diff --git a/Submissions/002795461_Namitha_JC/Assignment4.ipynb b/Submissions/002795461_Namitha_JC/Assignment4.ipynb new file mode 100644 index 0000000..17694dd --- /dev/null +++ b/Submissions/002795461_Namitha_JC/Assignment4.ipynb @@ -0,0 +1,1003 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "provenance": [] + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + }, + "language_info": { + "name": "python" + } + }, + "cells": [ + { + "cell_type": "markdown", + "source": [ + "**Assignment 4**" + ], + "metadata": { + "id": "QCgKS0lQevjq" + } + }, + { + "cell_type": "markdown", + "source": [ + "**Question 1:**\n", + "\n", + "\n", + "Given a weighted undirected graph G = (V,E) with positive weights, a matching M is a set of edges without common vertices. A perfect matching is a matching where every vertex v € V is incident to exactly one edge in M. In other words, a perfect matching of a graph G is a set of edges which are part of G and together involve all vertices of G exactly once. If the sum of the weights of the edges in the matching is minimized, it is called a minimum-weight perfect matching.\n", + "\n", + "The minimum-weight perfect matching problem asks whether a given weighted undirected graph has a minimum-weight perfect matching.\n", + "\n", + "A. Is the minimum-weight perfect matching problem in P? If so, prove it.\n", + "\n", + "B. Suppose we require the matching to include exactly one edge with weight greater than a specified threshold T. We call this the constrained-weight matching problem. Is the constrained-weight matching problem in NP? If so, prove it.\n", + "\n", + "C. Is the constrained-weight matching problem in NP-complete? If so, prove it." + ], + "metadata": { + "id": "uoDWU6yqe2Vv" + } + }, + { + "cell_type": "code", + "source": [ + "import networkx as nx\n", + "import matplotlib.pyplot as plt\n", + "\n", + "# Creating a weighted undirected graph\n", + "G1 = nx.Graph()\n", + "G1.add_edge('A', 'B', weight=4)\n", + "G1.add_edge('A', 'C', weight=1)\n", + "G1.add_edge('A', 'D', weight=3)\n", + "G1.add_edge('B', 'C', weight=2)\n", + "G1.add_edge('B', 'D', weight=5)\n", + "G1.add_edge('C', 'D', weight=2)\n", + "\n", + "# Plotting the graph\n", + "plt.figure(figsize=(8, 6))\n", + "pos = nx.spring_layout(G1)\n", + "nx.draw(G1, pos, with_labels=True, node_color='lightblue', node_size=2000, font_size=20)\n", + "labels = nx.get_edge_attributes(G1, 'weight')\n", + "nx.draw_networkx_edge_labels(G1, pos, edge_labels=labels)\n", + "plt.title(\"Graph for Minimum-Weight Perfect Matching Problem\")\n", + "plt.show()\n" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 659 + }, + "id": "Up_R4ffskHEa", + "outputId": "e9107b84-e382-4819-9b0e-c0dea71e2bc7" + }, + "execution_count": 1, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "Answer 1:\n", + "\n", + "A. Minimum-Weight Perfect Matching in P\n", + "The minimum-weight perfect matching problem for a general graph is a well-known problem in computational graph theory. It is solvable in polynomial time using algorithms like the Blossom algorithm, developed by Jack Edmonds. This algorithm effectively finds a minimum-weight perfect matching by iteratively improving a matching using augmenting paths and shrinking cycles (blossoms) in the graph.\n", + "\n", + "**Example**:\n", + "\n", + "Imagine a graph where vertices represent people and edges represent potential partnerships, with weights indicating the cost of each partnership.\n", + "A perfect matching would pair off all people so that everyone has a partner, and a minimum-weight perfect matching would do this at the lowest total cost.\n", + "For instance, if you have four people (A, B, C, D) and potential partnerships (A-B, B-C, C-D, D-A, A-C, and B-D) with various costs, the Blossom algorithm would find the pairing that results in the lowest total cost while ensuring everyone is paired.\n", + "\n", + "B. Constrained-Weight Matching Problem in NP\n", + "The constrained-weight matching problem, where a matching must include exactly one edge with weight greater than a specified threshold T, is in NP. The reason is that any proposed solution (a matching with one edge above the threshold) can be verified in polynomial time: check that each vertex is incident to exactly one edge and that one and only one edge has a weight greater than T.