Page rank

[ArpitaHanjagi]

Algorithm: PageRank

Purpose: Measures the importance of vertices (pages) in a directed graph based on incoming links.

Theory: Pages linked by important pages receive higher rank. Iterative computation with damping factor models random surfing behavior.

Time Complexity: O(V^2) for dense graphs (or O(E) for sparse graphs with adjacency lists)

Space Complexity: O(V)

Input: Directed graph as an adjacency list, damping factor, max iterations, tolerance

Output: PageRank scores for each vertex

[Copilot]

Pull Request Overview

This PR implements the PageRank algorithm along with several other graph and dynamic programming algorithms, machine learning implementations, and mathematics utilities for the R repository.

Key changes:

• Addition of PageRank algorithm for measuring vertex importance in directed graphs
• Implementation of multiple graph algorithms (Kruskal's MST, Prim's MST, topological sort, DFS/BFS, etc.)
• Addition of dynamic programming solutions (knapsack, LCS, LIS, coin change, etc.)
• Machine learning implementations (gradient boosting)
• Mathematics utilities (Armstrong numbers, amicable numbers)

Reviewed Changes

Copilot reviewed 139 out of 216 changed files in this pull request and generated 5 comments.

Show a summary per file

File	Description
graph_algorithms/page_rank.r	Implements PageRank algorithm with iterative computation and damping factor
graph_algorithms/kruskal_mst.r	Kruskal's MST algorithm using Union-Find for cycle detection
graph_algorithms/prim_mst.r	Prim's MST algorithm for finding minimum spanning trees
graph_algorithms/dijkstra_shortest_path.r	Dijkstra's algorithm with priority queue implementation
graph_algorithms/bellman_ford_shortest_path.r	Bellman-Ford for shortest paths with negative weights
graph_algorithms/floyd_warshall.r	All-pairs shortest paths with negative cycle detection
dynamic_programming/coin_change.r	Coin change problem using dynamic programming
dynamic_programming/longest_increasing_subsequence.r	LIS with O(n²) and O(n log n) implementations
dynamic_programming/longest_common_subsequence.r	LCS for string/array comparison
machine_learning/gradient_boosting.r	Gradient boosting regressor with decision trees
mathematics/armstrong_number.r	Armstrong number validation function
mathematics/amicable_numbers.r	Amicable numbers checker with divisor sum calculation

[siriak]

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