[ACM] POJ 1218 THE DRUNK JAILER （关灯问题）

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THE DRUNK JAILER

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 23246		Accepted: 14641

Description

A certain prison contains a long hall of n cells, each right next to each other. Each cell has a prisoner in it, and each cell is locked.
One night, the jailer gets bored and decides to play a game. For round 1 of the game, he takes a drink of whiskey,and then runs down the hall unlocking each cell. For round 2, he takes a drink of whiskey, and then runs down the
hall locking every other cell (cells 2, 4, 6, ?

). For round 3, he takes a drink of whiskey, and then runs down the hall. He visits every third cell (cells 3, 6, 9, ?). If the cell is locked, he unlocks it; if it is unlocked, he locks it. He
repeats this for n rounds, takes a final drink, and passes out.
Some number of prisoners, possibly zero, realizes that their cells are unlocked and the jailer is incapacitated. They immediately escape.
Given the number of cells, determine how many prisoners escape jail.

Input

The first line of input contains a single positive integer. This is the number of lines that follow. Each of the following lines contains a single integer between 5 and 100, inclusive, which is the number of cells n.

Output

For each line, you must print out the number of prisoners that escape when the prison has n cells.

Sample Input

2
5
100

Sample Output

2
10

Source

Greater New York 2002

 

解题思路：

题意为n个监狱,编号1到n，初始均关闭，进行n局游戏，第一局，把全部的监狱都打开，第i(i>=2)局，把编号为 i 的倍数的监狱的状态改变（打开变为关闭或关闭变为打开）。问n局游戏以后，有多少个监狱为打开状态。 用d[]数组来保存监狱的状态。模拟n局游戏就能够了。

代码：

 

#include <iostream>
#include <string.h>
#include <stack>
#include <iomanip>
#include <cmath>
using namespace std;
bool d[110];

int main()
{
    int t,n;
    cin>>t;
    while(t--)
    {
        cin>>n;
        int cnt=0;
        memset(d,0,sizeof(d));
        for(int i=2;i<=n;i++)
        {
            for(int j=i;j<=n;j+=i)
                d[j]=1-d[j];//状态改变
        }
        for(int i=1;i<=n;i++)
            if(d[i]==0)
            cnt++;
        cout<<cnt<<endl;
    }
    return 0;
}