POJ 3349 Snowflake Snow Snowflakes 解题报告

一、问题描述

Description

You may have heard that no two snowflakes are alike. Your task is to write a program to determine whether this is really true. Your program will read information about a collection of snowflakes, and search for a pair that may be identical. Each snowflake has six arms. For each snowflake, your program will be provided with a measurement of the length of each of the six arms. Any pair of snowflakes which have the same lengths of corresponding arms should be flagged by your program as possibly identical.

Input

The first line of input will contain a single integer n, 0 < n ≤ 100000, the number of snowflakes to follow. This will be followed by n lines, each describing a snowflake. Each snowflake will be described by a line containing six integers (each integer is at least 0 and less than 10000000), the lengths of the arms of the snow ake. The lengths of the arms will be given in order around the snowflake (either clockwise or counterclockwise), but they may begin with any of the six arms. For example, the same snowflake could be described as 1 2 3 4 5 6 or 4 3 2 1 6 5.

Output

If all of the snowflakes are distinct, your program should print the message:
No two snowflakes are alike.
If there is a pair of possibly identical snow akes, your program should print the message:
Twin snowflakes found.

Sample Input

2

1 2 3 4 5 6

4 3 2 1 6 5

Sample Output

Twin snowflakes found.

二、解题思想

如果用穷举遍历则复杂度为O(n*n)，n最大为10万，会超时。采用哈希法。将6个数的和对一个大的数取模进行哈希，使用了STL中的vector保存具有相同哈希值的雪花的下标。如遇到相同的哈希值，则判断是否有相同的雪花，如果有相同的则输出结果马上退出。提交结果显示耗时3000MS，勉强过了。

三、代码

 

#include<vector>
using namespace std;
int d[100001][6];
const int MAXVALUE=99991;
vector<int> hash[MAXVALUE];
bool isSame(int a,int b)
{
    int i;
    for(i=0;i<6;i++)
    {
        if( ( d[a][0]==d[b][i] &&
        d[a][1]==d[b][(i+1)%6] &&
        d[a][2]==d[b][(i+2)%6] &&
        d[a][3]==d[b][(i+3)%6] &&
        d[a][4]==d[b][(i+4)%6] &&
        d[a][5]==d[b][(i+5)%6]) || (

        d[a][0]==d[b][i] &&
        d[a][1]==d[b][(i+5)%6] &&
        d[a][2]==d[b][(i+4)%6] &&
        d[a][3]==d[b][(i+3)%6] &&
        d[a][4]==d[b][(i+2)%6] &&
        d[a][5]==d[b][(i+1)%6]))
        return true;
    }
    return false;
}
int main()
{
    int n;
    int i,j;
    scanf("%d",&n);
    for(i=0;i<n;++i)
    {
        int sum=0;
        for(j=0;j<6;++j)
        {
            scanf("%d",&d[i][j]);
            sum+=d[i][j];
        }
        sum%=MAXVALUE;
        for(j=0;j<hash[sum].size();++j)
        {
            if(isSame(hash[sum][j],i))
            {
                printf("%s\n","Twin snowflakes found.");
                exit(0);
            }
        }
        hash[sum].push_back(i);
    }
    printf("%s\n","No two snowflakes are alike.");
    return 0;
}