POJ 1011 Sticks

Sticks

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 103596		Accepted: 23602

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

9
5 2 1 5 2 1 5 2 1
4
1 2 3 4
0

Sample Output

6
5

 ====================================================

这个题目就是深度优先搜索了.之前尝试过把每根棍子安排到1-n节组合棍子上,在中间可以稍微剪枝.无奈超时(后边才发现超得还不是一点点)

然后再一个棍子一个棍子地组合,这样能剪的地方就变多了.

1.最后一节棍子是不用组装的.能组合到第n-1节棍子就ok了(其实对性能貌似没影响)

2.组装每一节棍子用的第一节短棍子不行地话,那就可以判定这个方案是不靠谱的了

3.组装同一节棍子的时候,用的下一节短棍限制到上一节短棍所在的序号后边

4.记录一下当前短棍的长度,下一次尝试就跳过与当前短棍长度相同的棍子

5.棍子从大到小排序.先用大的,再用小的.这样相同的棍子也能在一起了.

以上几点保证了,勉强能过了.测试了两次.一次32MS,一次16MS.估计服务器不稳定把.但是看到那些0MS+4k的答案..应该还有蛮多可以优化的地方.

#include <stdio.h>
#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;

bool check(vector<int> &x,vector<bool> &y,int l,int n,int c=0,int dep=0,int left=0) //left 搜索起点
{
	if(dep == n-1) return true;
	int old = -1;
	for(unsigned int i = left;i < y.size();++i)
	{
		int v = x[i];
		if(y[i] || v==old || c+v>l) continue;
		old = v; y[i] = true;
		if(c+v==l)
		{
			if(check(x,y,l,n,0,dep+1,0)) return true;
		}
		else
		{
			if(check(x,y,l,n,c+v,dep,i+1)) return true;
		}
		y[i] = false;
		if(c == 0 || c+v==l) return false; 
	}
	return false;
}

void solve(vector<int> &x,int mmax,int sum)
{
	for(int l = mmax;l<=sum;++l)
	{
		if(!(sum%l))
		{
			int n = sum/l; //n根
			vector<bool> y(x.size(),false);
			if(check(x,y,l,n))
			{
				cout<<l<<endl;
				return;
			}
		}
	}
}

int main()
{
	freopen("1011.data","r",stdin);
	int n;
	while(cin>>n,n)
	{
		vector<int> v; v.reserve(64);
		int mmax = -1,sum = 0;
		while(n--)
		{
			int x;
			cin>>x;
			v.push_back(x);
			mmax = max(x,mmax);
			sum += x;
		}
		sort(v.rbegin(),v.rend());
		solve(v,mmax,sum);
	};
	return 0;
}

 

附测试数据一组:

64
33 36 7 45 6 14 14 14 28 39 35 36 5 33 21 32 29 37 31 3 2 19 40 34 25 1 33 49 20 14 25 36 45 37 47 28 39 8 36 44 8 48 41 1 13 18 9 10 34 42 41 39 42 20 23 6 40 28 49 16 38 33 15 7
0

 

答案:81