Algorithms & data structures
Classic patterns — search, sort, stacks, queues, and practical complexity-aware code.
Container With Most Water: Two-Pointer Solution in Python
Find the maximum water a container can hold from a list of heights using an efficient two-pointer technique in O(n) time.
from typing import List
def max_water_container(heights: List[int]) -> int:
left, right = 0, len(heights) - 1
max_area = 0
while left < right:
width = right - left
height = min(heights[left], heights[right])
area = width * height
max_area = max(max_area, area)
…Find Minimum in Rotated Sorted List in Python
Uses binary search to find the minimum element in a rotated sorted list in O(log n) time.
def find_min(nums):
left, right = 0, len(nums) - 1
while left < right:
mid = (left + right) // 2
if nums[mid] > nums[right]:
left = mid + 1
else:
right = mid
return nums[left]
if __name__ == "__main__":
rotated = [4, 5, 6, 7, 0, 1, 2]
print(f"Minimu…Find Missing Numbers, Duplicates, and Ranges in Python
Analyze a list to identify missing numbers, duplicate values, and contiguous ranges using sets and the Counter class.
def find_missing_duplicates_ranges(numbers):
"""Find missing numbers, duplicates, and ranges in a list."""
from collections import Counter
if not numbers:
return {"missing": [], "duplicates": [], "ranges": []}
full_range = set(range(min(numbers), max(numbers) + 1))
present = set(n…Find the Duplicate Number in Python Using Floyd's Cycle Detection
Detects the duplicate integer in an array of n+1 numbers (values 1 to n) in O(n) time and O(1) space using Floyd's cycle detection algorithm applied to a linked-list model.
def find_duplicate(nums):
slow = nums[0]
fast = nums[0]
# Phase 1: Find intersection point of the cycle
while True:
slow = nums[slow]
fast = nums[nums[fast]]
if slow == fast:
break
# Phase 2: Find the start of the cycle (the duplicate)
slow = nums[0…Find two unique numbers in an array with Python
Returns the two numbers that appear exactly once in a list where every other number appears twice, using XOR bit manipulation.
def find_two_odd(arr):
"""Return the two numbers that appear exactly once, while all others appear twice."""
xor_all = 0
for num in arr:
xor_all ^= num
# xor_all now equals the XOR of the two unique numbers.
# Find a set bit (any bit where they differ).
diff_bit = xor_all & (-xor_all)
…How to Evaluate RPN Expressions in Python
Use a stack to evaluate Reverse Polish Notation token lists with a dictionary of operator lambdas, truncating division toward zero.
def eval_rpn(tokens):
stack = []
ops = {
'+': lambda a, b: a + b,
'-': lambda a, b: a - b,
'*': lambda a, b: a * b,
'/': lambda a, b: int(a / b) # truncate toward zero
}
for token in tokens:
if token in ops:
b = stack.pop()
a = stack.pop(…How to Find Intersection of Two Sorted Interval Lists in Python
A two-pointer algorithm that finds all overlapping intervals between two sorted lists of intervals.
def interval_intersection(list1, list2):
i = j = 0
result = []
while i < len(list1) and j < len(list2):
# Find the overlap between current intervals
lo = max(list1[i][0], list2[j][0])
hi = min(list1[i][1], list2[j][1])
# If there's an overlap, add it to result
…How to Find the Next Greater Element for Each List Item in Python
Use a monotonic stack to find the next greater element to the right for every item in a list, in O(n) time.
def next_greater_element(nums):
result = [-1] * len(nums)
stack = []
for i in range(len(nums) - 1, -1, -1):
while stack and stack[-1] <= nums[i]:
stack.pop()
result[i] = stack[-1] if stack else -1
stack.append(nums[i])
return result
if __name__ == "__main…How to Find the Previous Smaller Element in Python
Use a monotonic stack to find the nearest smaller element to the left of each item in a list, returning -1 when none exists.
from collections import deque
def previous_smaller_elements(arr):
stack = deque()
result = [-1] * len(arr)
for i in range(len(arr)):
while stack and arr[stack[-1]] >= arr[i]:
stack.pop()
if stack:
result[i] = arr[stack[-1]]
stack.append(i)
return resul…How to Find the n Smallest Items in a Large List with heapq in Python
This code demonstrates how to efficiently extract the n smallest items from a large list using Python's heapq module and a manual max-heap approach.
import heapq
def n_smallest_iterable(data, n):
"""Return the n smallest items without loading the whole list."""
if n <= 0:
return []
return heapq.nsmallest(n, data)
def n_smallest_manual(data, n):
"""Return the n smallest using a heap, O(n log k) time."""
if n <= 0:
return []
…How to Generate a Power Set in Python with Bitmasks
Generate the power set of a small list using a bitmask approach, producing all possible subsets.
def power_set(items):
"""Generate the power set of a list using bitmask approach."""
n = len(items)
result = []
for mask in range(1 << n):
subset = []
for i in range(n):
if mask & (1 << i):
subset.append(items[i])
result.append(subset)
r…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 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…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…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…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]
…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…Set Matrix Zeroes in Python: Markers List Grid Demo
Given a matrix, this code finds all rows and columns that contain a zero and sets every element in those rows and columns to zero, using boolean marker arrays.
def set_zeroes(matrix):
rows, cols = len(matrix), len(matrix[0])
row_markers = [False] * rows
col_markers = [False] * cols
# First pass: record which rows and columns contain zeros
for i in range(rows):
for j in range(cols):
if matrix[i][j] == 0:
row_markers[i] …Browse by section
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