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 …Binary Search on Answer in Python: Koko Eating Bananas
Find the minimum eating speed so Koko finishes all banana piles within a given hour limit using binary search on the answer.
import math
def min_eating_speed(piles, h):
"""Return minimum integer eating speed K so Koko finishes within h hours."""
def hours_needed(speed):
return sum(math.ceil(p / speed) for p in piles)
low, high = 1, max(piles)
while low < high:
mid = (low + high) // 2
if hours_needed…Find All Triplets with Sum Zero in Python
This code finds all unique triplets in an array that sum to zero using a sorted array and two-pointer technique.
def find_triplets(nums):
nums.sort()
n = len(nums)
triplets = []
for i in range(n - 2):
if i > 0 and nums[i] == nums[i - 1]:
continue
left, right = i + 1, n - 1
while left < right:
total = nums[i] + nums[left] + nums[right]
if total == 0:
…How to Find Four Sum Quadruplets in Python (Sorted Demo)
Find all unique quadruplets in a sorted array that sum to a target, with duplicate skipping.
def four_sum(nums, target):
nums.sort()
result = []
n = len(nums)
for i in range(n - 3):
if i > 0 and nums[i] == nums[i - 1]:
continue
for j in range(i + 1, n - 2):
if j > i + 1 and nums[j] == nums[j - 1]:
continue
left, right = j + 1…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 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…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]
…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…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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