\n", + "\n", + "**Example**:\n", + "\n", + "Continuing with the same graph, now suppose we add a constraint: one of the partnerships must have a cost higher than a specific threshold.\n", + "A solution might be a set of pairings where one specific pairing, say A-C, has a cost above the threshold.\n", + "Verifying this is straightforward: check all pairs to ensure everyone is matched and confirm that one pair, and only one, exceeds the threshold.\n", + "\n", + "C. Constrained-Weight Matching Problem in NP-complete\n", + "It's not straightforward to claim NP-completeness for this problem without a more detailed analysis or a known reduction from an NP-complete problem. NP-completeness requires proving that the problem is both in NP and NP-hard. While it's in NP (as shown in part B), the NP-hardness is not immediately clear and would require a reduction from a known NP-complete problem.\n", + "\n", + "**Example**:\n", + "\n", + "Demonstrating NP-completeness for this variant would involve a deeper theoretical analysis, possibly comparing it to other known NP-complete problems." + ], + "metadata": { + "id": "hkqXIhime2of" + } + }, + { + "cell_type": "markdown", + "source": [ + "Pseudo Code:\n", + "\n", + "The Blossom Algorithm is typically used for finding a minimum-weight perfect matching in a general graph. However, it is quite complex. Here is a simplified conceptual pseudocode:\n", + "\n", + "```\n", + "function BlossomAlgorithm(Graph G):\n", + " Initialize an empty matching M\n", + " while there are augmenting paths relative to M in G:\n", + " Find the shortest augmenting path P\n", + " Augment the matching along P\n", + " return M\n", + "```\n", + "\n", + "For the constrained problem where one edge must have a weight greater than a threshold, the pseudocode would include an additional check:\n", + "\n", + "\n", + "\n", + "```\n", + "function ConstrainedMatching(Graph G, Threshold T):\n", + " M = BlossomAlgorithm(G)\n", + " if any edge in M has a weight > T:\n", + " return M\n", + " else:\n", + " Modify G or M to meet the threshold requirement\n", + " return Modified M\n", + "```\n" + ], + "metadata": { + "id": "WxrSGMSViIV3" + } + }, + { + "cell_type": "markdown", + "source": [ + "**Question 2:**\n", + "\n", + "Consider a finite, undirected graph G = (V,E) where each edge e in E has an associated color. A color-spanning subgraph is a subgraph of G such that every color represented in E is also present in the subgraph. A minimum-edge color-spanning subgraph is a color-spanning subgraph that has the fewest possible edges.\n", + "\n", + "The minimum-edge color-spanning subgraph problem asks whether a given graph G has a color-spanning subgraph with the minimum number of edges.\n", + "\n", + "A. Is the minimum-edge color-spanning subgraph problem in P? If so, prove it.\n", + "\n", + "B. Suppose each vertex in the graph must be connected to edges of at least two different colors. We call this the multi-color connectivity problem. Is the multi-color connectivity problem in NP? If so, prove it.\n", + "\n", + "C. Is the multi-color connectivity problem in NP-complete? If so, prove it." + ], + "metadata": { + "id": "l7NA-iO5if-o" + } + }, + { + "cell_type": "code", + "source": [ + "import networkx as nx\n", + "import matplotlib.pyplot as plt\n", + "\n", + "# Creating an undirected graph with colored edges\n", + "G2 = nx.Graph()\n", + "G2.add_edge('A', 'B', color='red')\n", + "G2.add_edge('A', 'C', color='blue')\n", + "G2.add_edge('B', 'C', color='green')\n", + "G2.add_edge('B', 'D', color='red')\n", + "G2.add_edge('C', 'D', color='blue')\n", + "G2.add_edge('D', 'A', color='green')\n", + "\n", + "# Extracting colors for visualization\n", + "colors = [G2[u][v]['color'] for u, v in G2.edges()]\n", + "\n", + "# Plotting the graph\n", + "plt.figure(figsize=(8, 6))\n", + "pos = nx.spring_layout(G2)\n", + "nx.draw(G2, pos, edge_color=colors, with_labels=True, node_color='lightblue', node_size=2000, font_size=20)\n", + "plt.title(\"Graph for Minimum-Edge Color-Spanning Subgraph Problem\")\n", + "plt.show()\n" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 659 + }, + "id": "iKp8kr6IkNRc", + "outputId": "8395f773-57ff-4fd0-a495-5bc5e8dd7a7f" + }, + "execution_count": 2, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "**Answer 2:**\n", + "\n", + "A. Minimum-Edge Color-Spanning Subgraph in P\n", + "The decision version of the minimum-edge color-spanning subgraph problem (whether there exists a color-spanning subgraph with at most k edges) can be NP-hard, depending on how the colors are assigned and the structure of the graph. For simple cases, it might be in P, but in general, finding the exact complexity class would require a specific graph structure or color assignment scheme.