Competitive Programming and Algorithmic Solutions

A comprehensive, production-grade archive of competitive programming solutions, advanced algorithmic patterns, and data structure implementations developed by Mahmoud Mohamed Megahed during participation in ACPC / ECPC contest rounds and Codeforces training.

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🏆 Verified Online Credentials & Performance

• Codeforces Handle: mahmoud_megahed
• Total Solved Problems: 215 unique problems across 259 verified Accepted submissions.
• Problem Rating Range: 800 to 2000 (spanning Div 4 up to Div 1/2 hard problemsets).
• Full Problem Catalog: Browse the exhaustive, searchable table of all 215 solved problems with direct contest links and submission IDs in Codeforces-Catalog.md.

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📊 Algorithmic Topic Breakdown

Based on official Codeforces submission metadata, solved problems span the following core categories:

Domain / Tag	Solved Count	Max Rating Solved	Core Problem Archetypes
Implementation & Simulation	127	1500	State simulation, coordinate transforms, string parsing
Math & Number Theory	60	2000	Modular arithmetic, fast power, Euler totient, digital roots
Greedy Strategies	49	1500	Invariant maintenance, interval scheduling, exchange arguments
Brute Force & Complete Search	41	1600	Pruned search, backtracking, state space validation
Binary Search & Sortings	29	1600	Monotonic predicate search, custom lower/upper bounds, two pointers
Strings & Text Processing	28	1400	Subsequence matching, frequency counting, anagram validation
Constructive Algorithms	26	1600	Grid invariants, parity constructions, deterministic games
Graphs, Trees & Shortest Paths	18	1700	BFS path reconstruction, Dijkstra, Tree DFS, Valid BFS verification
Dynamic Programming (DP)	10	1400	0/1 Knapsack, subset reachability, memoized transformations
Data Structures & Priority Queues	9	1600	Custom AVL trees, binary heaps, Trie, heap consistency restoration
Bit Manipulation & Bitmasks	9	1200	Bitwise state compression, submask iteration, XOR properties
Disjoint Set Union (DSU)	5	1700	Path compression, union by rank/size, cycle detection
Combinatorics	6	1500	$nCr \pmod{10^9+7}$, permutations, inclusion-exclusion
Interactive Problems	1	1500	Binary search queries with stream flushing (cout.flush())

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🌟 Milestone Problem Highlights (Rating 1400 – 2000)

A curated selection of high-rating problems solved and verified on Codeforces:

Problem Code	Problem Name	Rating	Tags	Solved Submission	Core Technique Demonstrated
CF 216E	Martian Luck	2000	math, number theory	Submission #274432213	Digital roots, prefix sums modulo $(b-1)$
CF 1873H	Mad City	1700	graphs, dfs, dsu, trees	Submission #285359835	Cycle detection, entry node distance comparison
CF 1037D	Valid BFS?	1700	graphs, trees, shortest paths	Submission #279245279	Adjacency reordering by sequence & BFS validation
CF 216B	Forming Teams	1700	dfs, graphs, bipartite	Submission #279279152	2-coloring, odd-cycle detection, parity constraints
CF 1971F	Circle Perimeter	1600	binary search, geometry	Submission #315896057	Two-pointer / binary search over Euclidean boundaries
CF 681C	Heap Operations	1600	data structures, greedy	Submission #304566470	Priority queue state consistency & operation insertion
CF 580C	Kefa and Park	1500	dfs, graphs, trees	Submission #284463365	Tree DFS with path-accumulated state propagation
CF 1999F	Expected Median	1500	combinatorics, math	Submission #274864144	Precomputed fast combinatorics $nCr \pmod{10^9+7}$
CF 1999G1	Ruler (Easy Version)	1500	binary search, interactive	Submission #274867464	Ternary / interactive binary search with query flushing
CF 816B	Karen and Coffee	1400	data structures, prefix sums	Submission #293123675	Difference array $O(1)$ range updates & 2-pass prefix sums
CF 520B	Two Buttons	1400	graphs, bfs, greedy	Submission #278529121	Reverse greedy state reduction / BFS shortest path

