Algorithms & data structures
Classic patterns — search, sort, stacks, queues, and practical complexity-aware code.
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 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 Longest Consecutive Sequence in Python
Find the length of the longest consecutive elements sequence in an unsorted array using a set for O(n) lookups.
def longest_consecutive_length(nums):
num_set = set(nums)
longest = 0
for num in num_set:
if num - 1 not in num_set:
current = num
current_streak = 1
while current + 1 in num_set:
current += 1
current_streak += 1
…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 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 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…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 Find the Nearest Value to a Target in a Sorted List in Python
Use bisect to binary-search a sorted list and return the element closest to a target value.
import bisect
def nearest_value(sorted_list, target):
if not sorted_list:
return None
pos = bisect.bisect_left(sorted_list, target)
if pos == 0:
return sorted_list[0]
if pos == len(sorted_list):
return sorted_list[-1]
before = sorted_list[pos - 1]
after = sorted_list[po…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 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:
…Insert Multiple Values Into a Sorted List in Python
Insert multiple values into an already-sorted list while keeping it sorted using the bisect.insort function.
import bisect
def insert_sorted(sorted_list, values):
for value in values:
bisect.insort(sorted_list, value)
return sorted_list
if __name__ == "__main__":
original = [1, 3, 5, 7, 9]
new_values = [4, 6, 2, 8, 0]
result = insert_sorted(original, new_values)
print(f"Original: {original}"…Merge Two Sorted Arrays Without Extra Space in Python
Merge two sorted arrays in-place from the end, using the trailing zeros in the first array to avoid extra space.
def merge_sorted(arr1, arr2):
m, n = len(arr1), len(arr2)
i, j = m - 1, n - 1
while j >= 0:
if i >= 0 and arr1[i] > arr2[j]:
arr1[i + j + 1] = arr1[i]
i -= 1
else:
arr1[i + j + 1] = arr2[j]
j -= 1
return arr1
if __name__ == "__main__":
…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…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…Rearrange array alternately max min in Python
Rearranges a sorted list so its elements alternate between the current maximum and current minimum using two pointers in O(n) time.
def rearrange_alternately(arr):
"""
Rearrange sorted array so elements alternate: max, min, next max, next min...
Returns a new list in O(n) time using O(n) space.
"""
n = len(arr)
result = []
left, right = 0, n - 1
while left <= right:
if left == right:
result.appen…Stable merge two lists by custom comparator in Python
Merge two lists into one sorted output using a custom comparator while maintaining the original order of equal elements.
from functools import cmp_to_key
def compare(x, y):
# Custom comparator: sorts by length first, then by original index for stability
if len(x) != len(y):
return len(x) - len(y)
return 0 # Equal keys preserve original order (stable)
def merge_stable(left, right, cmp_func):
result = []
i =…Browse by section
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