hdu 5703 Desert

                                                    Desert

                                                        Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65535/32768 K (Java/Others)
                                                        Total Submission(s): 976    Accepted Submission(s): 712

Problem Description

A tourist gets lost in the desert with n liters of water. He drinks positive integer units of water each day.

Write a program to calculate how many different ways the tourist can drink up the water.

 

Input

The first line contains the number of test cases T(T≤10).
Next T lines contain the number n(1≤n≤1000000) for each test case.

 

Output

Output consists of T lines.
Each line contains the binary number which represents number of different ways to finish up the water specified in the test case.

 

Sample Input

13

 

Sample Output

100
Hint
3 liters of water can be comsumed in four different ways show in the following.  1. 1 1 1  2. 1 2  3. 2 1  4. 3  If we write 4 in binary, it's 100.
 

 简要题意及分析：

一个人有n升水，每天喝掉k（k<=n）升水，问一共有多少种不同的方法。

采用隔板法，把正整数n拆分成n个1，然后产生n-1的空，向这些空插入隔板，共有C（n-1，0）+C（n-1，1）+C（n-1，2）...+C（n-1，n-1）=pow（2，n-1）种方法。

注意数据规模过大，而且题目要求输出二进制数。由于2的整数幂的二进制表示具有特殊性，即2^n-1用二进制表示即为1后面跟着n-1个0，循环输出即可。

#include <iostream>#include <stdio.h>#include <string.h>#include <algorithm>#include <queue>using namespace std;int main(){    int T;    scanf("%d",&T);    while(T--)    {        int n;        scanf("%d",&n);        int i;        for(i=0;i<n;++i)        printf("%d",i==0?1:0);        printf("\n");    }    return 0;}