False Coin

时间限制：1秒空间限制：65536K 热度指数：412

算法知识视频讲解

题目描述

The "Gold Bar"bank received information from reliable sources that in their last group of N coins exactly one coin is false and differs in weight from other coins (while all other coins are equal in weight). After the economic crisis they have only a simple balance available (like one in the picture). Using this balance, one is able to determine if the weight of objects in the left pan is less than, greater than, or equal to the weight of objects in the right pan. In order to detect the false coin the bank employees numbered all coins by the integers from 1 to N, thus assigning each coin a unique integer identifier. After that they began to weight various groups of coins by placing equal numbers of coins in the left pan and in the right pan. The identifiers of coins and the results of the weightings were carefully recorded. You are to write a program that will help the bank employees to determine the identifier of the false coin using the results of these weightings.

输入描述:

The first line of the input file contains two integers N and K, separated by spaces, where N is the number of coins (2<=N<=1000 ) and K is the number of weightings fulfilled (1<=K<=100). The following 2K lines describe all weightings. Two consecutive lines describe each weighting. The first of them starts with a number Pi (1<=Pi<=N/2), representing the number of coins placed in the left and in the right pans, followed by Pi identifiers of coins placed in the left pan and Pi identifiers of coins placed in the right pan. All numbers are separated by spaces. The second line contains one of the following characters: '<', '>', or '='. It represents the result of the weighting:
'<' means that the weight of coins in the left pan is less than the weight of coins in the right pan,
'>' means that the weight of coins in the left pan is greater than the weight of coins in the right pan,
'=' means that the weight of coins in the left pan is equal to the weight of coins in the right pan.

输出描述:

Write to the output file the identifier of the false coin or 0, if it cannot be found by the results of the given weightings.

示例1

输入

输出

a[i]初始标记为2

a[i]为0表示普通硬币，当平衡或者既出现在重堆又出现在轻堆里

a[i]为1标记重的那些硬币

a[i]为-1标记轻的那些硬币

每次不平衡其实给出了特殊硬币的范围，取交集

// pat.cpp : 定义控制台应用程序的//#include "stdafx.h"
#include"stdio.h"
#include<iostream>
#include<cstring>using namespace std;
typedef long long ll;
const int maxn=1010;
int a[maxn];
int n,k,p;
char c;
vector<int>l,r;
int b;
int vis[maxn]={0};
int main(){//freopen("c://jin.txt","r",stdin);while(cin>>n>>k){fill(a,a+maxn,2);while(k--){l.clear();r.clear();cin>>p;for(int i=0;i<p;i++){cin>>b;vis[b]=1;l.push_back(b);}for(int i=0;i<p;i++){cin>>b;vis[b]=1;r.push_back(b);}cin>>c;if(c=='='){for(int i=0;i<l.size();i++)a[l[i]]=0;for(int i=0;i<r.size();i++)a[r[i]]=0;}else if(c=='>'){fill(vis,vis+maxn,0); //只有一个硬币的重量不一样，每次不平衡，特殊的那个硬币一定是在这两堆里面，开始把所有硬币标记为0,可能是特殊硬币的标记为1 for(int i=0;i<l.size();i++){ vis[l[i]]=1;if(a[l[i]]==2)a[l[i]]=1;else if(a[l[i]]==-1)a[l[i]]=0;//如果一个硬币既出现在小堆里又出现在大堆里，那一定是普通的硬币}for(int i=0;i<r.size();i++){ vis[r[i]]=1;if(a[r[i]]==2)a[r[i]]=-1;else if(a[r[i]]==1)a[r[i]]=0;}for(int i=1;i<=n;i++)if(vis[i]==0)a[i]=0;}else {    fill(vis,vis+maxn,0);  for(int i=0;i<l.size();i++){   vis[l[i]]=1;if(a[l[i]]==2)a[l[i]]=-1;else if(a[l[i]]==1)a[l[i]]=0;}for(int i=0;i<r.size();i++){vis[r[i]]=1;if(a[r[i]]==2)a[r[i]]=1;else if(a[r[i]]==-1)a[r[i]]=0;}for(int i=1;i<=n;i++)if(vis[i]==0)a[i]=0;}}int count=0,ans;for(int i=1;i<=n;i++){if(a[i]!=0)  {count++;ans=i;}}if(count==1)cout<<ans<<endl;else cout<<"0"<<endl;}//freopen("CON","r",stdin);//system("pause");return 0;
}

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False Coin

题目描述

输入描述:

输出描述:

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