Sticks

Time Limit : 2000/1000ms (Java/Other)   Memory Limit : 20000/10000K (Java/Other)

Total Submission(s) : 20   Accepted Submission(s) : 7

Problem Description

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

95 2 1 5 2 1 5 2 141 2 3 40

 

Sample Output

65

 

Source

PKU

 

思路：搜索+剪枝

            1.sum是木材的长度和，len是原来木材的长度，n 是给定的木材根数，i 是原来的木材根数，data[n-1]是给定木材的最大长度，那么sum/data[n-1] 大于等于sum/len;

所以原来最短木材为sum/i;

            2.如果每次的第一个木材不能找到其它木材组成目标长度，说明无法在当前组合方式下组合。

            3.由于所有棒子已降序排序，在DFS时，若某根棒子不合适，则跳过其后面所有与它等长的棒子；

         4.如加人一根木棍没有达到len，则下次在i-1个棍子中搜索

代码如下：

#include <iostream>#include <cstdio>#include <cstring>#include <algorithm>using namespace std;int n , sum;int data[70];int vist[70];int len;bool dfs(int temp , int time,int total , int x){    //printf("bfs\n");    if(time == total)return true;    int same = -1;    for(int i = x; i >= 0; i --)    {        if(vist[i] || data[i] == same)continue;        if(!vist[i])        {            vist[i] = 1;            if(temp+data[i] == len)            {                if(dfs(0 , time+1 , total , n-1)) return true;                else                    same = data[i];            }            else if(temp+data[i] < len)            {                if(dfs(temp+data[i] , time ,total,i-1)) return true;                else                    same = data[i];            }            vist[i] = 0;        }        if(temp == 0)break;    }    return false;}int main(){    while(scanf("%d",&n),n)    {        sum = 0;        for(int i = 0; i < n; i ++)        {            scanf("%d",&data[i]);            sum +=data[i];        }        sort(data , data+n);        for(int i = sum/data[n-1]; i >= 1; i --)        {            if(sum % i== 0 && data[n-1]<=sum/i)            {                memset(vist, 0 , sizeof(vist));                len = sum / i;                if(dfs(0,0,i-1, n-1)){                    printf("%d\n",len);                    break;                }            }        }    }    return 0;}