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Complexity & Foundations

Big O notation Big Omega notation Big Theta notation Constant time Logarithmic time Linear time Quadratic time Amortized analysis Space complexity Recursion stack

Arrays & Strings

Array traversal Array insertion Array deletion Two pointers Sliding window Prefix sums String reversal Palindrome check Frequency counting Matrix traversal

Linked Lists

Singly linked list Linked list insertion Linked list deletion Reverse linked list Find middle node Detect cycle Merge sorted lists Doubly linked list Circular linked list LRU list concept

Stacks & Queues

Stack push pop Balanced parentheses Monotonic stack Queue enqueue dequeue Circular queue Deque Priority queue concept Breadth-first queue Min stack Evaluate postfix expression

Hashing

Hash map lookup Hash set membership Two sum Group anagrams First unique character Collision concept Load factor concept Open addressing concept Separate chaining concept Memoization with hash map

Trees & Heaps

Binary tree traversal Preorder traversal Inorder traversal Postorder traversal Level order traversal Binary search tree search BST insertion Tree height Min heap Heap sort

Graphs

Adjacency list Adjacency matrix Depth-first search Breadth-first search Connected components Cycle detection directed graph Topological sort Dijkstra shortest path Union find Minimum spanning tree concept

Sorting Searching & DP

Bubble sort Insertion sort Selection sort Merge sort Quick sort Binary search Lower bound Dynamic programming Fibonacci 0 1 knapsack Longest increasing subsequence

Data Structures & Algorithms / Complexity & Foundations

Logarithmic time

Learn Logarithmic time in Data Structures & Algorithms with a focused explanation, a topic-specific example, edge guidance, and a mastery check.

12 min read • Beginner

data-structures-algorithms-005.py

python

def binary_search(a,x):
    lo,hi=0,len(a)-1
    while lo<=hi:
        mid=(lo+hi)//2
        if a[mid]==x:return mid
        lo,hi=(mid+1,hi) if a[mid]<x else (lo,mid-1)
    return -1
print(binary_search([1,4,7,9,12,18],12))

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Logarithmic time Mastery Check →