Three way partitioning of an array around a given range – Python

When working with arrays or lists in Python, sometimes we need to partition the elements into three separate groups based on a given range. The goal is to rearrange the elements such that:

1. Elements smaller than the lower bound of the range come first.
2. Elements within the range come next.
3. Elements greater than the upper bound of the range appear last.

Let’s explore various methods to achieve this using Python.

Using List Comprehension

We can efficiently use list comprehension to create three separate partitions in a single step.

# Input array and range
arr = [12, 5, 18, 7, 30, 15, 2, 9]
low, high = 10, 20

# Three-way partitioning using list comprehension
res = [x for x in arr if x < low] + [x for x in arr if low <= x <= high] + [x for x in arr if x > high]
print(res) 

[5, 7, 2, 9, 12, 18, 15, 30]

Explanation:

• We use three list comprehensions to filter elements less than low, within the range [low, high] and greater than high.
• final result is obtained by concatenating the three partitions.

Let’s explore some more methods and see how we can do three way partitioning of an array around a given range.

Using filter()

We can also use the function filter() function to create three separate partitions and concatenate them.

# Input array and range
arr = [12, 5, 18, 7, 30, 15, 2, 9]
low, high = 10, 20

# Create partitions using filter
less = list(filter(lambda x: x < low, arr))
within = list(filter(lambda x: low <= x <= high, arr))
greater = list(filter(lambda x: x > high, arr))

# Combine the partitions
res = less + within + greater
print(res) 

[5, 7, 2, 9, 12, 18, 15, 30]

Explanation:

• We use filter() with lambda functions to extract elements for each partition.
• Finally, we concatenate the partitions to get the desired result.

Using For Loop

This method uses a for loop to traverse the array and append elements into three separate lists based on the range.

# Input array and range
arr = [12, 5, 18, 7, 30, 15, 2, 9]
low, high = 10, 20

# Initialize lists for three partitions
less, within, greater = [], [], []

# Traverse and partition elements
for x in arr:
    if x < low:
        less.append(x)
    elif low <= x <= high:
        within.append(x)
    else:
        greater.append(x)

# Combine the partitions
res = less + within + greater
print(res)  

[5, 7, 2, 9, 12, 18, 15, 30]

Explanation:

• We iterate through the array and append elements to less, within or greater based on their values.
• Finally, we combine the three lists to form the partitioned array.

Using a Single Loop with In-place Rearrangement

This method modifies the array in-place without using additional space for separate lists.

# Input array and range
arr = [12, 5, 18, 7, 30, 15, 2, 9]
low, high = 10, 20

# Initialize pointers
start, mid, end = 0, 0, len(arr) - 1

# Partition the array in place
while mid <= end:
    if arr[mid] < low:
        arr[start], arr[mid] = arr[mid], arr[start]
        start += 1
        mid += 1
    elif low <= arr[mid] <= high:
        mid += 1
    else:
        arr[mid], arr[end] = arr[end], arr[mid]
        end -= 1
print(arr)  

[5, 7, 9, 2, 18, 15, 12, 30]

Explanation:

• The method uses three pointers to rearrange the array in one traversal.
• start trackselements less than low, mid tracks elements within the range, and end tracks elements greater than high.