Find Local Minima (Valleys) in a Numeric List in Python

This code finds indices of all local minima (valleys) in a numeric list, including edge cases, using a simple loop that compares each element with its neighbors.

Easy Python 3.9+ Aug 9, 2026 Lists & loops 14 views 0 copies

local minima valleys list loop algorithm

Python code

43 lines

Python 3.9+

def find_local_minima(numbers):
    """Find indices of local minima (valleys) in a numeric list.
    
    A value is a local minimum if it's less than or equal to its neighbors.
    Edge elements are considered minima if they're less than or equal to their single neighbor.
    """
    if not numbers:
        return []
    if len(numbers) == 1:
        return [0]
    
    minima_indices = []
    
    # Check first element
    if numbers[0] <= numbers[1]:
        minima_indices.append(0)
    
    # Check middle elements
    for i in range(1, len(numbers) - 1):
        if numbers[i] <= numbers[i - 1] and numbers[i] <= numbers[i + 1]:
            minima_indices.append(i)
    
    # Check last element
    if numbers[-1] <= numbers[-2]:
        minima_indices.append(len(numbers) - 1)
    
    return minima_indices


if __name__ == "__main__":
    test_cases = [
        [5, 2, 3, 1, 4, 2, 6],
        [1, 2, 3, 4, 5],
        [5, 4, 3, 2, 1],
        [3, 3, 3],
        [7]
    ]
    
    for i, case in enumerate(test_cases):
        indices = find_local_minima(case)
        values = [case[idx] for idx in indices]
        print(f"List {i + 1}: {case}")
        print(f"Local minima at indices {indices} with values {values}\n")

Output

stdout

List 1: [5, 2, 3, 1, 4, 2, 6]
Local minima at indices [1, 3, 5] with values [2, 1, 2]

List 2: [1, 2, 3, 4, 5]
Local minima at indices [0] with values [1]

List 3: [5, 4, 3, 2, 1]
Local minima at indices [4] with values [1]

List 4: [3, 3, 3]
Local minima at indices [0, 1, 2] with values [3, 3, 3]

List 5: [7]
Local minima at indices [0] with values [7]

How it works

The function checks each element against its immediate neighbors using <= to include plateaus. For edges, it compares with the single neighbor. A single-element list is always a local minimum. The loop iterates from index 1 to len(numbers)-2 to avoid index errors. This approach has O(n) time complexity because each element is checked exactly once.

Common mistakes

Forgetting to handle empty or single-element lists, causing index errors
Using `>` instead of `>=` to exclude equal neighbors, which would miss plateaus
Not treating edge elements as valid minima
Modifying the list while iterating over it

Variations

Use a list comprehension: `[i for i in range(len(arr)) if (i==0 or arr[i]<=arr[i-1]) and (i==len(arr)-1 or arr[i]<=arr[i+1])]`
Employ `numpy` with boolean masking for large arrays (requires numpy)

Real-world use cases

Detecting troughs in financial time series data to identify buying opportunities
Finding local minima in sensor readings to trigger alerts when conditions reach a low point
Analyzing signal data in signal processing to locate valleys for feature extraction

Find Local Minima (Valleys) in a Numeric List in Python

Python code

Output

How it works

Common mistakes

Variations

Real-world use cases

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Real-world use cases

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