从 1 到 n 生成二进制数的有趣方法
给定一个数 n，编写一个函数来生成并打印所有二进制数，其十进制值从 1 到 n。
例子：
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Input: n = 2
Output: 1, 10
Input: n = 5
Output: 1, 10, 11, 100, 101朴素的方法——
一个简单的方法是运行一个从 1 到 n 的循环，在循环内部调用十进制到二进制。
有效的方法——
下面是一个有趣的方法，它使用队列数据结构来打印二进制数。感谢 Vivek 提出这种方法。
1) Create an empty queue of strings
2) Enqueue the first binary number "1" to queue.
3) Now run a loop for generating and printing n binary numbers.
......a) Dequeue and Print the front of queue.
......b) Append "0" at the end of front item and enqueue it.
......c) Append "1" at the end of front item and enqueue it.以下是上述算法的实现。
C++
// C++ program to generate binary numbers from 1 to n
#include
using namespace std;
// This function uses queue data structure to print binary
// numbers
void generatePrintBinary(int n)
{
// Create an empty queue of strings
queue q;
// Enqueue the first binary number
q.push("1");
// This loops is like BFS of a tree with 1 as root
// 0 as left child and 1 as right child and so on
while (n--) {
// print the front of queue
string s1 = q.front();
q.pop();
cout << s1 << "\n";
string s2 = s1; // Store s1 before changing it
// Append "0" to s1 and enqueue it
q.push(s1.append("0"));
// Append "1" to s2 and enqueue it. Note that s2
// contains the previous front
q.push(s2.append("1"));
}
}
// Driver program to test above function
int main()
{
int n = 10;
generatePrintBinary(n);
return 0;
} Java
// Java program to generate binary numbers from 1 to n
import java.util.LinkedList;
import java.util.Queue;
public class GenerateBNo {
// This function uses queue data structure to print
// binary numbers
static void generatePrintBinary(int n)
{
// Create an empty queue of strings
Queue q = new LinkedList();
// Enqueue the first binary number
q.add("1");
// This loops is like BFS of a tree with 1 as root
// 0 as left child and 1 as right child and so on
while (n-- > 0) {
// print the front of queue
String s1 = q.peek();
q.remove();
System.out.println(s1);
// Store s1 before changing it
String s2 = s1;
// Append "0" to s1 and enqueue it
q.add(s1 + "0");
// Append "1" to s2 and enqueue it. Note that s2
// contains the previous front
q.add(s2 + "1");
}
}
// Driver program to test above function
public static void main(String[] args)
{
int n = 10;
generatePrintBinary(n);
}
}
// This code is contributed by Sumit Ghosh Python
# Python program to generate binary numbers from
# 1 to n
# This function uses queu data structure to print binary numbers
def generatePrintBinary(n):
# Create an empty queue
from Queue import Queue
q = Queue()
# Enqueu the first binary number
q.put("1")
# This loop is like BFS of a tree with 1 as root
# 0 as left child and 1 as right child and so on
while(n > 0):
n -= 1
# Print the front of queue
s1 = q.get()
print s1
s2 = s1 # Store s1 before changing it
# Append "0" to s1 and enqueue it
q.put(s1+"0")
# Append "1" to s2 and enqueue it. Note that s2
# contains the previous front
q.put(s2+"1")
# Driver program to test above function
n = 10
generatePrintBinary(n)
# This code is contributed by Nikhil Kumar Singh(nickzuck_007)C#
// C# program to generate binary
// numbers from 1 to n
using System;
using System.Collections.Generic;
class GFG {
// This function uses queue data
// structure to print binary numbers
public static void generatePrintBinary(int n)
{
// Create an empty queue of strings
LinkedList q = new LinkedList();
// Enqueue the first binary number
q.AddLast("1");
// This loops is like BFS of a tree
// with 1 as root 0 as left child
// and 1 as right child and so on
while (n-- > 0) {
// print the front of queue
string s1 = q.First.Value;
q.RemoveFirst();
Console.WriteLine(s1);
// Store s1 before changing it
string s2 = s1;
// Append "0" to s1 and enqueue it
q.AddLast(s1 + "0");
// Append "1" to s2 and enqueue it.
// Note that s2 contains the previous front
q.AddLast(s2 + "1");
}
}
// Driver Code
public static void Main(string[] args)
{
int n = 10;
generatePrintBinary(n);
}
}
// This code is contributed by Shrikant13 Javascript
输出
1
10
11
100
101
110
111
1000
1001
1010时间复杂度： O(n)