Algorithms & data structures
Classic patterns — search, sort, stacks, queues, and practical complexity-aware code.
Count Smaller Elements to the Right in Python
Return a list where each index counts how many elements to its right are smaller than that element using a clean O(n²) nested-loop approach.
def count_smaller_elements(arr):
"""
Return a list where result[i] is the number of elements
to the right of arr[i] that are smaller than arr[i].
"""
result = []
for i in range(len(arr)):
count = 0
for j in range(i + 1, len(arr)):
if arr[j] < arr[i]:
…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 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 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 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 Pivot Index in Python
Locate the index where the sum of elements to the left equals the sum to the right, using a single pass with prefix sums.
def find_pivot_index(nums):
total = sum(nums)
left_sum = 0
for i, num in enumerate(nums):
if left_sum == total - left_sum - num:
return i
left_sum += num
return -1
if __name__ == "__main__":
test_cases = [
[1, 7, 3, 6, 5, 6],
[1, 2, 3],
[2, 1, -…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 Rotate an Array by k Steps in Python
This code rotates a list to the right by k positions using modulo arithmetic to handle k larger than the list length.
def rotate_array(nums, k):
if not nums:
return []
n = len(nums)
k = k % n
return nums[-k:] + nums[:-k] if k else nums[:]
if __name__ == "__main__":
arr = [1, 2, 3, 4, 5, 6]
k = 2
result = rotate_array(arr, k)
print(f"Original: {arr}")
print(f"Rotated by {k}: {result}")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 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:
…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__":
…Move Zeroes to End in Python Maintaining Order
In-place algorithm that moves all zeroes to the end of a list while preserving the relative order of non-zero elements.
def move_zeroes(nums):
non_zero_index = 0
for i in range(len(nums)):
if nums[i] != 0:
nums[non_zero_index], nums[i] = nums[i], nums[non_zero_index]
non_zero_index += 1
return nums
if __name__ == "__main__":
example = [0, 1, 0, 3, 12]
result = move_zeroes(example)
…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…Browse by section
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