Sticks
George took sticks of the same length and cut them randomly until all parts became at most 50 units long. Now he wants to return sticks to the original state, but he forgot how many sticks he had originally and how long they were originally. Please help him and design a program which computes the smallest possible original length of those sticks. All lengths expressed in units are integers greater than zero.
Input
The input contains blocks of 2 lines. The first line contains the number of sticks parts after cutting, there are at most 64 sticks. The second line contains the lengths of those parts separated by the space. The last line of the file contains zero.
Output
The output should contains the smallest possible length of original sticks, one per line.
Sample Input
9
5 2 1 5 2 1 5 2 1
4
1 2 3 4
0
Sample Output
6
5
Source
题目类型：搜索
算法分析：本题采用DFS算法：
1首先将数据按照降序排序。
2从数据数值最大的开始，依次减去长度值，直到棒子的长度变为0为止，同时标记用到的数值。
3如果长度变为0，则把length恢复原值，再执行一次。
4如果失败，则返回到前一个状态。
5如果做出sum/length个长度是length的棒子就成功了。
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#include <cstdio> #include <cstring> #include <iostream> #include <fstream> using namespace std; int in[56]; int length; int finish; void check (int counts, int len, int plen) { int j; in[plen]--; if (counts == 0) finish = 1; if (finish == 0) { len -= plen; if (len) { j = len < plen ? len : plen; for (; j > 0; j--) if (in[j]) check (counts, len, j); } else { for (j = 50; !in[j]; ) j--; check (counts - 1, length, j); } } in[plen]++; } int main() { int b, n, sum, maxs; //ifstream cin ("aaa.txt"); while (cin >> n && n) { memset (in, 0, sizeof (in)); sum = 0; maxs = 0; finish = 0; for (; n--; ) { cin >> b; in[b]++; sum += b; if (maxs < b) maxs = b; } for (length = maxs; !finish; length++) if (sum % length == 0) check (sum / length, length, maxs); printf ("%d\n", length - 1); } return 0; } |
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