DSA + algorithms / Intermediate

Trees, heaps, and graphs

Hierarchical structures, priority queues, graph models, BFS/DFS, and how these structures map to real software problems.

treeheapgraphbfsdfs

01Trees

Trees represent hierarchy: file systems, DOM nodes, organization structures, indexes, and syntax trees. Binary-search trees maintain ordering; balanced variants keep height near logarithmic.

02Heaps and priority queues

A heap is optimized for repeatedly retrieving the minimum or maximum priority. It is ideal for schedulers, shortest-path algorithms, top-K processing, and event queues.

cppMax heap via priority_queue

std::priority_queue<int> highest;
highest.push(5);
highest.push(20);
highest.push(8);
std::cout << highest.top(); // 20

03Graphs

A graph contains vertices and edges. Use it for networks, roads, dependencies, social connections, device topology, and state transitions.

pythonBreadth-first traversal

from collections import deque

def bfs(graph, start):
    seen = {start}
    queue = deque([start])
    while queue:
        node = queue.popleft()
        yield node
        for neighbor in graph.get(node, []):
            if neighbor not in seen:
                seen.add(neighbor)
                queue.append(neighbor)