Algorithms & data structures
Classic patterns — search, sort, stacks, queues, and practical complexity-aware code.
How to Rotate an Array by k Steps in Python
This code rotates a list to the right by k positions using modulo arithmetic to handle k larger than the list length.
def rotate_array(nums, k):
if not nums:
return []
n = len(nums)
k = k % n
return nums[-k:] + nums[:-k] if k else nums[:]
if __name__ == "__main__":
arr = [1, 2, 3, 4, 5, 6]
k = 2
result = rotate_array(arr, k)
print(f"Original: {arr}")
print(f"Rotated by {k}: {result}")How to Sample Random Items Without Replacement in Python
Select k random unique items from a sequence using random.sample for uniform, non-repeating selection.
import random
def sample_without_replacement(population, k):
"""Return k random items from population without replacement."""
if k > len(population):
raise ValueError("k cannot exceed population size")
# Use random.sample for O(k) time, no mutation of the original
return random.sample(populati…How to Search a Rotated Sorted List in Python
Binary search a pivot-rotated sorted list for a target value and return its index in O(log n) time.
from typing import List
def search_rotated(nums: List[int], target: int) -> int:
left, right = 0, len(nums) - 1
while left <= right:
mid = (left + right) // 2
if nums[mid] == target:
return mid
# left half is sorted
if nums[left] <= nums[mid]:
if nums[…How to Solve Daily Temperatures Days Until Warmer in Python
Compute the number of days until a warmer temperature for each day using a monotonic stack.
def daily_temperatures(temps):
n = len(temps)
result = [0] * n
stack = []
for i, temp in enumerate(temps):
while stack and temps[stack[-1]] < temp:
prev_idx = stack.pop()
result[prev_idx] = i - prev_idx
stack.append(i)
return result
if __name__ == …How to Solve the Trapping Rain Water Problem in Python
Compute the total water trapped between elevation bars using a two-pointer O(n) algorithm.
def trap(height):
if not height:
return 0
left, right = 0, len(height) - 1
left_max, right_max = 0, 0
water = 0
while left < right:
if height[left] < height[right]:
if height[left] >= left_max:
left_max = height[left]
else:
…How to Sort Array by Parity (Even Before Odd) in Python
Rearrange an array so all even numbers appear before all odd numbers using a simple two-list partition approach.
def sort_array_by_parity(nums):
"""
Rearrange the array so that all even integers come first,
followed by all odd integers. The order within even and odd
groups is not required to be sorted.
"""
even = []
odd = []
for num in nums:
if num % 2 == 0:
even.append(nu…How to Sort Colors (Dutch National Flag) in Python
In-place sorting of a list of 0s, 1s, and 2s using the Dutch National Flag algorithm with O(n) time and O(1) space.
def sort_colors(nums):
low, mid, high = 0, 0, len(nums) - 1
while mid <= high:
if nums[mid] == 0:
nums[low], nums[mid] = nums[mid], nums[low]
low += 1
mid += 1
elif nums[mid] == 1:
mid += 1
else: # nums[mid] == 2
nums[mid], n…How to Split a List by a Predicate into Two Lists in Python
Partition any Python list into two lists based on a predicate: items that match go into one list, everything else into the other.
from typing import Callable, List, TypeVar
T = TypeVar("T")
def split_by_predicate(items: List[T], predicate: Callable[[T], bool]) -> tuple[List[T], List[T]]:
matching = []
non_matching = []
for item in items:
if predicate(item):
matching.append(item)
else:
non_mat…How to compress consecutive numbers into range strings in Python
Convert a sorted list of consecutive integers into compact range strings like '1-3', '5-6', and '15'.
def compress_ranges(nums):
"""Convert a list of sorted consecutive numbers into range strings."""
if not nums:
return []
ranges = []
start = prev = nums[0]
for num in nums[1:]:
if num == prev + 1:
prev = num
else:
if start == prev:
…How to partition a list into n nearly equal parts in Python
Divide a list into n contiguous chunks of nearly equal size using an average-length calculation that distributes the remainder evenly.
def partition(lst, n):
"""Partition a list into n nearly equal contiguous parts."""
if n <= 0:
raise ValueError("n must be positive")
if not lst:
return [[] for _ in range(n)]
parts = []
avg = len(lst) / n
last_idx = 0.0
while last_idx < len(lst):
end_idx =…How to solve the stock span problem in Python
Calculate the stock span for each day's price using a monotonic stack in O(n) time.
def stock_span(prices):
span = [1] * len(prices)
stack = []
for i in range(len(prices)):
while stack and prices[stack[-1]] <= prices[i]:
stack.pop()
span[i] = i - stack[-1] if stack else i + 1
stack.append(i)
return span
if __name__ == "__main__":
pric…Implement Insert Delete GetRandom O(1) in Python
Build a RandomizedSet class that supports insert, delete, and get_random in average O(1) time using a list and a dictionary mapping values to indices.
import random
class RandomizedSet:
def __init__(self):
self.values = []
self.index_map = {}
def insert(self, val):
if val in self.index_map:
return False
self.index_map[val] = len(self.values)
self.values.append(val)
return True
def delete(self…Implement Queue Using Two Stacks in Python
Python class that implements a FIFO queue using two stacks, with enqueue, dequeue, peek, and emptiness checks.
