给定一个由N 个整数组成的数组arr[] ，任务是使用冒泡排序而不使用循环对给定数组进行排序。
例子：
Input: arr[] = {1, 3, 4, 2, 5}
Output: 1 2 3 4 5
Input: arr[] = {1, 3, 4, 2}
Output: 1 2 3 4
方法：不使用循环实现冒泡排序的想法基于以下观察：
- 冒泡排序的排序算法执行以下步骤：
- 外循环遍历给定数组(N – 1)次。
- 如果arr[i] > arr[i + 1] ，则内部循环遍历数组并交换两个相邻元素，对于[0, N – 1]范围内的每个i 。
- 可以观察到，在每一个N – 1迭代中，在范围中的最大元素[0，N – 1 – i]于转换到位置(N – 1 – i)用于每个i在范围[0，N – 1 ] 。
- 因此，想法是使用递归来避免循环。
请按照以下步骤解决问题：
- 考虑以下基本情况：
- 如果数组包含单个元素，只需打印数组。
- 如果数组包含两个元素，交换这对元素(如果需要)以获得数组元素的排序序列。打印排序后的数组。
- 将当前数组中的前两个元素存储在变量中，例如a和b 。
- 初始化一个数组，比如bs[] ，以存储剩余的数组元素。
- 将a和b中较小的值放在当前数组的前面。
- 使用通过将bs[]附加到a和b 中较大值的末尾而形成的新数组递归重复上述步骤。
- 将返回的排序列表存储在一个变量中，比如res[] 。
- 现在，使用通过将res[] (不包括最后一个元素)附加到 res[res.size() – 1](最后一个元素)的末尾而形成的新数组递归重复上述步骤。
- 完成上述步骤后，打印返回的列表。
下面是上述方法的实现：
C++
// C++ program for the above approach
#include
using namespace std;
// Function to implement bubble
// sort without using loops
vector bubble_sort(vector ar)
{
// Base Case: If array
// contains a single element
if (ar.size() <= 1)
return ar;
// Base Case: If array
// contains two elements
if (ar.size() == 2){
if(ar[0] < ar[1])
return ar;
else
return {ar[1], ar[0]};
}
// Store the first two elements
// of the list in variables a and b
int a = ar[0];
int b = ar[1];
// Store remaining elements
// in the list bs
vector bs;
for(int i = 2; i < ar.size(); i++)
bs.push_back(ar[i]);
// Store the list after
// each recursive call
vector res;
// If a < b
if (a < b){
vector temp1;
temp1.push_back(b);
for(int i = 0; i < bs.size(); i++)
temp1.push_back(bs[i]);
vector v = bubble_sort(temp1);
v.insert(v.begin(), a);
res = v;
}
// Otherwise, if b >= a
else{
vector temp1;
temp1.push_back(a);
for(int i = 0; i < bs.size(); i++)
temp1.push_back(bs[i]);
vector v = bubble_sort(temp1);
v.insert(v.begin(), b);
res = v;
}
// Recursively call for the list
// less than the last element and
// and return the newly formed list
vector pass;
for(int i = 0; i < res.size() - 1; i++)
pass.push_back(res[i]);
vector ans = bubble_sort(pass);
ans.push_back(res[res.size() - 1]);
return ans;
}
// Driver Code
int main()
{
vector arr{1, 3, 4, 5, 6, 2};
vector res = bubble_sort(arr);
// Print the array
for(int i = 0; i < res.size(); i++)
cout << res[i] << " ";
}
// This code is contributed by ipg2016107. Java
// java program for the above approach
import java.io.*;
import java.lang.*;
import java.util.*;
class GFG {
// Function to implement bubble
// sort without using loops
static ArrayList bubble_sort(ArrayList ar)
{
// Base Case: If array
// contains a single element
if (ar.size() <= 1)
return ar;
// Base Case: If array
// contains two elements
if (ar.size() == 2) {
if (ar.get(0) < ar.get(1))
return ar;
else
return new ArrayList(
Arrays.asList(ar.get(1), ar.get(0)));
}
// Store the first two elements
// of the list in variables a and b
int a = ar.get(0);
int b = ar.get(1);
// Store remaining elements
// in the list bs
ArrayList bs = new ArrayList<>();
for (int i = 2; i < ar.size(); i++)
bs.add(ar.get(i));
// Store the list after
// each recursive call
ArrayList res = new ArrayList<>();
// If a < b
if (a < b) {
ArrayList temp1 = new ArrayList<>();
temp1.add(b);
for (int i = 0; i < bs.size(); i++)
temp1.add(bs.get(i));
ArrayList v = bubble_sort(temp1);
v.add(0, a);
res = v;
}
// Otherwise, if b >= a
else {
ArrayList temp1 = new ArrayList<>();
