一道经典B（打）F（表）S（题）之“Find The Multiple”

最新推荐文章于 2020-02-17 00:26:49 发布

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原文链接：http://www.cnblogs.com/love-fromAtoZ/p/7551264.html

文章标签：

#c/c++ #java

本文探讨了一种使用广度优先搜索(BFS)策略解决特定数学问题的方法，即寻找一个正整数n的倍数m，且m仅由0和1组成。通过对比两种不同的实现方式，一种是直接使用BFS算法，另一种是预先计算并存储所有可能的解，展示了如何在时间和空间复杂度之间做出权衡。

题目：

　　　Given a positive integer n, write a program to find out a nonzero multiple m of n whose decimal representation contains only the digits 0 and 1.

　　　You may assume that n is not greater than 200 and there is a corresponding m containing no more than 100 decimal digits.

　　　The input file may contain multiple test cases. Each line contains a value of n (1 <= n <= 200). A line containing a zero terminates the input.

　　　For each value of n in the input print a line containing the corresponding value of m. The decimal representation of m must not contain more than 100 digits. If there are multiple solutions for a given value of n, any one of them is acceptable.

　　Sample Input

　　Sample Output

　　　　100100100100100100

　　　　111111111111111111

题目大意：

　　输入一个不超过200的整数 n，找出一个整数 m 使得 m 是 n 的整数倍，而且 m 只能由 0 和 1 组成。

解题思路：

　　一道经典的BFS。

　　一开始我们可能会认为这道题的结果很大，long 型存不下，但是我用程序实际跑了一下，发现 long 是能存下的，c++应该是unsign long long能存下。

　　所以就交了几次，一发超时，一发超内存。。。。十分尴尬。

　　然后我就特么的 打了个表。。。了个表。。。个表。。。表。。。

超内存代码（BFS思想，java语言）：

 1 import java.util.*;
 2 import java.math.BigInteger;
 3 public class Main{
 4 
 5     public static void main(String[] args){
 6         Scanner sc = new Scanner(System.in);
 7         while(sc.hasNext()){
 8             int n = sc.nextInt();
 9             if(n == 0){break;}
10             Queue<String> m = new LinkedList<String>();
11             m.offer("1");
12             long p = Long.valueOf(m.peek());
13             while(p % n != 0){
14                 String t = m.peek();
15                 m.poll();
16                 m.offer(t + "0");
17                 m.offer(t + "1");
18                 p = Long.valueOf(m.peek());
19             }    
20             System.out.println(m.peek());
21         }
22     }
23 }

AC代码（打表）：

  1 import java.util.*;
  2 import java.math.BigInteger;
  3 public class POJ1426{
  4     
  5     static String list[] = {
  6         "1",
  7         "10",
  8         "111",
  9         "100",
 10         "10",
 11         "1110",
 12         "1001",
 13         "1000",
 14         "111111111",
 15         "10",
 16         "11",
 17         "11100",
 18         "1001",
 19         "10010",
 20         "1110",
 21         "10000",
 22         "11101",
 23         "1111111110",
 24         "11001",
 25         "100",
 26         "10101",
 27         "110",
 28         "110101",
 29         "111000",
 30         "100",
 31         "10010",
 32         "1101111111",
 33         "100100",
 34         "1101101",
 35         "1110",
 36         "111011",
 37         "100000",
 38         "111111",
 39         "111010",
 40         "10010",
 41         "11111111100",
 42         "111",
 43         "110010",
 44         "10101",
 45         "1000",
 46         "11111",
 47         "101010",
 48         "1101101",
 49         "1100",
 50         "1111111110",
 51         "1101010",
 52         "10011",
 53         "1110000",
 54         "1100001",
 55         "100",
 56         "100011",
 57         "100100",
 58         "100011",
 59         "11011111110",
 60         "110",
 61         "1001000",
 62         "11001",
 63         "11011010",
 64         "11011111",
 65         "11100",
 66         "100101",
 67         "1110110",
 68         "1111011111",
 69         "1000000",
 70         "10010",
 71         "1111110",
 72         "1101011",
 73         "1110100",
 74         "10000101",
 75         "10010",
 76         "10011",
 77         "111111111000",
 78         "10001",
 79         "1110",
 80         "11100",
 81         "1100100",
 82         "1001",
 83         "101010",
 84         "10010011",
 85         "10000",
 86         "1111111101",
 87         "111110",
 88         "101011",
 89         "1010100",
 90         "111010",
 91         "11011010",
 92         "11010111",
 93         "11000",
 94         "11010101",
 95         "1111111110",
 96         "1001",
 97         "11010100",
 98         "10000011",
 99         "100110",
100         "110010",
101         "11100000",
102         "11100001",
103         "11000010",
104         "111111111111111111",
105         "100",
106         "101",
107         "1000110",
108         "11100001",
109         "1001000",
110         "101010",
111         "1000110",
112         "100010011",
113         "110111111100",
114         "1001010111",
115         "110",
116         "111",
117         "10010000",
118         "1011011",
119         "110010",
120         "1101010",
121         "110110100",
122         "10101111111",
123         "110111110",
124         "100111011",
125         "111000",
126         "11011",
127         "1001010",
128         "10001100111",
129         "11101100",
130         "1000",
131         "11110111110",
132         "11010011",
133         "10000000",
134         "100100001",
135         "10010",
136         "101001",
137         "11111100",
138         "11101111",
139         "11010110",
140         "11011111110",
141         "11101000",
142         "10001",
143         "100001010",
144         "110110101",
145         "100100",
146         "10011",
147         "100110",
148         "1001",
149         "1111111110000",
150         "11011010",
151         "100010",
152         "1100001",
153         "11100",
154         "110111",
155         "11100",
156         "1110001",
157         "11001000",
158         "10111110111",
159         "10010",
160         "1110110",
161         "1010100",
162         "10101101011",
163         "100100110",
164         "100011",
165         "100000",
166         "11101111",
167         "11111111010",
168         "1010111",
169         "1111100",
170         "1111110",
171         "1010110",
172         "11111011",
173         "10101000",
174         "10111101",
175         "111010",
176         "1111011111",
177         "110110100",
178         "1011001101",
179         "110101110",
180         "100100",
181         "110000",
182         "100101111",
183         "110101010",
184         "11010111",
185         "11111111100",
186         "1001111",
187         "10010",
188         "100101",
189         "110101000",
190         "1110",
191         "100000110",
192         "1001011",
193         "1001100",
194         "1010111010111",
195         "110010",
196         "11101111",
197         "111000000",
198         "11001",
199         "111000010",
200         "101010",
201         "110000100",
202         "1101000101",
203         "1111111111111111110",
204         "111000011",
205         "1000"
206     };
207     public static void main(String[] args){
208         Scanner sc = new Scanner(System.in);
209         while(sc.hasNext()){
210             int n = sc.nextInt();
211             if(n == 0){break;}
212             System.out.println(list[n - 1]);
213         }
214     }
215 }