poj 1416 Shredding Company

Description

You have just been put in charge of developing a new shredder for the Shredding Company Although a "normal" shredder would just shred sheets of paper into little pieces so that the contents would become unreadable, this new shredder needs to have the following unusual basic characteristics.

1.The shredder takes as input a target number and a sheet of paper with a number written on it.

2.It shreds (or cuts) the sheet into pieces each of which has one or more digits on it.

3.The sum of the numbers written on each piece is the closest possible number to the target number, without going over it.

For example, suppose that the target number is 50, and the sheet of paper has the number 12346. The shredder would cut the sheet into four pieces, where one piece has 1, another has 2, the third has 34, and the fourth has 6. This is because their sum 43 (= 1 + 2 + 34 + 6) is closest to the target number 50 of all possible combinations without going over 50. For example, a combination where the pieces are 1, 23, 4, and 6 is not valid, because the sum of this combination 34 (= 1 + 23 + 4 + 6) is less than the above combination's 43. The combination of 12, 34, and 6 is not valid either, because the sum 52 (= 12 + 34 + 6) is greater than the target number of 50.

Figure 1. Shredding a sheet of paper having the number 12346 when the target number is 50

There are also three special rules :

1.If the target number is the same as the number on the sheet of paper, then the paper is not cut.

For example, if the target number is 100 and the number on the sheet of paper is also 100, then

the paper is not cut.

2.If it is not possible to make any combination whose sum is less than or equal to the target number, then error is printed on a display. For example, if the target number is 1 and the number on the sheet of paper is 123, it is not possible to make any valid combination, as the combination with the smallest possible sum is 1, 2, 3. The sum for this combination is 6, which is greater than the target number, and thus error is printed.

3.If there is more than one possible combination where the sum is closest to the target number without going over it, then rejected is printed on a display. For example, if the target number is 15, and the number on the sheet of paper is 111, then there are two possible combinations with the highest possible sum of 12: (a) 1 and 11 and (b) 11 and 1; thus rejected is printed. In order to develop such a shredder, you have decided to first make a simple program that would simulate the above characteristics and rules. Given two numbers, where the first is the target number and the second is the number on the sheet of paper to be shredded, you need to figure out how the shredder should "cut up" the second number.

Input

The input consists of several test cases, each on one line, as follows :

tl num1
t2 num2
...
tn numn
0 0

Each test case consists of the following two positive integers, which are separated by one space : (1) the first integer (ti above) is the target number, (2) the second integer (numi above) is the number that is on the paper to be shredded.

Neither integers may have a 0 as the first digit, e.g., 123 is allowed but 0123 is not. You may assume that both integers are at most 6 digits in length. A line consisting of two zeros signals the end of the input.

Output

For each test case in the input, the corresponding output takes one of the following three types :

sum part1 part2 ...
rejected
error

In the first type, partj and sum have the following meaning :

1.Each partj is a number on one piece of shredded paper. The order of partj corresponds to the order of the original digits on the sheet of paper.

2.sum is the sum of the numbers after being shredded, i.e., sum = part1 + part2 +...

Each number should be separated by one space.
The message error is printed if it is not possible to make any combination, and rejected if there is
more than one possible combination.
No extra characters including spaces are allowed at the beginning of each line, nor at the end of each line.

Sample Input

50 12346
376 144139
927438 927438
18 3312
9 3142
25 1299
111 33333
103 862150
6 1104
0 0

Sample Output

43 1 2 34 6
283 144 139
927438 927438
18 3 3 12
error
21 1 2 9 9
rejected
103 86 2 15 0
rejected

http://poj.org/problem?id=1416

此题DFS的思想；
将一串数字在不改变相对顺序的条件下进行分组，比如12346，你可以分成1,2,3,4,6五组，也可以分成12,3,4,6；或者1,23,4,6等各种可能；
题目要求分成的组的和要小于等于target number并且在所有可能里面去最大的值，如果最大的值有多个则输出rejected;
如果所有的组和都要比

target number要大则输出error;
接下来就是dfs思想来解决问题了。
具体看下面代码：

  1 #include <iostream>
  2 #include <stdio.h>
  3 #include <string.h>
  4 #include <cmath>
  5 using namespace std;
  6 int a,b;
  7 int flag[7];
  8 int num[6];
  9 int res[6];
 10 int maxS;
 11 int len;
 12 bool mark;
 13 int p;
 14 void dfs(int step,int pre)
 15 {
 16     if(step==len)
 17     {
 18         int i;
 19         int sum=0;
 20         for(i=0;i<len;i++)
 21         {
 22             if(flag[i]==-1)
 23             break;
 24             int j=i;
 25             int digit=0;
 26             while(flag[j]==flag[j+1] && flag[j]!=-1)
 27             {
 28                 digit=digit*10+num[j];
 29                 j++;
 30             }
 31             digit=digit*10+num[j];
 32             sum+=digit;
 33             i=j;
 34         }
 35         if(sum<=a)
 36         {
 37             if(sum>=maxS)
 38             {
 39                 if(sum==maxS)
 40                 {
 41                     mark=true;
 42                 }
 43                 else
 44                 {
 45                     memset(res,0,sizeof(res));
 46                     p=0;
 47                     for(i=0;i<len;i++)
 48                     {
 49                         if(flag[i]==-1)
 50                         break;
 51                         int j=i;
 52                         int digit=0;
 53                         while(flag[j]==flag[j+1] && flag[j]!=-1)
 54                         {
 55                             digit=digit*10+num[j];
 56                             j++;
 57                         }
 58                         i=j;
 59                         digit=digit*10+num[j];
 60                         res[p++]=digit;
 61                     }
 62                     maxS=sum;
 63                     mark=false;
 64                 }
 65             }
 66         }
 67         return;
 68     }
 69     int i;
 70     for(i=0;i<len;i++)
 71     {
 72         if((i-pre)==0 || (i-pre)==1)
 73         {
 74             flag[step]=i;
 75             dfs(step+1,i);
 76         }
 77     }
 78 }
 79 int main()
 80 {
 81     while(~scanf("%d%d",&a,&b))
 82     {
 83         if(a==0 && b==0)
 84         {
 85             break;
 86         }
 87         if(a==b)
 88         {
 89             printf("%d %d\n",a,b);
 90             continue;
 91         }
 92         int ff1=0,i;
 93         int ff2=b;
 94         memset(num,0,sizeof(num));
 95         len=0;
 96         while(ff2)
 97         {
 98             len++;
 99             ff1+=(ff2%10);
100             ff2=ff2/10;
101         }
102         if(a<ff1)
103         {
104             printf("error\n");
105             continue;
106         }
107         for(i=0;i<len;i++)
108         {
109             int k=pow(10.0,len-i-1);
110             num[i]=b/k%10;
111         }
112         memset(flag,-1,sizeof(flag));
113         maxS=0;
114         mark=false;
115         dfs(0,-1);
116         if(mark)
117         {
118             printf("rejected\n");
119             continue;
120         }
121         printf("%d",maxS);
122         for(i=0;i<p;i++)
123         {
124             printf(" %d",res[i]);
125         }
126         printf("\n");
127     }
128     return 0;
129 }

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