Curriculum
Learn DSA from scratch
Learn each topic in four steps: handwritten notebook notes, an animated walkthrough, a fast cost check, and curated practice problems.
Arrays
An array is a row of fixed boxes laid side by side in computer memory, like numbered lockers in a hallway. Because each box occupies identical space and sits directly next to its neighbors, jumping to locker zero or locker ten thousand takes the exact same tiny fraction of time. Every box holds an item of the same type, addressed by an offset number called an index.
Strings
A string is an ordered necklace of text characters, like letters printed along a ribbon of paper. Each character sits at an exact numeric slot, holding a glyph such as a letter, punctuation mark, or digit. In many programming languages, ribbons cannot be edited after creation, meaning changing a single character requires pressing an entirely new ribbon from scratch.
Linked List
A linked list is a chain of separate cargo cars connected by coupling hooks, scattered anywhere across memory rather than sitting in a tidy contiguous row. Each car, called a node, holds a single piece of data and a pointer directing traffic to the address of the next car in line. Because nodes connect only by directional links, jumping straight to the tenth car is impossible without walking past the first nine.
Binary Trees
A binary tree is a branching data structure that starts at a single top node called the root, like an upside-down family tree. Every node holds a piece of data and can branch out to at most two children below it, known as the left child and the right child. Because there is no ordering rule about which values go left or right, finding a specific item can require checking every single node in the entire tree.
BST
A binary search tree is a binary tree that enforces a strict ordering rule at every node. Every value stored in a node's left branch must be smaller than the node itself, and every value in its right branch must be larger. Because this rule holds true everywhere down the tree, searching for a value does not require checking every branch. At each step, a single comparison lets you discard an entire half of the remaining nodes.
Graph
A graph is a network of individual points, called vertices or nodes, connected by lines called edges. Think of a subway transit map, an electrical circuit, or a web of social friends. Unlike a tree, a graph has no designated top node and no parent-child hierarchy. Connections can run one-way or both ways, and paths can loop back on themselves to form closed cycles.
Dynamic Programming
Dynamic programming is a method for solving a complex problem by breaking it into overlapping subproblems, solving each subproblem only once, and remembering the answers in a lookup table. Instead of recalculating identical questions over and over, future steps look up previous answers directly. By assembling these saved pieces from the bottom up or storing them during recursion, a task that would take billions of steps finishes in a fraction of a second.
Stack
A stack is a vertical pile of cafeteria trays where items enter and depart from one single opening at the top. The most recent item set down is the first one retrieved, while items deposited earlier remain buried underneath until newer arrivals are lifted away. This strict last-in, first-out sequence guarantees that older context stays preserved until all newer nested actions run to completion.
Queue
A queue is an orderly checkout line at a grocery store counter where patrons enter at the back and leave from the front. The person who arrives first gets served first, while newcomers wait patiently behind whoever came before them. Unlike a stack which turns back on its latest arrival, a queue preserves fair chronological arrival order, processing tasks strictly from oldest to newest.
Binary Search
Binary search is the guessing strategy used when searching a thick telephone directory or guessing a secret number between one and a hundred. Rather than inspecting names one by one from the first page, the search opens straight to the middle page. If the target precedes that middle entry, the entire back half is discarded; if it follows, the front half is eliminated. Repeating this halved split finds the item with remarkable speed.
Backtracking
Backtracking is an organized trial-and-error search through a maze of possibilities. You make a tentative choice, move forward to explore where that path leads, and if you hit a dead end or finish finding an answer, you back up and undo that choice. By cleaning up your changes before trying the next option, a single shared board or list is explored thoroughly without needing to clone full copies of your data at every turn.
Heap
A heap is a specialized tree that keeps only the single most extreme item at the very top. In a min-heap, every parent node is smaller than its children, so the smallest element in the entire collection sits immediately at the root. Unlike a binary search tree, a heap does not keep all items in full sorted order. It maintains only a partial order, making it fast at giving you the single smallest or largest item without spending time sorting everything else.
Two Pointers
Two pointers is a search coordinated by two fingers placed on different entries of an ordered row, stepping inward toward each other or advancing at different speeds. Instead of scanning with nested loops that re-examine identical pairs, each pointer moves unidirectionally based on comparisons. Because every movement permanently prunes bad candidate combinations, the search inspects the collection in a single joint pass.
Sliding Window
A sliding window is an adjustable magnifying lens placed over a continuous segment of a sequence. Rather than recalculating metrics for every potential subsection from scratch, the window expands rightward by absorbing fresh elements and contracts leftward to expel stale entries. Only data currently framed within the window borders contributes to the active calculation.
Recursion
Recursion is a nesting doll that opens to reveal an identical smaller doll inside. In programming, a function solves a substantial problem by delegating smaller versions of the exact same question to fresh invocations of itself. Each invocation operates on shrunken input until hitting an irreducible foundation called a base case, which returns an immediate answer and permits the waiting cascade to resolve backwards.
Math
Algorithmic math is the application of number properties, modular arithmetic, and geometric patterns to compute results without simulating every step. Rather than filling memory buffers with millions of simulated counters or walking endless loops, mathematical formulation uses identities like prime factorization, digit extraction, and greatest common divisors to jump directly to target answers through closed-form rules.
Bit Manipulation
Bit manipulation is the practice of working directly on the individual ones and zeros that form numbers in computer memory. Every integer is stored as a tiny row of electrical switches that are either on or off. Instead of running arithmetic loops, bitwise operations flip, mask, shift, or combine these switches in a single hardware cycle. This allows compact storage of sets and blazing-fast checks without allocating extra memory.
Trie
A trie, also called a prefix tree, is a tree structured for storing words character by character. Instead of storing entire words in individual nodes, each step down a branch represents a single letter. Words that share the same beginning, like car, card, and care, share the exact same starting path down the tree. A special boolean marker sits at the end of each valid word to show that a complete word terminates at that letter.
Intervals
An interval is a continuous range of numbers defined by two values: a start point and an end point. Think of a calendar event booked from two to four o'clock, or a cut segment on a ruler. Because each interval covers every number between its boundaries, two intervals can sit apart with empty room between them, touch at an edge, or overlap across a shared span of numbers.
Matrix
A matrix is a flat grid of cells laid out in rows and columns, like a checkerboard or a spreadsheet. Each cell has an address made of two numbers: its row index going down and its column index going across. Because computer memory stores these rows one after another or as arrays of arrays, jumping straight to any individual cell takes the same tiny fraction of time no matter where it sits on the board.
Sorting
Sorting is the act of arranging a scrambled hand of playing cards into ascending rank from left to right. It reorganizes scattered data according to a consistent comparison rule, like numbering index cards or alphabetizing names. While unsorted data requires searching every single entry to verify whether an item exists, ordered data establishes predictable relationships that make duplicates, clusters, and extreme values immediately visible.
Greedy
A greedy algorithm makes the best-looking choice available right now, at every step, without ever looking back or second-guessing its decision. Think of a cashier making change by handing over the largest possible coin first, repeatedly, until the total is reached. Unlike dynamic programming, which saves and compares answers to multiple overlapping paths, a greedy strategy commits to one immediate option and keeps moving forward.