\n", + "\n", + "**Example**:\n", + "\n", + "Consider a graph where vertices are cities, and edges are roads colored based on their type (highway, local road, etc.).\n", + "A color-spanning subgraph would be a network of roads including at least one of each type.\n", + "The minimum-edge color-spanning subgraph finds the smallest such network.\n", + "If each road type must be present, the problem could become complex, depending on how roads are distributed and connected.\n", + "\n", + "B. Multi-Color Connectivity Problem in NP\n", + "The multi-color connectivity problem is in NP. Given a solution (a subgraph where each vertex is connected to edges of at least two different colors), it can be verified in polynomial time by checking the color of edges incident to each vertex.\n", + "\n", + "**Example**:\n", + "\n", + "Extend the city graph example, but now every city must be connected to at least two different types of roads.\n", + "A solution might be a subgraph where each city has access to, say, a highway and a local road.\n", + "Verifying this involves checking the connections of each city to ensure they meet the two-color road requirement.\n", + "\n", + "C. Multi-Color Connectivity Problem in NP-complete\n", + "As with the constrained-weight matching problem, asserting NP-completeness for the multi-color connectivity problem is non-trivial. It requires establishing that the problem is NP-hard, which typically involves demonstrating a reduction from a known NP-complete problem. The complexity might vary based on the graph's structure and the color distribution among the edges.\n", + "\n", + "**Example**:\n", + "\n", + "Proving NP-completeness would require a more complex theoretical approach, similar to what's needed in Question 2C." + ], + "metadata": { + "id": "nFyHunkOi6Gx" + } + }, + { + "cell_type": "markdown", + "source": [ + "Pseudo Code:\n", + "\n", + "For finding a minimum-edge color-spanning subgraph, one approach is to use a greedy algorithm. This is a conceptual pseudocode:\n", + "\n", + "```\n", + "function MinEdgeColorSpanningSubgraph(Graph G):\n", + " Subgraph S = empty subgraph of G\n", + " For each color c in G:\n", + " Find the shortest edge of color c\n", + " Add this edge to S if it does not create a cycle\n", + " return S\n", + "```\n", + "\n", + "For the multi-color connectivity problem, the algorithm needs to ensure that each vertex is connected to edges of at least two different colors:\n", + "\n", + "```\n", + "function MultiColorConnectivity(Graph G):\n", + " Subgraph S = MinEdgeColorSpanningSubgraph(G)\n", + " For each vertex v in G:\n", + " If v is not connected to at least two different colored edges in S:\n", + " Find the shortest edge connecting v with a new color\n", + " Add this edge to S if it does not create a cycle\n", + " return S\n", + "```\n", + "\n", + "\n" + ], + "metadata": { + "id": "WXX2aU8kjXcj" + } + }, + { + "cell_type": "markdown", + "source": [ + "**Question 3:**\n", + "\n", + "The Directed Vertex Cover Problem is defined as follows. We are given a directed graph G and an integer k. The problem is to decide whether there exists a set of at most k vertices in G such that every edge in G is incident to at least one vertex in the set.\n", + "\n", + "Demonstrate that the Directed Vertex Cover Problem is NP-complete." + ], + "metadata": { + "id": "JPXJoUxxe292" + } + }, + { + "cell_type": "markdown", + "source": [ + "**Answer 3:**\n", + "\n", + "Proving NP-Completeness of the Directed Vertex Cover Problem\n", + "\n", + "Showing that Directed Vertex Cover is in NP:\n", + "\n", + "A problem is in NP if a solution to it can be verified in polynomial time.\n", + "For the Directed Vertex Cover Problem, given a set of vertices, we can efficiently check if every edge in the graph is incident to at least one vertex in this set. This verification involves examining each edge against the set of selected vertices, a task that can be accomplished in polynomial time relative to the graph's size.