feat : Add Iterative Deepening DFS)

[Erennn7]

Iterative Deepening Depth-First Search (IDDFS) in R

This PR introduces a fully documented, optimized, and production-ready implementation of the Iterative Deepening Depth-First Search (IDDFS) algorithm in R.
IDDFS combines the completeness of Breadth-First Search (BFS) with the space efficiency of Depth-First Search (DFS), making it suitable for exploring large or infinite state spaces where depth is unknown.

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🔍 Overview

The iddfs() function repeatedly performs Depth-Limited Search (DLS) from depth 0 up to a user-defined max_depth.
It halts once the target vertex is found, ensuring the shallowest (shortest depth) solution is discovered efficiently.

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✨ Key Features

• 🚀 Optimized implementation — no global assignments, magic numbers, or redundant loops
• 🧩 Graph normalization through normalize_graph() ensures robust adjacency handling
• 🛡️ Cycle-safe search using path-based cycle detection
• 📊 Verbose tracing for step-by-step exploration visualization
• 🧠 Comprehensive examples in example_iddfs() demonstrating typical graph search cases

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⚙️ Algorithm Details

• Time Complexity: O(b^d) — where b is the branching factor and d is the depth of the solution
• Space Complexity: O(d) — proportional to recursion or stack depth

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🧮 Applications

• Artificial Intelligence search problems (e.g., puzzles, decision trees)
• Graph traversal in unweighted or depth-limited problems
• Optimal exploration in unknown-depth environments

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🧱 Example Usage

# Example: Simple directed graph
graph <- list(
  "1" = c(2, 3),
  "2" = c(4),
  "3" = c(5),
  "4" = c(),
  "5" = c()
)

iddfs(graph, start = 1, target = 5, max_depth = 5, verbose = TRUE)

# Output:
# Iterative Deepening DFS
# ============================================================
# Searching at depth limit: 0
# Searching at depth limit: 1
# Searching at depth limit: 2
# ✓ Target 5 found at depth 2

[Erennn7]

@siriak please have a look sir.

[Copilot]

Pull Request Overview

This PR adds a comprehensive implementation of the Iterative Deepening Depth-First Search (IDDFS) algorithm to the R repository. IDDFS combines the space efficiency of DFS with the optimality guarantees of BFS by performing repeated depth-limited searches with increasing depth limits.

• Implements IDDFS with robust graph normalization and cycle detection
• Includes comprehensive documentation, examples, and verbose output options
• Provides production-ready code with proper error handling and input validation

[Copilot]

Pull Request Overview

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