Advanced Algorithms

// Advanced Algorithms Framework class AdvancedAlgorithms { constructor() { this.data = []; this.results = []; this.complexity = {}; this.performance = {}; } // Dynamic Programming dynamicProgramming(problem, memo = {}) { if (problem in memo) { return memo[problem]; } if (this.isBaseCase(problem)) { return this.solveBaseCase(problem); } const subproblems = this.decomposeProblem(problem); const solutions = subproblems.map(sub => this.dynamicProgramming(sub, memo) ); const result = this.combineSolutions(solutions); memo[problem] = result; return result; } // Greedy Algorithm greedyAlgorithm(problem) { const solution = []; let currentState = this.initializeState(problem); while (!this.isComplete(currentState)) { const choice = this.makeGreedyChoice(currentState); solution.push(choice); currentState = this.updateState(currentState, choice); } return solution; } // Divide and Conquer divideAndConquer(problem) { if (this.isSmallEnough(problem)) { return this.solveDirectly(problem); } const subproblems = this.divide(problem); const solutions = subproblems.map(sub => this.divideAndConquer(sub) ); return this.combine(solutions); } // Graph Algorithm graphAlgorithm(graph, start, end) { const visited = new Set(); const queue = [start]; const distances = new Map(); distances.set(start, 0); while (queue.length > 0) { const current = queue.shift(); if (current === end) { return this.reconstructPath(distances, start, end); } if (!visited.has(current)) { visited.add(current); const neighbors = this.getNeighbors(graph, current); neighbors.forEach(neighbor => { if (!visited.has(neighbor)) { distances.set(neighbor, distances.get(current) + 1); queue.push(neighbor); } }); } } return null; // No path found } // Approximation Algorithm approximationAlgorithm(problem, epsilon = 0.1) { const solution = this.constructSolution(problem); const optimal = this.estimateOptimal(problem); const ratio = solution.value / optimal.value; if (ratio <= 1 + epsilon) { return solution; } else { return this.improveSolution(solution, problem); } } }