class QueueUsingStacks:
def __init__(self):
self.stack_in = []
self.stack_out = []
def enqueue(self, value):
self.stack_in.append(value)
def dequeue(self):
if not self.stack_out:
while self.stack_in:
self.stack_out.append(self.stack_in.pop())
…Implement a Stack Using List Push Pop in Python
A minimal Stack class built on a Python list, with push, pop, peek, is_empty, and size methods, including empty-stack guards.
class Stack:
def __init__(self):
self.items = []
def push(self, item):
self.items.append(item)
def pop(self):
if self.is_empty():
raise IndexError("pop from empty stack")
return self.items.pop()
def peek(self):
if self.is_empty():
raise…Insert Multiple Values Into a Sorted List in Python
Insert multiple values into an already-sorted list while keeping it sorted using the bisect.insort function.
import bisect
def insert_sorted(sorted_list, values):
for value in values:
bisect.insort(sorted_list, value)
return sorted_list
if __name__ == "__main__":
original = [1, 3, 5, 7, 9]
new_values = [4, 6, 2, 8, 0]
result = insert_sorted(original, new_values)
print(f"Original: {original}"…Insert an Element Every n Positions in Python
Insert a given element before or after every n-th position in a Python list, returning a new list with the placements applied.
def insert_every_n(seq, element, n, position="after"):
"""Insert an element before or after every n-th position in a list.
Args:
seq: Input list
element: Element to insert
n: Insert every n positions (n > 0)
position: 'before' or 'after' (default: 'after')
Returns:
…Merge Two Sorted Arrays Without Extra Space in Python
Merge two sorted arrays in-place from the end, using the trailing zeros in the first array to avoid extra space.
def merge_sorted(arr1, arr2):
m, n = len(arr1), len(arr2)
i, j = m - 1, n - 1
while j >= 0:
if i >= 0 and arr1[i] > arr2[j]:
arr1[i + j + 1] = arr1[i]
i -= 1
else:
arr1[i + j + 1] = arr2[j]
j -= 1
return arr1
if __name__ == "__main__":
…Merge k sorted lists in Python using a heap
Merge k individually sorted lists into one sorted list in Python using a min-heap.
import heapq
def merge_k_sorted_lists(lists):
heap = []
# Push the first element of each list onto the heap
for i, lst in enumerate(lists):
if lst:
heapq.heappush(heap, (lst[0], i, 0))
result = []
while heap:
val, list_idx, elem_idx = heapq.heappop(heap)
re…Move Zeroes to End in Python Maintaining Order
In-place algorithm that moves all zeroes to the end of a list while preserving the relative order of non-zero elements.
def move_zeroes(nums):
non_zero_index = 0
for i in range(len(nums)):
if nums[i] != 0:
nums[non_zero_index], nums[i] = nums[i], nums[non_zero_index]
non_zero_index += 1
return nums
if __name__ == "__main__":
example = [0, 1, 0, 3, 12]
result = move_zeroes(example)
…Pair Elements with Next Cyclic Neighbor in Python
Create tuples pairing every element with its next element, wrapping around to the first element for the last one.
def cyclic_pairs(lst):
if not lst:
return []
return [(lst[i], lst[(i + 1) % len(lst)]) for i in range(len(lst))]
if __name__ == "__main__":
sample = [1, 2, 3, 4, 5]
result = cyclic_pairs(sample)
print(result)Product of All Elements Except Self in Python
Given a list of integers, return a list where each element is the product of all other elements except itself, using prefix and suffix products in O(n) time and O(1) extra space.
def product_except_self(nums):
n = len(nums)
result = [1] * n
left_product = 1
for i in range(n):
result[i] = left_product
left_product *= nums[i]
right_product = 1
for i in range(n - 1, -1, -1):
result[i] *= right_product
right_product *= nums[i]
…Product of Array Except Self in Python Without Division
Compute the product of all array elements except the current one in O(n) time using prefix and suffix products, without using division.
from math import prod
def product_except_self(nums):
n = len(nums)
result = [1] * n
left_product = 1
for i in range(n):
result[i] = left_product
left_product *= nums[i]
right_product = 1
for i in range(n - 1, -1, -1):
result[i] *= right_product
right_product *…Quickselect in Python: Find the kth Smallest Element
Python implementation of the Quickselect algorithm to find the kth smallest element in an unsorted list with average O(n) time complexity.
def quickselect(arr, k):
"""
Returns the k-th smallest element (0-indexed) using Quickselect.
Average: O(n), Worst: O(n^2)
"""
if len(arr) == 1:
return arr[0]
pivot = arr[-1]
left = [x for x in arr[:-1] if x <= pivot]
right = [x for x in arr[:-1] if x > pivot]
if k < len(l…Rearrange array alternately max min in Python
Rearranges a sorted list so its elements alternate between the current maximum and current minimum using two pointers in O(n) time.
def rearrange_alternately(arr):
"""
Rearrange sorted array so elements alternate: max, min, next max, next min...
Returns a new list in O(n) time using O(n) space.
"""
n = len(arr)
result = []
left, right = 0, n - 1
while left <= right:
if left == right:
result.appen…Browse by section
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