【九度】题目1486：False coin

题目地址：http://ac.jobdu.com/problem.php?pid=1486
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：

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：

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.

样例输入：

5 3
2 1 2 3 4
<
1 1 4
=
1 2 5
=

样例输出：

3

来源：

2012年北京大学计算机研究生机试真题

区分假币的问题，和题目1150：Counterfeit Dollar思路一样。
北大真喜欢出类似的题目。
这两个题都只有一个假币。
1、如果出现在等号两边，说明一定为真币。
2、如果出现在大于或者小于号，相应的值递加或者递减。
3、如果某个值最后的结果和不等号出现的次数相等，说明该币为假币。

C++ AC 注意编号从1开始

#include <stdio.h>
#include <string.h>
const int maxn = 1002;
int arrayA[maxn];
int arrayB[maxn];
char symbol[2];
int n,i,j,k;
int abs(int x){
    return x < 0 ? -x : x;
}
void initArray(){
    for(i = 1; i < n+1; i++){
        arrayA[i] = 0;
        arrayB[i] = 1;
    }
}
int main(){
    while(scanf("%d%d",&n,&k) != EOF){
        int num = 0;
        initArray();
        for(i = 0; i < k ; i++){
            int first;
            scanf("%d",&first);
            int *tempArrayA = new int[first];
            int *tempArrayB = new int[first];
            for (j = 0; j < first; j++) {        
                scanf("%d",&tempArrayA[j]);
            }
            for (j = 0; j < first; j++) {        
                scanf("%d",&tempArrayB[j]);
            }
            scanf("%s",symbol);
            if(symbol[0] == '='){
                for(j = 0; j < first; j++){
                    arrayB[tempArrayA[j]] = 0;
                    arrayB[tempArrayB[j]] = 0;
                }
            }else if(symbol[0] == '>'){
                num++;
                for(j = 0; j < first; j++){
                    arrayA[tempArrayA[j]]++;
                    arrayA[tempArrayB[j]]--;
                }
            }else if(symbol[0] == '<'){
                num++;
                for(j = 0; j < first; j++){
                    arrayA[tempArrayA[j]]--;
                    arrayA[tempArrayB[j]]++;
                }
            }
        }
        int maxId = 0;
        int count = 0;
        for(j = 1; j < n+1; j++){
            if(arrayB[j] == 1 && abs(arrayA[j]) == num){
                maxId = j;
                count++;
            }
        }
        printf("%d\n",count == 1 ? maxId : 0);
    }
    return 0;
}
/**************************************************************
    Problem: 1486
    User: wangzhenqing
    Language: C++
    Result: Accepted
    Time:30 ms
    Memory:1428 kb
****************************************************************/

Java AC

import java.util.Arrays;
import java.util.Scanner;  
public class Main {
    /*
     * 1486
     */
    public static void main(String[] args) throws Exception {
        Scanner scanner = new Scanner(System.in);
        while (scanner.hasNext()) {
            int n = scanner.nextInt();
            int k = scanner.nextInt();
            int num = 0;
            int arrayA[] = new int[n + 1];
            int arrayB[] = new int[n + 1];
            Arrays.fill(arrayB, 1);
            while (k > 0) {
                int first = scanner.nextInt();
                int tempArrayA[] = new int[first];
                int tempArrayB[] = new int[first];
                for (int i = 0; i < first; i++) {
                    tempArrayA[i] = scanner.nextInt();
                }
                for (int i = 0; i < first; i++) {
                    tempArrayB[i] = scanner.nextInt();
                }
                String symbol = scanner.next();
                if (symbol.equals("=")) {
                    for (int i = 0; i < first; i++) {
                        arrayB[tempArrayA[i]] = 0;
                        arrayB[tempArrayB[i]] = 0;
                    }
                }else if (symbol.equals(">")) {
                    num++;
                    for (int i = 0; i < first; i++) {
                        arrayA[tempArrayA[i]]++;
                        arrayA[tempArrayB[i]]--;
                    }
                }else if (symbol.equals("<")) {
                    num++;
                    for (int i = 0; i < first; i++) {
                        arrayA[tempArrayA[i]]--;
                        arrayA[tempArrayB[i]]++;
                    }
                }
                k --;
            }
            int max = 0;
            int maxId = 0;
            int j = 1;
            while (j < n + 1) {
                int tempNum =  Math.abs(arrayA[j]);
                if (arrayB[j] == 1 && tempNum == num ) {
                    max++;
                    maxId = j;
                }
                j++;
            }
            System.out.println(max != 1 ? 0 : maxId);
        }
    }
} 
/**************************************************************
    Problem: 1486
    User: wzqwsrf
    Language: Java
    Result: Accepted
    Time:640 ms
    Memory:106776 kb
****************************************************************/