在本文中，我们将学习一个Python程序，用于对数组进行波形排序。
假设我们有一个未排序的输入数组。我们现在将以波形的方式对输入数组进行排序。如果数组 ‘arr [0..n-1]’ 满足 arr [0] >= arr [1] = arr [3] = …..，则该数组被排序为波形。
Methods Used
以下是用于完成此任务的各种方法 &miinus;
使用内置的sort()函数
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Without Using Built-in functions
Method 1: Using the Built-in sort() function
算法（步骤）
Following are the Algorithms/steps to be followed to perform the desired task. −
创建一个函数来按照波形对输入数组进行排序，接受输入数组和数组长度作为参数。
Use the sort() function(sorts the list in ascending/descending order ) to sort the input array in ascending order.
Use the for loop to traverse till the array length alternatively(step=2)
Swap the adjacent elements i.e, current and its next using the ‘,’ operator.
Create a variable to store the input array.
使用 len() 函数（返回对象中的项目数）来获取输入数组的长度。
Call the above-defined sortingInWaveform() function by passing the input array, and length of the array as arguments
使用for循环遍历数组的所有元素
Print the current element of an array.
Example
The following program sorts the input array in waveform using the python Built-in sort() function −
# creating a function to sort the array in waveform by accepting# the input array, array length as argumentsdef sortingInWaveform(inputArray, arrayLength): # sorting the input array in ascending order using the sort() function inputArray.sort() # travsersing till the array length alternatively(step=2) for k in range(0, arrayLength-1, 2): # swapping the adjacent elements i.e, current and it's next inputArray[k], inputArray[k+1] = inputArray[k+1], inputArray[k]# input arrayinputArray = [12, 45, 15, 4, 6, 70, 68, 3, 25]# getting the length of the input arrayarrayLength = len(inputArray)# printing the given array/listprint("The Given list is:", inputArray)# calling the above defined sortingInWaveform() function by# passing input array, length of the array as argumentssortingInWaveform(inputArray, arrayLength)print("The Result Array after sorting in wave form is:")# traversing through all the elements of the arrayfor k in range(0, arrayLength): # printing the current element of the array/list print(inputArray[k], end=" ")
Output
On execution, the above program will generate the following output &miinus;
The Given list is: [12, 45, 15, 4, 6, 70, 68, 3, 25]The Result Array after sorting in wave form is:4 3 12 6 25 15 68 45 70
Time complexity − O(nLogn).
Here, the array that was given was sorted using the sort function, which typically has an O(NlogN) time complexity.
如果应用O(nLogn)的排序算法，如Merge Sort，Heap Sort等，上述给出的方法的时间复杂度为O(nLogn)。
方法2：只使用一个循环
算法（步骤）
Following are the Algorithms/steps to be followed to perform the desired task. −
Use the for loop to traverse through all the even index elements by passing 0, array length, and step value as arguments
使用if条件语句来检查当前偶数索引元素是否小于前一个元素。
Swap the elements if the condition is true.
使用 if 条件语句 来检查当前偶数索引元素是否小于下一个元素。
Swap the elements if the condition is true.
Call the above-defined sortingInWaveform() function by passing the input array, and length of the array as arguments
使用for循环遍历数组的元素。
Print the corresponding element of the array/list.
Example
The following program sorts the input array in wave form using only one for loop and without Built-in functions −
# creating a function to sort the array in waveform by accepting# the input array, array length as argumentsdef sortingInWaveform(inputArray, arrayLength): # traversing through all the even index elements for p in range(0, arrayLength, 2): # checking whether the current even index element # is smaller than the previous if (p > 0 and inputArray[p] < inputArray[p-1]): # swapping the elements if the condition is true inputArray[p], inputArray[p-1] = inputArray[p-1], inputArray[p] # checking whether the current even index element # is smaller than the next element if (p < arrayLength-1 and inputArray[p] < inputArray[p+1]): # swapping the elements if the condition is true inputArray[p], inputArray[p+1] = inputArray[p+1], inputArray[p]# input arrayinputArray = [12, 45, 15, 4, 6, 70, 68, 3, 25]# getting the length of the input arrayarrayLength = len(inputArray)print("The Given list is:", inputArray)# calling the above defined sortingInWaveform() function by# passing input array, length of the array as argumentssortingInWaveform(inputArray, arrayLength)print("The Result Array after sorting in wave form is:")# traversing through all the elements of the arrayfor k in range(0, arrayLength): # printing the current element print(inputArray[k], end=" ")
Output
执行上述程序后，将生成以下输出 –
The Given list is: [12, 45, 15, 4, 6, 70, 68, 3, 25]The Result Array after sorting in wave form is:45 12 15 4 70 6 68 3 25
时间复杂度 – O(n)。
Here, we didn’t use the sort function; instead, we just used the for loop to iterate through the elements of the given array, which, on average, has O(N) time complexity.
结论
在本文中，我们学习了如何使用两种不同的方法对给定的波形数组进行排序。我们使用了一种新的逻辑，它的时间复杂度比第一种方法降低了O(log N)。在许多情况下，这些类型的算法有助于减少时间复杂度并实施有效的解决方案。
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