a list:

1,1,1  2,2,4  3,4,2  4,4,5  5,4,8  6,5,6  7,5,9  3,50,2  50,1,4 
1,1,2  2,2,5  3,4,3  4,4,6  5,4,9  6,5,7  7,6,5  3,50,3  50,1,5 
1,1,3  2,3,1  3,4,4  4,4,7  5,5,5  6,5,8  7,6,6  3,50,4  50,2,1 
1,1,4  2,3,2  3,4,5  4,4,8  5,5,6  6,5,9  7,6,7  3,50,5  50,2,2 
1,1,5  2,3,3  3,4,6  4,4,9  5,5,7  6,6,5  7,6,8  49,1,1  50,2,3 
1,2,1  2,3,4  3,4,7  4,5,5  5,5,8  6,6,6  7,6,9  49,1,2  50,2,4 
1,2,2  2,3,5  3,4,8  4,5,6  5,5,9  6,6,7  7,7,5  49,1,3  50,2,5 
1,2,3  2,4,1  3,4,9  4,5,7  5,6,5  6,6,8  7,7,6  49,1,4  50,3,1 
1,2,4  2,4,2  3,5,5  4,5,8  5,6,6  6,6,9  7,7,7  49,1,5  50,3,2 
1,2,5  2,4,3  3,5,6  4,5,9  5,6,7  6,7,5  7,7,8  49,2,1  50,3,3 
1,3,1  2,4,4  3,5,7  4,6,5  5,6,8  6,7,6  7,7,9  49,2,2  50,3,4 
1,3,2  2,4,5  3,5,8  4,6,6  5,6,9  6,7,7  7,8,5  49,2,3  50,3,5 
1,3,3  3,1,1  3,5,9  4,6,7  5,7,5  6,7,8  7,8,6  49,2,4  50,4,1 
1,3,4  3,1,2  3,6,5  4,6,8  5,7,6  6,7,9  7,8,7  49,2,5  50,4,2 
1,3,5  3,1,3  3,6,6  4,6,9  5,7,7  6,8,5  7,8,8  49,3,1  50,4,3 
1,4,1  3,1,4  3,6,7  4,7,5  5,7,8  6,8,6  7,8,9  49,3,2  50,4,4 
1,4,2  3,1,5  3,6,8  4,7,6  5,7,9  6,8,7  1,50,1 49,3,3  50,4,5 
1,4,3  3,2,1  3,6,9  4,7,7  5,8,5  6,8,8  1,50,2 49,3,4  49,50,1
1,4,4  3,2,2  3,7,5  4,7,8  5,8,6  6,8,9  1,50,3 49,3,5  49,50,2
1,4,5  3,2,3  3,7,6  4,7,9  5,8,7  7,4,5  1,50,4 49,4,1  49,50,3
2,1,1  3,2,4  3,7,7  4,8,5  5,8,8  7,4,6  1,50,5 49,4,2  49,50,4
2,1,2  3,2,5  3,7,8  4,8,6  5,8,9  7,4,7  2,50,1 49,4,3  49,50,5
2,1,3  3,3,1  3,7,9  4,8,7  6,4,5  7,4,8  2,50,2 49,4,4  50,50,1
2,1,4  3,3,2  3,8,5  4,8,8  6,4,6  7,4,9  2,50,3 49,4,5  50,50,2
2,1,5  3,3,3  3,8,6  4,8,9  6,4,7  7,5,5  2,50,4 50,1,1  50,50,3
2,2,1  3,3,4  3,8,7  5,4,5  6,4,8  7,5,6  2,50,5 50,1,2  50,50,4
2,2,2  3,3,5  3,8,8  5,4,6  6,4,9  7,5,7  3,50,1 50,1,3  50,50,5
2,2,3  3,4,1  3,8,9  5,4,7  6,5,5  7,5,8

本题比较简单，唯一要注意的是，数字1~N是连在一起的，而且N后面是1（数字在字母盘上的嘛）

 1 /*
 2 ID:pekingt1
 3 TASK:combo
 4 LANG:C++
 5 */
 6 #include<iostream>
 7 #include<cstdio>
 8 #include<math.h>
 9 #include<cstring>
10 #include<algorithm>
11 #include<cstdlib>
12 using namespace std;
13 
14 const int maxn=101;
15 
16 int N;
17 int farmer[maxn],origin[maxn];
18 int signal[maxn][maxn][maxn];
19 
20 bool isvalid(int x,int y)
21 {
22     if(abs(x-y)<=2)
23         return true;
24     if(abs(x-y)>=N-2)
25         return true;
26     return false;
27 }
28 
29 int main()
30 {
31     //int N;
32 
33     freopen("combo.in","r",stdin);
34     freopen("combo.out","w",stdout);
35 
36     while(scanf("%d",&N)!=EOF)
37     {
38         for(int i=0;i<3;i++)
39             cin>>farmer[i];
40         for(int i=0;i<3;i++)
41             cin>>origin[i];
42 
43         int key_count=0;
44 
45         memset(signal,0,sizeof(signal));
46 
47         for(int i=1;i<=N;i++)
48             for(int j=1;j<=N;j++)
49                 for(int k=1;k<=N;k++)
50                 {
51                     if(signal[i][j][k]==0)
52                     if(isvalid(i,farmer[0])&&isvalid(j,farmer[1])&&isvalid(k,farmer[2])||isvalid(i,origin[0])&&isvalid(j,origin[1])&&isvalid(k,origin[2]))
53                     {
54                         key_count++;
55                     }
56                     signal[i][j][k]=1;
57                 }
58                 cout<<key_count<<endl;
59     }
60     return 0;
61 }