\n", + "Demonstrating Directed Vertex Cover is NP-hard:\n", + "\n", + "Establishing NP-hardness typically involves reducing a known NP-complete problem to the problem in question. The Vertex Cover Problem, known to be NP-complete, is often used for such reductions.\n", + "Reduction Process from Vertex Cover to Directed Vertex Cover:\n", + "Begin with an instance of the Vertex Cover Problem: an undirected graph G' and an integer k.\n", + "Transform this into an instance of the Directed Vertex Cover Problem. For each edge (u, v) in G', create two directed edges (u, v) and (v, u) in a new directed graph G.\n", + "The graph G and the integer k form the instance for the Directed Vertex Cover Problem.\n", + "This conversion can be executed in polynomial time.\n", + "If a vertex cover of size k exists in G', the same set of vertices will suffice for covering all directed edges in G. Conversely, a vertex cover in G implies a vertex cover in G'.\n", + "By showing that the Directed Vertex Cover Problem is in NP and that an instance of the NP-complete Vertex Cover Problem can be polynomially reduced to an instance of the Directed Vertex Cover Problem, we prove that the Directed Vertex Cover Problem is NP-complete." + ], + "metadata": { + "id": "pPO00Pp6m8pE" + } + }, + { + "cell_type": "markdown", + "source": [ + "Pseudo Code:\n", + "\n", + "```\n", + "Algorithm DirectedVertexCover(G, k)\n", + " Input: A directed graph G(V, E), an integer k\n", + " Output: A set of vertices that form a vertex cover of size at most k, if it exists\n", + "\n", + " 1. If k < 0, return NO SOLUTION (since we cannot have a negative number of vertices)\n", + " 2. If E is empty, return EMPTY SET (since no vertices are needed to cover an empty set of edges)\n", + "\n", + " 3. For each vertex v in V:\n", + " a. Create a new graph G' by removing v and all edges incident to v from G\n", + " b. Recursively call DirectedVertexCover(G', k - 1)\n", + " c. If the recursive call returns a solution S:\n", + " i. Add v to S\n", + " ii. Return S\n", + "\n", + " 4. Return NO SOLUTION (if no vertex cover of size at most k is found)\n", + "\n", + "// Main execution\n", + "G = [Graph input]\n", + "k = [Size input]\n", + "result = DirectedVertexCover(G, k)\n", + "\n", + "if result is NO SOLUTION:\n", + " Print \"No vertex cover of size k exists.\"\n", + "else:\n", + " Print \"Vertex cover of size k found: \", result\n", + "\n", + "```\n", + "\n" + ], + "metadata": { + "id": "mM_ygBZ7orbn" + } + }, + { + "cell_type": "markdown", + "source": [ + "**Question 4:**\n", + "\n", + "The Directed Cycle Cover Problem is defined as follows: Given a directed graph G, the task is to decide whether there exists a set of vertex-disjoint cycles that together cover all the vertices of G.\n", + "\n", + "Demonstrate that the Directed Cycle Cover Problem is NP-complete." + ], + "metadata": { + "id": "8pINFI05e3WU" + } + }, + { + "cell_type": "markdown", + "source": [ + "**Answer 4:**\n", + "\n", + "The Directed Cycle Cover Problem is defined as follows: Given a directed graph G, determine if there exists a set of vertex-disjoint cycles that together cover all the vertices of G. Prove that this problem is NP-complete.\n", + "\n", + "Solution\n", + "1. Showing that Directed Cycle Cover is in NP:\n", + "\n", + "A problem is in NP if a given solution can be verified in polynomial time.\n", + "For the Directed Cycle Cover Problem, given a set of cycles, it can be verified in polynomial time whether these cycles are vertex-disjoint and cover all vertices in G.\n", + "2. Showing that Directed Cycle Cover is NP-hard:\n", + "\n", + "Use reduction from the Hamiltonian Cycle Problem, which is known to be NP-complete.\n", + "Reduction from Hamiltonian Cycle to Directed Cycle Cover:\n", + "Take an instance of the Hamiltonian Cycle Problem (a directed graph G').\n", + "Use the same graph as an instance for the Directed Cycle Cover Problem.\n", + "A Hamiltonian cycle in G' would be a valid cycle cover in G, covering all vertices with a single cycle.\n", + "Conversely, if a directed graph has a cycle cover covering all vertices, it implies the existence of a Hamiltonian cycle if the cover consists of exactly one cycle." + ], + "metadata": { + "id": "GYa4Gyq9pTiJ" + } + }, + { + "cell_type": "markdown", + "source": [ + "**Pseudo code:**\n", + "\n", + "```\n", + "Algorithm VerifyDirectedCycleCover(G, Cycles)\n", + " Input: A directed graph G(V, E), a set of cycles Cycles\n", + " Output: True if Cycles form a valid cycle cover of G, False otherwise\n", + "\n", + " 1. Create a set CoveredVertices to keep track of covered vertices.