Find your present （位异或）

Posted 2020-06-17

Problem Description In the new year party, everybody will get a "special present".Now it‘s your turn to get your special present, a lot of presents now putting on the desk, and only one of them will be yours.Each present has a card number on it, and your present‘s card number will be the one that different from all the others, and you can assume that only one number appear odd times.For example, there are 5 present, and their card numbers are 1, 2, 3, 2, 1.so your present will be the one with the card number of 3, because 3 is the number that different from all the others.

Input The input file will consist of several cases.  Each case will be presented by an integer n (1<=n<1000000, and n is odd) at first. Following that, n positive integers will be given in a line, all integers will smaller than 2^31. These numbers indicate the card numbers of the presents.n = 0 ends the input.

Output             For each case, output an integer in a line, which is the card number of your present.

Sample Input 5 1 1 3 2 2 3 1 2 1 0

Sample Output 3 2 Hint Hint use scanf to avoid Time Limit Exceeded

Author 8600

Source HDU 2007-Spring Programming Contest - Warm Up （1）

Recommend 8600

 

 

题目内存限制：1024K，所以不能简单地用数组存然后再处理。

这题有一个好的方法—位异或。

 位异或的运算法则吧：

1、a^b = b^a。

2、(a^b)^c = a^(b^c)。

3、a^b^a = b。

对于一个任意一个数n，它有几个特殊的性质：

1、0^n = n。

2、n^n = 0。

所以可以通过每次异或运算，最后剩下的值就是出现奇数次的那个数字。

 

 #include <stdio.h> 
int main() 
{ 
    int n,x,ans; 
    while(scanf("%d",&n),n) 
    { 
        ans = 0; 
        while(n--) 
        { 
            scanf("%d",&x); 
            ans ^= x; 
        } 
        printf("%d\n",ans); 
    } 
    return 0; 
}