HDU2095find your present (2)

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http://acm.hdu.edu.cn/showproblem.php?pid=2095


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
51 1 3 2 231 2 10
 

Sample Output
32
Hint
Hint
use scanf to avoid Time Limit Exceeded
 

Author
8600
 

解题思路:

题目内存限制:1024K,所以不能简单地用数组存然后再处理。

为了节约内存,可以用STL里面的set,map等容器。

当容器里没有这个元素的时候,就插入这个元素,否则,删除这个元素。

最后,容器中肯定只剩下一个元素,便是我们所要的结果。


#include <set>  #include <stdio.h>  using namespace std;  int main()  {      int n,x;      set <int> S;      while(scanf("%d",&n),n)      {          while(n--)          {              scanf("%d",&x);              if(S.find(x) == S.end())    //没找到,插入                  S.insert(x);              else                        //找到了,删除                  S.erase(x);          }          printf("%d\n",*S.begin());          S.clear();      }      return 0;  }  
其实,这题还有个更好的方法————位异或。

这个题目你要理解2点第一, 为什么要用 异或来算。第二, 异或是怎么来算的。 题目给的数据量特别大 如果之前试过用hash算的话,(既开一个1000000的数组来保存每一个数字出现得次数,然后扫描值为1的) 很可能会Memory Limit Exceeded 。  所以才想到了用异或。 异或:就是按位比较相同则为0不同则是1;  比如   3^5,   3=011,5=101,两数按位异或后为110,即6。     偶数次出现的异或结果为0 基数次结果为1     然后  异或满足交换率。再举一个例子。   如 数据  1 2 3 2 1      先让result=0    那么可以看成是  result^1^2^3^2^1        交换律     result^1^1^2^2^3       很明显      1^1 和  2^2 都为 0        所以最后得    result^3 =0^3 =3(二进制 101)
整数的异或是先把它们化成二进制,再按位异或。
比如3^5,3=011,5=101,两数按位异或后为110,即6。
几个数异或满足交换律。2^3^2=2^2^3=0^3=3.
两个相同的数异或为0,普通数都出现了偶数次,
所以它们异或后都是0,而0与那个特别数异或后还是那个特殊数。
#include<stdio.h>int main(){    int n,i,x,y;    while(scanf("%d",&n)!=EOF&&n)    {           x=0;           while(n--)           {                scanf("%d",&y);                x^=y;                }                    printf("%d\n",x);                 }    return 0;}




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