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📂 Repository Structure

Competitive-Programming/
├── Codeforces-Catalog.md                   # Full catalog of 215 unique solved problems with direct links
├── Competitive-Template.cpp                # Fast I/O, modular arithmetic & competitive programming macros
├── Data-Structures/
│   ├── AVL-Tree.cpp                        # Self-balancing BST (Rotations, Insertions, Height balancing)
│   ├── Binary-Heap.cpp                     # Min/Max Priority Queue with heapify operations
│   ├── Trie-Tree.cpp                       # Prefix tree for high-speed string lookup and autocomplete
│   └── Disjoint-Set-Union.cpp              # DSU with Path Compression and Union by Size/Rank
├── Graphs/
│   ├── Dijkstra.cpp                        # Single-source shortest path using adjacency lists & priority queues
│   ├── BFS-Shortest-Path.cpp               # Breadth-First Search with full path reconstruction
│   └── Problem-900.cpp                     # Graph connectivity and traversal routines
├── Trees-and-Advanced-Graphs/
│   └── Tree-DFS-and-Cycle-Detection.cpp    # Subtree sizes, path constraints (Kefa & Park), bipartite checking
├── Search-Techniques/
│   └── Binary-Search-Patterns.cpp          # Monotonic predicate binary search, custom lower/upper bounds, two pointers
├── Dynamic-Programming/
│   └── 01-Knapsack-and-Subset-Sum.cpp      # 0/1 Knapsack (1D space optimization), Subset Sum reachability, LCS
├── Prefix-Sums-and-Difference-Arrays/
│   └── Difference-Array.cpp                # O(1) interval range updates & prefix sum reconstruction (Karen & Coffee)
├── Bit-Manipulation/
│   └── Bitmask-Techniques.cpp              # Bitwise flags, subset generation, submask iteration O(3^N)
├── Number-Theory-and-Math/
│   ├── Modular-Arithmetic.cpp              # Fast power O(log N), modular inverse, fast nCr % MOD
│   ├── Modular-Arithmetic-Reference.pdf    # Comprehensive modular arithmetic theoretical guide
│   ├── Primes-1-to-N.cpp                   # Sieve of Eratosthenes & prime factorization
│   ├── Lucky-Numbers.cpp                   # Digit property checking and base conversion
│   ├── Fibonacci.cpp                       # Recurrence relation modeling
│   ├── Digits.cpp                          # Numerical manipulation algorithms
│   └── Palindrome.cpp                      # Numerical and string symmetry validation
├── Backtracking/
│   └── N-Queens.cpp                        # Classical N-Queens constraint satisfaction problem
├── Contests/
│   └── ACPC-Contest-2/                     # Official ACPC contest solutions
│       ├── c.cpp
│       ├── d.cpp
│       ├── f.cpp
│       ├── h.cpp
│       └── i.cpp
└── Practice-Sheets/
    ├── Sheet3-Arrays-Strings.cpp           # Linear data structure manipulations
    ├── Homework-07-Answer.cpp              # Advanced structural programming exercises
    ├── Homework-11-Answer.cpp              # Recursive algorithms
    └── AskMe-Console-System.cpp            # Object-oriented terminal Q&A system

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⚡ Algorithmic Complexity Cheat Sheet

Structure / Algorithm	File	Time Complexity	Space Complexity
AVL Tree	Data-Structures/AVL-Tree.cpp	$O(\log N)$ Search, Insert, Delete	$O(N)$
Binary Heap	Data-Structures/Binary-Heap.cpp	$O(\log N)$ Push/Pop, $O(1)$ Top	$O(N)$
Trie (Prefix Tree)	Data-Structures/Trie-Tree.cpp	$O(L)$ where $L$ is string length	$O(\Sigma \cdot L \cdot N)$
Disjoint Set Union (DSU)	Data-Structures/Disjoint-Set-Union.cpp	$O(\alpha(N))$ amortized per op	$O(N)$
Dijkstra Algorithm	Graphs/Dijkstra.cpp	$O((V + E) \log V)$	$O(V + E)$
BFS Path Reconstruction	Graphs/BFS-Shortest-Path.cpp	$O(V + E)$	$O(V)$
Tree DFS & Subtree Size	Trees-and-Advanced-Graphs/Tree-DFS...	$O(V)$	$O(V)$
Bipartite 2-Coloring	Trees-and-Advanced-Graphs/Tree-DFS...	$O(V + E)$	$O(V)$
Binary Search on Answer	Search-Techniques/Binary-Search...	$O(\log(\text{Range}) \cdot \text{Cost})$	$O(1)$
Difference Array	Prefix-Sums.../Difference-Array.cpp	$O(1)$ Update, $O(N)$ Reconstruct	$O(N)$
0/1 Knapsack (1D Space)	Dynamic-Programming/01-Knapsack...	$O(N \cdot W)$	$O(W)$
Fast Exponentiation	Number-Theory-and-Math/Modular-Arithmetic.cpp	$O(\log \text{EXP})$	$O(1)$
Fast Modular $nCr$	Number-Theory-and-Math/Modular-Arithmetic.cpp	$O(1)$ query ($O(N)$ precomputed)	$O(N)$
N-Queens Solver	Backtracking/N-Queens.cpp	$O(N!)$	$O(N)$
Sieve of Eratosthenes	Number-Theory-and-Math/Primes-1-to-N.cpp	$O(N \log(\log N))$	$O(N)$

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🛠️ Practical Engineering Synergy

The rigorous algorithmic discipline developed through competitive programming directly powers backend software engineering:

• Graph Traversal & DAGs: Powers dependency injection container resolution, task scheduling pipelines, and distributed tracing.
• Prefix Sums & Difference Arrays: Informs high-throughput financial ledger aggregation and real-time metrics time-windowing.
• Tree & Trie Structures: Powers prefix indexing, database B-Tree operations, routing tables, and autocomplete caches.
• Space-Time Intuition: Eliminates catastrophic $N+1$ query cascades, optimizes memory allocations, and prevents memory leaks under sustained load.

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👤 Author

Mahmoud Mohamed Megahed

• Fullstack .NET Developer | Competitive Programmer
• Portfolio: portfolio-mahmoudmegahed.vercel.app
• LinkedIn: linkedin.com/in/mahmoud---megahed
• Codeforces: codeforces.com/profile/mahmoud_megahed

📄 License

This repository is open-source under the MIT License.