题目：

Ignatius and the Princess IV

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32767 K (Java/Others)
Total Submission(s): 42940 Accepted Submission(s): 18774

Problem Description

"OK, you are not too bad, em... But you can never pass the next test." feng5166 says.

"I will tell you an odd number N, and then N integers. There will be a special integer among them, you have to tell me which integer is the special one after I tell you all the integers." feng5166 says.

"But what is the characteristic of the special integer?" Ignatius asks.

"The integer will appear at least (N+1)/2 times. If you can't find the right integer, I will kill the Princess, and you will be my dinner, too. Hahahaha....." feng5166 says.

Can you find the special integer for Ignatius?

Input

The input contains several test cases. Each test case contains two lines. The first line consists of an odd integer N(1<=N<=999999) which indicate the number of the integers feng5166 will tell our hero. The second line contains the N integers. The input is terminated by the end of file.

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Output

For each test case, you have to output only one line which contains the special number you have found.

Sample Input

5 1 3 2 3 3 11 1 1 1 1 1 5 5 5 5 5 5 7 1 1 1 1 1 1 1

Sample Output

3 5 1

题意：一个奇数长的序列中有一个数字出现了至少（ n + 1 ) / 2次，输出这个数。

这题目乍一看觉得异常简单，不就是找数么，出现了那么多次还不好找么，然后想了想就会“真香~”

题解：其实只要明白一件事，这个题目就非常简单了，我们把要找的那个数字称作“多数”，在这个数列中我们任意去掉两个不相同的数字，之后的数列里，多数还是多数。所以我们只要遍历一遍数列，记录下当前的数字以及出现的次数，每遇到不同的书就将出现次数减一，出现次数为零时更新数字。

AC代码：

#include<cstdio>
#include<iostream>
using namespace std;
int main()
{
    int i, j, n, q, t, cnt = 0;
    while(~scanf("%d", &n)){
        cnt = 0;//计数器
        for(i = 0;i < n;i++){
            scanf("%d", &q);
            if(!cnt){//cnt为零t肯定不是“多数”
                cnt = 1;
                t = q;//更新数字
            }
            else{
                if(t == q)cnt += 1;//出现次数++
                else cnt -= 1;//去掉一个t 和 一个q
            }
        }
        printf("%d\n", t);//最后剩下的肯定是多数
    }
    return 0;
}

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HDU 1029 Ignatius and the Princess IV （简单DP)

Ignatius and the Princess IV

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