给定一个由N 个整数组成的数组 arr[] ,任务是对数组元素进行右移操作,将给定的数组转换为双调数组。
例子:
Input: arr[] = {7, 3, 4, 5, 3}
Output: 56 96 128 80 48
Explanation:
Perform the operation on the array elements as:
- 7 → 00000111 → 3 right shifts → 00111000 → 56
- 3 → 00000011 → 5 right shifts → 01100000 → 96
- 4 → 00000100 → 5 right shifts → 10000000 → 128
- 5 → 00000101 → 4 right shifts → 01010000 → 80
- 3 → 00000011 → 4 right shifts → 00110000 → 48
After the above operations the modified array is {56, 96, 128, 80, 48}, which is Bitonic array.
Input: arr[] = {255, 243, 23, 141, 46}
Output: -1
方法:按照给定的步骤解决问题
- 使用右移操作最大化数组的中间元素,即arr[N / 2] 。
- 遍历给定的数组arr[],通过对数组元素执行右移操作(如果需要)将数组的前半部分升序转换。
- 遍历给定的数组arr[],通过对数组元素的右移操作(如果需要)按降序转换数组的后半部分。
- 完成上述步骤后,检查数组是否是双音的。然后打印数组arr[]作为结果数组。
- 否则,打印“-1” 。
下面是上述方法的实现:
Python3
# Python program for the above approach
# Function to check if an
# array arr[] is Bitonic or not
def isPeak(arr):
# Traverse the first half of arr[]
for i in range(len(arr)//2, len(arr)-1):
if arr[i] < arr[i + 1]:
return False
# Traverse the second half of arr[]
for i in range(len(arr)//2):
if arr[i] > arr[i + 1]:
return False
# Return true if arr[] is bitonic
return True
# Function to maximize the value of N
# by performing right shift operations
def maximize(n):
Ele = n
ans = n
for idx in range(7):
# Right shift by 1
if Ele & 1:
Ele >>= 1
Ele += 2**32
else:
Ele >>= 1
# Update the value of ans
ans = max(ans, Ele)
return ans
# Function to arrange array in descending
# order by right shift operations
def makeDec(arr):
# Maximise the array arr[0]
prev = maximize(arr[0])
arr[0] = prev
# Iterate through array arr[]
for i in range(1, len(arr)):
optEle = arr[i]
# Flag to find the first
# element less than prev
flag = True
# Update Ele as arr[i]
Ele = arr[i]
for idx in range(7):
# Right shift by 1
if Ele & 1:
Ele >>= 1
Ele += 2**32
else:
Ele >>= 1
if Ele < prev and flag:
# Update the optEle
optEle = Ele
# Unset the flag
flag = False
if Ele < prev:
# Update the optEle
optEle = max(optEle, Ele)
# Update the array arr[i]
arr[i] = optEle
# Update the value of prev
prev = arr[i]
# Return the array
return arr
# Function to find the peak
# element of the array arr[]
def makePeak(arr):
# First half of the array
first = arr[:len(arr)//2 + 1]
first.reverse()
# Second half of the array
second = arr[len(arr)//2:]
# Merg both halves
ans = makeDec(first)[::-1] + makeDec(second)[1:]
# Function Call
if isPeak(ans):
return ans
return -1
# Driver Code
# Given array
arr = [7, 3, 4, 5, 3]
# Function Call
print(makePeak(arr))
输出:
[1879048192, 3221225472, 4294967296, 2684354560, 1610612736]
时间复杂度: O(N * log(M)),其中 M 是arr[]的最大元素。
辅助空间: O(1)
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