\n", + " 2. For each cycle in Cycles:\n", + " a. For each vertex v in the cycle:\n", + " i. If v is already in CoveredVertices, return False (as cycles are not disjoint).\n", + " ii. Add v to CoveredVertices.\n", + " 3. If CoveredVertices contains all vertices in V, return True.\n", + " 4. Else, return False.\n", + "\n", + "// Main execution\n", + "G = [Graph input]\n", + "Cycles = [Set of cycles input]\n", + "result = VerifyDirectedCycleCover(G, Cycles)\n", + "\n", + "if result:\n", + " Print \"The cycles form a valid cycle cover.\"\n", + "else:\n", + " Print \"The cycles do not form a valid cycle cover.\"\n", + "\n", + "```\n", + "\n" + ], + "metadata": { + "id": "3c2fGR76prOT" + } + }, + { + "cell_type": "markdown", + "source": [ + "**Question 5:**\n", + "\n", + "The Cheapest Teacher Set Problem is defined as follows: You are organizing a game development workshop and need instructors proficient in each of the n required skills for game development (like programming, art, animation, modeling, artificial intelligence, and analytics). You have m potential instructors, each skilled in a subset of these skills. The question is: For a given number k ≤ m, is it possible to hire at most k instructors who collectively possess all n required skills? This is known as the Cheapest Teacher Set Problem." + ], + "metadata": { + "id": "KJPA4h5oe3nh" + } + }, + { + "cell_type": "markdown", + "source": [ + "**Answer 5:**\n", + "\n", + "Cheapest Teacher Set is in NP:\n", + "\n", + "A problem is in NP if a given solution can be verified quickly (in polynomial time).\n", + "For the Cheapest Teacher Set Problem, given a set of k instructors, we can verify in polynomial time if between them they cover all n skills. This involves checking each skill against the skillsets of the selected instructors.\n", + "Cheapest Teacher Set is NP-hard:\n", + "\n", + "To show NP-hardness, we typically reduce a known NP-complete problem to our problem. In this case, we can use the Set Cover Problem, which is known to be NP-complete.\n", + "Reduction from Set Cover to Cheapest Teacher Set:\n", + "Given an instance of the Set Cover Problem (a universe of elements and a collection of sets), interpret each element as a required skill and each set as a potential instructor's skillset.\n", + "The task in the Set Cover Problem of covering all elements with a minimum number of sets parallels hiring the smallest number of instructors to cover all skills.\n", + "Thus, a solution to the Set Cover Problem provides a solution to the Cheapest Teacher Set Problem, and vice versa.\n", + "\n", + "Conclusion:\n", + "By demonstrating that the Cheapest Teacher Set Problem is in NP and that it is as hard as the Set Cover Problem (an NP-complete problem), we establish that the Cheapest Teacher Set Problem is NP-complete." + ], + "metadata": { + "id": "s1Jc7hmExbHW" + } + }, + { + "cell_type": "markdown", + "source": [ + "**Pseudo Code:**\n", + "\n", + "```\n", + "Algorithm VerifyCheapestTeacherSet(Instructors, Skills, k)\n", + " Input: A set of potential instructors Instructors, each with their own set of skills,\n", + " A set of required skills Skills,\n", + " An integer k representing the maximum number of instructors to hire\n", + " Output: True if it is possible to hire at most k instructors that cover all skills, False otherwise\n", + "\n", + " 1. If the size of Instructors is greater than k, return False (as we cannot hire more than k instructors)\n", + "\n", + " 2. Create a set CoveredSkills to keep track of covered skills\n", + "\n", + " 3. For each instructor in Instructors:\n", + " a. Add the skills of this instructor to CoveredSkills\n", + "\n", + " 4. For each skill in Skills:\n", + " a. If this skill is not in CoveredSkills, return False (as not all skills are covered)\n", + "\n", + " 5. Return True (all skills are covered with at most k instructors)\n", + "\n", + "// Main execution\n", + "Instructors = [Set of potential instructors with their skills]\n", + "Skills = [Set of required skills]\n", + "k = [Maximum number of instructors to hire]\n", + "\n", + "result = VerifyCheapestTeacherSet(Instructors, Skills, k)\n", + "\n", + "if result:\n", + " Print \"It is possible to hire at most k instructors to cover all skills.