Algorithms & data structures
Classic patterns — search, sort, stacks, queues, and practical complexity-aware code.
Binary Search for Ship Capacity in Python
Use binary search to find the minimum ship capacity that can transport all packages within a given number of days.
def ship_within_days(weights, days):
def can_ship(capacity):
current = 0
needed_days = 1
for weight in weights:
if current + weight > capacity:
needed_days += 1
current = 0
current += weight
return needed_days <= days
low …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 Peak Element in Python Using Binary Search
A binary search solution that finds any peak element (an element strictly greater than its neighbors) in an unsorted array in O(log n) time.
def find_peak_element(nums):
left, right = 0, len(nums) - 1
while left < right:
mid = (left + right) // 2
if nums[mid] > nums[mid + 1]:
right = mid
else:
left = mid + 1
return left
if __name__ == "__main__":
test1 = [1, 2, 3, 1]
tes…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)
…Game of Life Next State Grid in Python
Compute the next generation of Conway's Game of Life from a 2D grid using the standard three rules with neighbor counting.
def next_state(grid):
m, n = len(grid), len(grid[0])
new = [[0] * n for _ in range(m)]
for r in range(m):
for c in range(n):
total = 0
for dr in (-1, 0, 1):
for dc in (-1, 0, 1):
if dr == 0 and dc == 0:
continue
…How to Detect Hardcoded Secrets in Python Source Code
A Python utility that scans source code for common hardcoded secrets like API keys, passwords, tokens, and AWS credentials using regex patterns.
import re
def detect_secrets(text):
"""Detect potential hardcoded secrets in source code."""
patterns = {
'api_key': r'(?i)(api[_-]?key|apikey)\s*[=:]\s*["\']([^"\']+)["\']',
'password': r'(?i)(password|passwd)\s*[=:]\s*["\']([^"\']+)["\']',
'token': r'(?i)(\b(token|secret)\b)\s*[=:]\s…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 Minimum Swaps to Sort an Array in Python
Calculate the minimum number of adjacent-free swaps needed to sort a permutation array using cycle detection in Python.
def min_swaps_to_sort(arr):
n = len(arr)
arr_pos = sorted((val, idx) for idx, val in enumerate(arr))
visited = [False] * n
swaps = 0
for i in range(n):
if visited[i] or arr_pos[i][1] == i:
continue
cycle_size = 0
j = i
while not visited[j]:
…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 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 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…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…Split Array Largest Sum in Python (Minimize Largest Subarray Sum)
Binary search + greedy check to split an array into k subarrays while minimizing the largest subarray sum.
def can_split(nums, k, max_sum):
subarrays = 1
current_sum = 0
for num in nums:
if current_sum + num <= max_sum:
current_sum += num
else:
subarrays += 1
current_sum = num
if subarrays > k:
return False
return True
def spli…Validate Sudoku Board Rows Columns and Boxes in Python
Validate a 9x9 Sudoku board by checking that each row, column, and 3x3 box contains the numbers 1 through 9 exactly once.
def validate_sudoku(board):
def is_valid_group(group):
return sorted(group) == list(range(1, 10))
def get_columns():
return [[board[r][c] for r in range(9)] for c in range(9)]
def get_boxes():
boxes = []
for box_row in range(0, 9, 3):
for box_col in range(0, 9,…Browse by section
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