在本文中，我們將學習一個Python程序，用於對陣列進行波形排序。
假設我們有一個未排序的輸入陣列。我們現在將以波形的方式對輸入數組進行排序。若陣列'arr [0..n-1]' 滿足arr [0] >= arr [1] = arr [3] = . ....，則該數組被排序為波形。
以下是用於完成此任務的各種方法 &miinus;
使用內建的sort()函數
Without Using Built-in functions
Following are the Algorithms/steps to be followed to perform the desired task. −
建立一個函數來依照波形對輸入陣列進行排序，接受輸入陣列和陣列長度作為參數。
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() 函數（傳回物件中的項目數）來取得輸入陣列的長度。
Call the above-defined sortingInWaveform() function by passing the input array, and length of the array as arguments
#使用for迴圈遍歷陣列的所有元素
Print the current element of an array.
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 arguments
def 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 array
inputArray = [12, 45, 15, 4, 6, 70, 68, 3, 25]
# getting the length of the input array
arrayLength = len(inputArray)
# printing the given array/list
print("The Given list is:", inputArray)
# calling the above defined sortingInWaveform() function by
# passing input array, length of the array as arguments
sortingInWaveform(inputArray, arrayLength)
print("The Result Array after sorting in wave form is:")
# traversing through all the elements of the array
for k in range(0, arrayLength):
# printing the current element of the array/list
print(inputArray[k], end=" ")
#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.
若應用O(nLogn)的排序演算法，如Merge Sort，Heap Sort等，上述給出的方法的時間複雜度為O(nLogn)。
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條件語句來檢查目前偶數索引元素是否小於前一個元素。
Swap the elements if the condition is true.
#使用 if 條件語句 來檢查目前偶數索引元素是否小於下一個元素。
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迴圈遍歷陣列的元素。
Print the corresponding element of the array/list.
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 arguments
def 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 array
inputArray = [12, 45, 15, 4, 6, 70, 68, 3, 25]
# getting the length of the input array
arrayLength = len(inputArray)
print("The Given list is:", inputArray)
# calling the above defined sortingInWaveform() function by
# passing input array, length of the array as arguments
sortingInWaveform(inputArray, arrayLength)
print("The Result Array after sorting in wave form is:")
# traversing through all the elements of the array
for k in range(0, arrayLength):
# printing the current element
print(inputArray[k], end=" ")
#執行上述程式後，將產生以下輸出 -
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
時間複雜度 - 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.
在本文中，我們學習如何使用兩種不同的方法對給定的波形陣列進行排序。我們使用了一種新的邏輯，它的時間複雜度比第一種方法降低了O(log N)。在許多情況下，這些類型的演算法有助於減少時間複雜度並實施有效的解決方案。
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