尋找局部最小值和最大值

Question

Geeksforgeeks https://www.geeksforgeeks.org/find-indices-of-all-local-maxima-and-local-minima-in-an-array/的實施是錯誤的。 如果你有連續的重復，事情就會分崩離析！

Example 1: values = [ 1, 2, 3, 7, 11, 15, 13, 12, 11, 6, 5, 7, 11, 8]
    The default implementation correctly identify "15" as a peak.

Example 2: values = [ 1, 2, 3, 7, 11, 15, 15, 13, 12, 11, 6, 5, 7, 11, 8]
    The default implementation will mark "11" as local maxima because there are two consecutive 15's.

下面是來自 geekforgeeks 的代碼，突出顯示了問題 - 當與左右進行更大/更小的比較時，如果你的鄰居的值 ==，則向左或向右看：

def findLocalMaximaMinima(n, arr):

    # Empty lists to store points of
    # local maxima and minima
    mx = []
    mn = []

    # Checking whether the first point is
    # local maxima or minima or neither
    if(arr[0] > arr[1]):
        mx.append(0)
    elif(arr[0] < arr[1]):
        mn.append(0)

    # Iterating over all points to check
    # local maxima and local minima
    for i in range(1, n-1):

        # Condition for local minima
        if(arr[i-1] > arr[i] < arr[i + 1]):     <-- Problem is here
            mn.append(i)

        # Condition for local maxima
        elif(arr[i-1] < arr[i] > arr[i + 1]):    <-- Problem is here
            mx.append(i)

    # Checking whether the last point is
    # local maxima or minima or neither
    if(arr[-1] > arr[-2]):
        mx.append(n-1)
    elif(arr[-1] < arr[-2]):
        mn.append(n-1)

        # Print all the local maxima and
        # local minima indexes stored
    if(len(mx) > 0):
        print("Points of Local maxima"\
            " are : ", end ='')
        print(*mx)
    else:
        print("There are no points of"\
            " Local maxima.")

    if(len(mn) > 0):
        print("Points of Local minima"\
            " are : ", end ='')
        print(*mn)
    else:
        print("There are no points"\
            " of Local minima.")

Answer 1

這是修復方法（由於某種原因我無法在那里上傳代碼，所以在這里上傳）：

from datetime import datetime
from typing import List

def is_greater(index1, index2, values, increment_when_eq : bool):
    if values[index1]>values[index2]:
        return True
    elif values[index1]<values[index2]:
        return False
    else:
        # Case when: values[index1] == values[index2]
        index2_shifted = index2+1 if increment_when_eq else index2-1
        if index2_shifted < len(values):
            return is_greater(index1=index1, index2 = index2_shifted, values = values, increment_when_eq = increment_when_eq)
        else:
            return False
 
def find_local_max_min(values : List):
    mx = []
    mn = []

    n = len(values)
    if n==0:
        return None

    if(values[0] > values[1]):
        mx.append(0)
    elif(values[0] < values[1]):
        mn.append(0)
    
    for i in range(1, n-1):
        if (not is_greater(i, i-1, values, False) and not is_greater(i, i+1, values, True)):
            mn.append(i)
        elif(is_greater(i, i-1, values, False) and is_greater(i, i+1, values, True)):
            mx.append(i)

    if(values[-1] > values[-2]):
        mx.append(n-1)
    elif(values[-1] < values[-2]):
        mn.append(n-1)

    return {
        'local_max' : mx,
        'local_min' : mn
    }

if __name__ == '__main__':
    values = [ 1, 2, 3, 7, 11, 15, 15, 13, 12, 11, 6, 5, 7, 11 , 8, 19, 19, 18, 18, 18, 15, 7, 3]
    start = datetime.now()
    local_min_max = find_local_max_min(values)
    local_max = local_min_max['local_max']
    local_min = local_min_max['local_min']

Answer 2

我同意 Pranav 的觀點，即在進行比較時只需修復相等性即可解決問題。 修復將更加簡潔。 謝謝普拉納夫

def findLocalMaximaMinima(n, arr):
    mx = []
    mn = []

    if(arr[0] > arr[1]):
        mx.append(0)
    elif(arr[0] < arr[1]):
        mn.append(0)

    for i in range(1, n-1):
        if(arr[i-1] >= arr[i] < arr[i + 1]):
            mn.append(i)
        elif(arr[i-1] < arr[i] >= arr[i + 1]):
            mx.append(i)

    if(arr[-1] > arr[-2]):
        mx.append(n-1)
    elif(arr[-1] < arr[-2]):
        mn.append(n-1)

    return mx, mn

arrs = [[ 1, 2, 3, 7, 11, 15, 15, 13, 12, 11, 6, 5, 7, 11, 8],
[4, 5, 6, 6, 6, 4, 3, 2, 1, 3, 5, 7, 9]]
for arr in arrs:

    mx, mn = findLocalMaximaMinima(len(arr), arr)
    print(*[f"{a}, {'max'*(i in mx)}, {'min' * (i in mn)}" for i, a in enumerate(arr)], sep='\n', end='\n\n')

https://tio.run/##bVLhboIwEP7PU1z8A3V1sTqdM7onmE/A@qMZZWsCJ6mYsBifnbVXVFggQK5fv@@79u6q3/rniMu2zXQOucHs4/ilioNqTKkOBt0/QQ7KWraNwD1lA3tIZYgxxLQweeJY6VzCu6enQnaKoHpWVaUxS@aMQF08@LsRPvb4hOZHCwYMglX4rRPBAWeip@jszEy4A@zJ0dysDTzBwH6YwrD7xv1Y5LO72dwMR32ank@/EnQS0s0W47XwNxhW45H1nwYHGsKtrs8WnR1321HkRCffjhRcbRYclhxeOQi3EKvuc5BYBGzNYXUnbCSP0g0t1/S@kNxTKQjMNykj3wWXyPfB59tG3UzwMAvj81No9JdjYYxIUVmDdTJN88lFXTlc4lI18TShBpcNC5DBGKbQgciukzAEzsYjGs@ltqrW5C05nHS1jz8x5m4r85GLWdv@AQ