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 …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)
…Depth First Search Traversal Order in Python
Recursive depth-first search that returns the visit order of nodes in an adjacency list graph starting from a given node.
def dfs_order(adj, start):
visited = set()
order = []
def dfs(node):
visited.add(node)
order.append(node)
for neighbor in adj.get(node, []):
if neighbor not in visited:
dfs(neighbor)
dfs(start)
return order
if __name__ == "__main__":
# Dem…Drop Elements From Start While Condition Is True in Python
This generator function drops elements from the beginning of an iterable while a predicate returns true, then yields the rest.
def drop_while(predicate, iterable):
"""Drop elements from the start while predicate is true."""
it = iter(iterable)
for item in it:
if not predicate(item):
yield item
break
yield from it
if __name__ == "__main__":
numbers = [1, 2, 3, 4, 1, 2, 5]
result = list(d…Extract n largest elements from a large list using heapq
Uses heapq.nlargest to efficiently extract the top n largest numbers from a large list, even with millions of elements.
import heapq
import random
def n_largest(numbers, n):
"""Return the n largest numbers from a list using heapq."""
if n <= 0:
return []
return heapq.nlargest(n, numbers)
if __name__ == "__main__":
# Create a large list with 1,000,000 random numbers
large_list = [random.randint(1, 1_000_000…Filter List to Keep Only Whitelist Values in Python
Filter a list of values to keep only those present in a predefined whitelist set using a list comprehension.
def filter_whitelist(values, whitelist):
"""Return only values that are present in the whitelist set."""
return [value for value in values if value in whitelist]
if __name__ == "__main__":
raw_values = ["apple", "banana", "cherry", "date", "apple", "elderberry"]
allowed = {"apple", "banana", "date"}
…Find All Indices of a Target Value in a Python List
Returns a list of all indices where a given target value appears in a Python list using a list comprehension with enumerate.
def find_all_indices(arr, target):
return [i for i, value in enumerate(arr) if value == target]
if __name__ == "__main__":
sample_list = [4, 2, 7, 2, 9, 2, 1, 2]
target = 2
result = find_all_indices(sample_list, target)
print(result)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 Elements Appearing More Than n/3 Times in Python
Return all elements that occur more than len(array)/3 times using a simple dictionary counter.
def majority_third(arr):
"""Return elements appearing more than len(arr)/3 times."""
cutoff = len(arr) / 3
counts = {}
for x in arr:
counts[x] = counts.get(x, 0) + 1
return [x for x, c in counts.items() if c > cutoff]
if __name__ == "__main__":
test1 = [3, 2, 3]
test2 = [1, 1, 1, …Find First Duplicate Index in Python
Return the index of the first element that appears more than once in a list, using a dictionary for O(n) time.
def find_first_duplicate(arr):
seen = {}
for index, value in enumerate(arr):
if value in seen:
return index
seen[value] = index
return -1
if __name__ == "__main__":
test_array = [3, 5, 2, 8, 5, 1, 2]
result = find_first_duplicate(test_array)
print(f"Array: {test_arr…Find Maximum Distance Between Identical Elements in Python
Compute the maximum index distance between any two identical elements in a list using a dictionary to track first occurrences.
from collections import defaultdict
def max_distance_between_identical(nums):
first_occurrence = {}
max_dist = 0
for i, num in enumerate(nums):
if num in first_occurrence:
dist = i - first_occurrence[num]
max_dist = max(max_dist, dist)
else:
first_occur…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 Single Number Appearing Once in Python
Count frequency of each number in a list and return the one that appears exactly once when all others appear twice.
from collections import Counter
def find_single_number(nums):
counts = Counter(nums)
for num, count in counts.items():
if count == 1:
return num
return None
if __name__ == "__main__":
nums = [4, 1, 2, 1, 2]
result = find_single_number(nums)
print(f"Single number in {nums} …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 First Index Where a Condition Is True in Python
Search any iterable for the first element matching a predicate and return its index, or -1 if none match.
def first_true_index(items, condition):
"""Return the first index where condition(item) is True, or -1 if none match."""
for i, item in enumerate(items):
if condition(item):
return i
return -1
if __name__ == "__main__":
numbers = [1, 3, 5, 8, 10, 12]
# Find first number greate…Find the Last Index Where a Condition Is True in Python
This code scans a sequence from the end and returns the index of the last element that satisfies a given condition, or -1 if none do.
def last_index_where(sequence, condition):
"""Return the index of the last element in sequence that satisfies condition."""
for i in range(len(sequence) - 1, -1, -1):
if condition(sequence[i]):
return i
return -1
if __name__ == "__main__":
numbers = [1, 4, 7, 2, 9, 5, 8, 3]
is_…Find the Second Largest Unique Number in a Python List
This Python function finds the second largest unique number from a list by converting it to a set, removing the maximum, and returning the new maximum.
def second_largest_unique(numbers):
unique_numbers = set(numbers)
if len(unique_numbers) < 2:
return None
unique_numbers.remove(max(unique_numbers))
return max(unique_numbers)
if __name__ == "__main__":
test_list = [4, 2, 9, 5, 2, 9, 1, 5]
result = second_largest_unique(test_list)
…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 Add Two Lists Elementwise in Python
Add two equal-length lists element by element using a list comprehension with zip, returning a new list of summed values.
def elementwise_add(list1, list2):
return [a + b for a, b in zip(list1, list2)]
if __name__ == "__main__":
list_a = [1, 2, 3, 4]
list_b = [10, 20, 30, 40]
result = elementwise_add(list_a, list_b)
print(result)How to Apply a Function to Sliding Window Slices in Python
This Python code applies a given function to every contiguous window of a specified size in a list, returning a list of results.
def apply_to_sliding_windows(data, window_size, func):
return [func(data[i:i + window_size]) for i in range(len(data) - window_size + 1)]
if __name__ == "__main__":
numbers = [1, 2, 3, 4, 5, 6]
window_size = 3
results = apply_to_sliding_windows(numbers, window_size, sum)
print(results)
results…How to Combine filter and map with a List Comprehension in Python
This Python code demonstrates how to combine filtering and mapping in a single list comprehension and shows the equivalent filter() and map() approach.
def square(x):
return x * x
def is_even(x):
return x % 2 == 0
numbers = [1, 2, 3, 4, 5, 6, 7, 8]
result = [square(x) for x in numbers if is_even(x)]
print(f"Original numbers: {numbers}")
print(f"Squares of even numbers: {result}")
# Combined filter + map equivalent
filtered = filter(is_even, numbers)
mapp…How to Compare Two Lists Elementwise for Greater Flags in Python
Compare two equal-length lists element by element and return a list of booleans marking where list_a values are greater than list_b values.
def compare_lists_greater(list_a, list_b):
"""
Compare two lists elementwise and return a list of booleans
indicating whether each element in list_a is greater than the
corresponding element in list_b.
"""
if len(list_a) != len(list_b):
raise ValueError("Lists must have the same length"…Browse by section
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