Algorithms & data structures
Classic patterns — search, sort, stacks, queues, and practical complexity-aware code.
Bucket Numbers into Histogram Bin Counts in Python
Partition a list of numbers into equal-width histogram bins and count how many fall into each bin using only the Python standard library.
from collections import Counter
def histogram_bins(numbers, num_bins):
"""Bucket numbers into histogram bin counts."""
if not numbers:
return []
min_val = min(numbers)
max_val = max(numbers)
bin_width = (max_val - min_val) / num_bins
# Handle edge case where all values are id…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 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:
…Find Common Elements in List of Lists in Python
Return elements that appear in every sublist of a nested list, preserving duplicates with Counter intersection.
from collections import Counter
def common_elements(list_of_lists):
"""Return elements present in every sublist."""
if not list_of_lists:
return []
counts = Counter(list_of_lists[0])
for sublist in list_of_lists[1:]:
counts &= Counter(sublist)
return list(counts.elements())
if _…Find Longest Consecutive Run in an Unsorted List in Python
Find the length of the longest sequence of consecutive integers in an unsorted list using a set and a linear scan.
def longest_run(nums):
if not nums:
return 0
num_set = set(nums)
longest = 0
for num in num_set:
# Only start counting from the smallest number in a sequence
if num - 1 not in num_set:
current = num
length = 1
while current + 1 in num_set:
…Find Median of Two Sorted Arrays in Python
Merges two sorted arrays with a two-pointer walk and returns the median of the combined sorted sequence.
def median_of_two_sorted_arrays(nums1, nums2):
merged = []
i = j = 0
while i < len(nums1) and j < len(nums2):
if nums1[i] <= nums2[j]:
merged.append(nums1[i])
i += 1
else:
merged.append(nums2[j])
j += 1
merged.extend(nums1[i:])
merged.…Find k Closest Points to Origin in Python
Sorts a list of (x, y) point tuples by their Euclidean distance from the origin and returns the k nearest points.
import math
def k_closest(points, k):
points.sort(key=lambda p: math.sqrt(p[0]**2 + p[1]**2))
return points[:k]
if __name__ == "__main__":
points = [(1, 2), (3, 4), (-1, 0), (5, 5), (0, 1)]
k = 3
result = k_closest(points, k)
print(f"Original points: {points}")
print(f"K closest points (k…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 the Equilibrium Index of a List in Python
Find every index in a list where the sum of elements to its left equals the sum to its right, using a single pass.
def find_equilibrium_indexes(arr):
total = sum(arr)
left_sum = 0
indexes = []
for i, num in enumerate(arr):
total -= num
if left_sum == total:
indexes.append(i)
left_sum += num
return indexes
if __name__ == "__main__":
test = [1, 2, 3, -1, 2, 3]
result =…How to Compute Jaccard Similarity in Python
Compute the Jaccard similarity between two lists by converting them to sets and dividing the intersection size by the union size.
def jaccard_similarity(list1, list2):
set1 = set(list1)
set2 = set(list2)
intersection = set1 & set2
union = set1 | set2
if not union:
return 0.0
return len(intersection) / len(union)
if __name__ == "__main__":
a = [1, 2, 3, 4, 5]
b = [3, 4, 5, 6, 7]
pri…How to Compute the Cartesian Product of Two Lists in Python
Generates all ordered pairs from two lists using itertools.product and prints each combination.
from itertools import product
# Two small input lists
list_a = [1, 2, 3]
list_b = ["x", "y"]
# Compute the Cartesian product
result = list(product(list_a, list_b))
# Display the result
print("Cartesian product of", list_a, "and", list_b, "is:")
for pair in result:
print(pair)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 Gaps Between Sorted Intervals in Python
This code finds gap ranges between sorted intervals using pairwise iteration, returning ranges where no interval covers.
from itertools import pairwise
def find_gaps(intervals):
intervals = sorted(intervals)
gaps = []
for prev, curr in pairwise(intervals):
if prev[1] < curr[0]:
gaps.append((prev[1] + 1, curr[0] - 1))
return gaps
if __name__ == "__main__":
intervals = [(1, 3), (5, 7), (10, 12), (…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 Flatten List of Dict Values in Python
This code flattens the values of a list of dictionaries into a single list, handling both list values and scalar values.
def flatten_dict_values(dicts):
flattened = []
for d in dicts:
for value in d.values():
if isinstance(value, list):
flattened.extend(value)
else:
flattened.append(value)
return flattened
if __name__ == "__main__":
data = [
{"a": …How to Generate Permutations of Length r in Python
Generate and print all r-length permutations of a list using Python's itertools.permutations.
from itertools import permutations
def show_permutations(items, r):
result = list(permutations(items, r))
for perm in result:
print(perm)
print(f"Total: {len(result)}")
if __name__ == "__main__":
data = ["A", "B", "C"]
show_permutations(data, 2)How to Heapify a List into a Min Heap with heapq in Python
Convert any list into a valid min heap in-place using Python's heapq.heapify(), then pop the smallest element to verify heap order.
import heapq
data = [5, 3, 8, 1, 9, 2, 7, 4, 6]
print("Original list:", data)
heapq.heapify(data)
print("Min heap:", data)
popped = heapq.heappop(data)
print("Smallest element popped:", popped)
print("Heap after pop:", data)How to Remove Duplicates in Python Preserving Order
Removes duplicate items from a list while keeping the first occurrence order intact using a set for fast membership checks.
def remove_duplicates_preserving_order(items):
seen = set()
result = []
for item in items:
if item not in seen:
seen.add(item)
result.append(item)
return result
if __name__ == "__main__":
sample = [3, 1, 2, 1, 3, 4, 2, 5]
unique_items = remove_duplicates_preserv…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 =…Browse by section
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