Iterative Deepening Search 🚀

Iterative Deepening Search is a systematic and versatile search algorithm that gradually increases the depth of exploration in a tree or graph. It starts with a shallow depth limit and incrementally deepens it until the desired solution is found. This approach combines the advantages of BFS, which guarantees optimality, with the memory efficiency of DFS.

How Does Iterative Deepening Search Work? 👒

IDS operates with the following steps:

Start with a shallow depth limit (usually 0) and perform a Depth-Limited Search (DLS) with this limit.
If the solution is found within the current depth limit, return it. Otherwise, continue to step 3.
Increment the depth limit by 1 and repeat the DLS with the new limit.
Continue this process until the solution is found or all nodes in the tree or graph have been explored.

The key insight of IDS is that it ensures the optimal solution is found by gradually increasing the depth limit. It explores nodes level by level, which is why it is often considered an improvement over pure DFS while maintaining memory efficiency.

Here's a simplified pseudocode representation of Iterative Deepening Search:

pseudocode

function iterativeDeepeningSearch(graph, source, target):
    depthLimit = 0
    while true:
        result = depthLimitedSearch(graph, source, target, depthLimit)
        if result is a solution:
            return result
        depthLimit++

DLS

Complexity Analysis for Iterative Deepening Search (IDS)

Time Complexity:

The time complexity of Iterative Deepening Search depends on the branching factor (average number of successors per node) and the depth of the optimal solution. In the worst case, IDS explores nodes up to the depth of the optimal solution, leading to a time complexity of O(b^d), where "b" is the branching factor, and "d" is the depth of the optimal solution. This makes IDS optimal.

Space Complexity:

The space complexity is determined by the depth limit of the search. In the worst case, it can be O(b*d), where "b" is the branching factor and "d" is the depth limit. However, it should be noted that IDS maintains relatively low memory usage compared to traditional BFS.

Optimality:

Iterative Deepening Search is optimal because it explores nodes in order of increasing depth. When a solution is found, it is guaranteed to be the optimal solution at that depth.

Applications of Iterative Deepening Search (IDS)

IDS has applications in various fields, including:

Puzzle Solving: Solving puzzles with unknown depths, such as the Towers of Hanoi or sliding tile puzzles.
Game AI: In game AI, IDS is used for searching game trees to find the best move within a limited time frame.
Planning and Scheduling: Solving planning and scheduling problems where the depth of a solution may vary.
Network Routing: In network routing, where the optimal path needs to be found with limited computational resources.

Implementation

function iterativeDeepeningSearch(graph, source, target) {
    let depthLimit = 0;
    while (true) {
        const result = depthLimitedSearch(graph, source, target, depthLimit);
        if (result !== null) {
            return result; // Solution found
        }
        depthLimit++;
    }
    return null; // No solution found
}
 
function depthLimitedSearch(graph, current, target, depthLimit) {
    if (current === target) {
        return current; // Solution found
    }
    if (depthLimit <= 0) {
        return null; // Depth limit reached
    }
    for (const neighbor of graph[current]) {
        const result = depthLimitedSearch(graph, neighbor, target, depthLimit - 1);
        if (result !== null) {
            return result; // Solution found in a child node
        }
    }
    return null; // No solution found in this branch
}
 
// Example tree
const graph = {
    A: ['B', 'C'],
    B: ['D', 'E'],
    C: ['F', 'G'],
    D: ['H', 'I'],
    E: [],
    F: [],
    G: [],
    H: [],
    I: ['J'],
    J: [],
};
 
const sourceNode = 'A';
const targetNode = 'J';
 
const result = iterativeDeepeningSearch(graph, sourceNode, targetNode);
 
if (result !== null) {
    console.log('Solution found:', result);
} else {
    console.log('No solution found.');
}
 
// Result : Solution found: "J"

This JavaScript code demonstrates an implementation of Iterative Deepening Search for a simple tree structure.

Conclusion 🌟

Iterative Deepening Search (IDS or IDDFS) is a powerful and efficient search algorithm that combines the best aspects of BFS and DFS. It allows you to explore data structures systematically while ensuring the optimal solution is found. Whether you're tackling puzzles, game AI, or planning problems, IDS equips you with a versatile tool for efficiently searching through complex spaces.

Depth-Limited Search String Matching