temp1.add(a);
for (int i = 0; i < bs.size(); i++)
temp1.add(bs.get(i));
ArrayList v = bubble_sort(temp1);
v.add(0, b);
res = v;
}
// Recursively call for the list
// less than the last element and
// and return the newly formed list
ArrayList pass = new ArrayList<>();
for (int i = 0; i < res.size() - 1; i++)
pass.add(res.get(i));
ArrayList ans = bubble_sort(pass);
ans.add(res.get(res.size() - 1));
return ans;
}
// Driver Code
public static void main(String[] args)
{
ArrayList arr = new ArrayList(
Arrays.asList(1, 3, 4, 5, 6, 2));
ArrayList res = bubble_sort(arr);
// Print the array
for (int i = 0; i < res.size(); i++)
System.out.print(res.get(i) + " ");
}
}
// This code is contributed by Kingash. Python3
# Python3 program for the above approach
# Function to implement bubble
# sort without using loops
def bubble_sort(ar):
# Base Case: If array
# contains a single element
if len(ar) <= 1:
return ar
# Base Case: If array
# contains two elements
if len(ar) == 2:
return ar if ar[0] < ar[1] else [ar[1], ar[0]]
# Store the first two elements
# of the list in variables a and b
a, b = ar[0], ar[1]
# Store remaining elements
# in the list bs
bs = ar[2:]
# Store the list after
# each recursive call
res = []
# If a < b
if a < b:
res = [a] + bubble_sort([b] + bs)
# Otherwise, if b >= a
else:
res = [b] + bubble_sort([a] + bs)
# Recursively call for the list
# less than the last element and
# and return the newly formed list
return bubble_sort(res[:-1]) + res[-1:]
# Driver Code
arr = [1, 3, 4, 5, 6, 2]
res = bubble_sort(arr)
# Print the array
print(*res)C#
// C# program for the above approach
using System;
using System.Collections.Generic;
class GFG{
// Function to implement bubble
// sort without using loops
static List bubble_sort(List ar)
{
// Base Case: If array
// contains a single element
List temp = new List();
if (ar.Count <= 1)
return ar;
// Base Case: If array
// contains two elements
if (ar.Count == 2)
{
if (ar[0] < ar[1])
return ar;
else
{
temp.Add(ar[1]);
temp.Add(ar[0]);
return temp;
}
}
// Store the first two elements
// of the list in variables a and b
int a = ar[0];
int b = ar[1];
// Store remaining elements
// in the list bs
List bs = new List();
for(int i = 2; i < ar.Count; i++)
bs.Add(ar[i]);
// Store the list after
// each recursive call
List res = new List();
// If a < b
if (a < b)
{
List temp1 = new List();
temp1.Add(b);
for(int i = 0; i < bs.Count; i++)
temp1.Add(bs[i]);
List v = bubble_sort(temp1);
v.Insert(0, a);
res = v;
}
// Otherwise, if b >= a
else
{
List temp1 = new List();
temp1.Add(a);
for(int i = 0; i < bs.Count; i++)
temp1.Add(bs[i]);
List v = bubble_sort(temp1);
v.Insert(0, b);
res = v;
}
// Recursively call for the list
// less than the last element and
// and return the newly formed list
List pass = new List();
for(int i = 0; i < res.Count - 1; i++)
pass.Add(res[i]);
List ans = bubble_sort(pass);
ans.Add(res[res.Count - 1]);
return ans;
}
// Driver Code
public static void Main()
{
List arr = new List{ 1, 3, 4, 5, 6, 2 };
List res = bubble_sort(arr);
// Print the array
for(int i = 0; i < res.Count; i++)
Console.Write(res[i] + " ");
}
}
// This code is contributed by ukasp 输出：
1 2 3 4 5 6时间复杂度： O(N 2 )
辅助空间： O(N)
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