Algorithms & data structures
Classic patterns — search, sort, stacks, queues, and practical complexity-aware code.
Find Missing Numbers, Duplicates, and Ranges in Python
Analyze a list to identify missing numbers, duplicate values, and contiguous ranges using sets and the Counter class.
def find_missing_duplicates_ranges(numbers):
"""Find missing numbers, duplicates, and ranges in a list."""
from collections import Counter
if not numbers:
return {"missing": [], "duplicates": [], "ranges": []}
full_range = set(range(min(numbers), max(numbers) + 1))
present = set(n…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)
…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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Algorithms & data structures — Python code examples
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