UVA 11384 - Help is needed for Dexter(递归)

Problem H
Help is needed for Dexter
Time Limit: 3 Second
 
Dexter is tired of Dee Dee. So he decided to keep Dee Dee busy in a game. The game he planned for her is quite easy to play but not easy to win at least not for Dee Dee. But Dexter does not have time to spend on this silly task, so he wants your help.

 

There will be a button, when it will be pushed a random number N will be chosen by computer. Then on screen there will be numbers from 1 to N. Dee Dee can choose any number of numbers from the numbers on the screen, and then she will command computer to
subtract a positive number chosen by her (not necessarily on screen) from the selected numbers. Her objective will be to make all the numbers 0.

 

For example if N = 3, then on screen there will be 3 numbers on screen: 1, 2, 3. Say she now selects 1 and 2. Commands to subtract 1, then the numbers on the screen will be: 0, 1, 3. Then she selects 1 and 3 and commands to subtract 1. Now the numbers are
0, 0, 2. Now she subtracts 2 from 2 and all the numbers become 0.

 

Dexter is not so dumb to understand that this can be done very easily, so to make a twist he will give a limit L for each N and surely L will be as minimum as possible so that it is still possible to win within L moves. But Dexter does not have time to think
how to determine L for each N, so he asks you to write a code which will take N as input and give L as output.

 

Input and Output:

Input consists of several lines each with N such that 1 ≤ N ≤ 1,000,000,000. Input will be terminated by end of file. For each N output L in separate lines.

 

SAMPLE INPUT	OUTPUT FOR SAMPLE INPUT
1 2 3	1 2 2

                                   

题意：

将序列1，2，3...n (1<=n<=10^9) 中的所有数都变为0，每一次操作可以从中选择一个或多个整数，同时减去一个相同的数，求出最小的操作数。

思路：

通过列举可以得到每一次从中间分成两边，将大的那一边减去最小的那一个可以得到最小操作数。

CODE：

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cmath>
#include <string>
#include <cstring>
#include <queue>
#include <stack>
#include <vector>
#include <set>
#include <map>
const int inf=0xfffffff;
typedef long long ll;
using namespace std;

int main()
{
int n;
while(~scanf("%d", &n)){
int ans = 0;
while(n > 0){
n /= 2;
ans ++;
}
printf("%d\n", ans);
}
return 0;
}