Algorithms

⏱ 5 min read 1D DP Space Optimization # Fibonacci: O(n) -> O(1) space def fib(n: int) -> int: if n int: prev2 = […] Read article

⏱ 6 min read Binary Indexed Tree (Fenwick Tree / BIT) A BIT supports prefix sum queries and point updates in O(log n) time Read article

⏱ 6 min read Dijkstra’s Algorithm – Shortest Path (Non-negative Weights) import heapq from collections import defaultdict def dijkstra(graph: dict, start: int, n: int) Read article

⏱ 4 min read Heap Fundamentals A heap is a complete binary tree where every parent satisfies the heap property (min-heap: parent = children). Read article

⏱ 4 min read GCD, LCM, and Euclidean Algorithm import math def gcd(a: int, b: int) -> int: while b: a, b = b, Read article

⏱ 6 min read Recursion Fundamentals Every recursive solution has: a base case (stops the recursion), a recursive case (reduces the problem), and a Read article

⏱ 5 min read String Fundamentals for Interviews Strings are immutable in Python and Java — concatenating in a loop is O(n^2). Use a Read article

⏱ 7 min read Trie Fundamentals and Implementation A trie (prefix tree) stores strings character by character, sharing prefixes among strings. Each node represents Read article

⏱ 6 min read Binary Search Fundamentals Binary search finds a target in a sorted collection in O(log n). The key insight: at each Read article

⏱ 6 min read Union-Find Data Structure Union-Find (also called Disjoint Set Union, DSU) tracks which elements belong to the same connected component. Supports Read article

⏱ 6 min read The Monotonic Stack Pattern A monotonic stack maintains elements in strictly increasing or strictly decreasing order. When a new element Read article

⏱ 5 min read Stack: LIFO and Its Applications A stack (Last In, First Out) is the go-to structure when you need to process Read article

⏱ 6 min read The Two Pointers Pattern Two pointers uses two indices that move toward each other (or in the same direction) to Read article

⏱ 6 min read The Sliding Window Pattern Sliding window optimizes O(n^2) brute-force approaches on contiguous subarrays/substrings to O(n). The key insight: instead of Read article

⏱ 7 min read Why Bit Manipulation Matters in Interviews Bit manipulation problems test your understanding of how integers are represented in binary and Read article