\"\n", + "else:\n", + " Print \"It is not possible to hire at most k instructors to cover all skills.\"\n", + "\n", + "```\n", + "\n", + "\n" + ], + "metadata": { + "id": "qjofE6C8xbaQ" + } + }, + { + "cell_type": "markdown", + "source": [ + "**Question 6:**\n", + "\n", + "The Optimal Workshop Schedule Problem is defined as follows: You are organizing a series of technical workshops, each requiring a specific set of expertise areas (like cloud computing, cybersecurity, data science, etc.). You have a pool of n experts, each with expertise in a variety of these areas. The goal is to determine, for a given number k ≤ n, whether it's possible to schedule at most k experts in such a way that each workshop has at least one expert in its required expertise area. This challenge is known as the Optimal Workshop Schedule Problem." + ], + "metadata": { + "id": "qrP36eiuxb-D" + } + }, + { + "cell_type": "markdown", + "source": [ + "**Answer 6:**\n", + "\n", + "Optimal Workshop Schedule is in NP:\n", + "\n", + "A problem is in NP if any given solution can be verified quickly (in polynomial time).\n", + "For the Optimal Workshop Schedule Problem, given a set of k experts, you can verify in polynomial time whether these experts collectively cover all the expertise areas required by the workshops. This involves checking each workshop’s requirements against the expertise of the selected experts.\n", + "Optimal Workshop Schedule is NP-hard:\n", + "\n", + "To prove NP-hardness, a known NP-complete problem is typically reduced to the problem in question. For this scenario, the Set Cover Problem, which is NP-complete, can be used for reduction.\n", + "Reduction from Set Cover to Optimal Workshop Schedule:\n", + "Take an instance of the Set Cover Problem (a universe of elements and a collection of sets) and interpret each element as a required expertise area and each set as the expertise profile of a potential expert.\n", + "The task of covering all elements in the Set Cover Problem with a minimum number of sets parallels scheduling the fewest experts to cover all required expertise areas in the workshops.\n", + "Thus, a solution to the Set Cover Problem is equivalent to a solution to the Optimal Workshop Schedule Problem and vice versa.\n", + "\n", + "By demonstrating that the Optimal Workshop Schedule Problem is in NP and that it can be transformed from the Set Cover Problem, we establish that the Optimal Workshop Schedule Problem is NP-complete." + ], + "metadata": { + "id": "O0p1Xfs-zQYT" + } + }, + { + "cell_type": "markdown", + "source": [ + "**Pseudo Code:**\n", + "\n", + "```\n", + "Algorithm VerifyOptimalWorkshopSchedule(Experts, Workshops, k)\n", + " Input: A set of experts Experts, each with their own expertise areas,\n", + " A set of workshops Workshops, each requiring specific expertise areas,\n", + " An integer k representing the maximum number of experts to schedule\n", + " Output: True if it is possible to schedule at most k experts covering all workshops, False otherwise\n", + "\n", + " 1. If the size of Experts is greater than k, return False (can't schedule more than k experts)\n", + "\n", + " 2. Create a set CoveredWorkshops to keep track of covered workshops\n", + "\n", + " 3. For each expert in Experts:\n", + " a. For each workshop in Workshops:\n", + " i. If the expert covers the required expertise area of the workshop:\n", + " - Add the workshop to CoveredWorkshops\n", + "\n", + " 4. If CoveredWorkshops contains all workshops in Workshops, return True\n", + " 5. Else, return False\n", + "\n", + "// Main execution\n", + "Experts = [Set of experts with their expertise areas]\n", + "Workshops = [Set of workshops with required expertise areas]\n", + "k = [Maximum number of experts to schedule]\n", + "\n", + "result = VerifyOptimalWorkshopSchedule(Experts, Workshops, k)\n", + "\n", + "if result:\n", + " Print \"It is possible to schedule at most k experts covering all workshops.\"\n", + "else:\n", + " Print \"It is not possible to schedule at most k experts covering all workshops.\"\n", + "\n", + "```\n", + "\n" + ], + "metadata": { + "id": "o8aJHVLCxcWa" + } + }, + { + "cell_type": "markdown", + "source": [ + "**Question 7:**\n", + "\n", + "Suppose you are involved in organizing a summer sports camp, which leads to the following challenge. The camp needs to ensure that there is at least one counselor skilled in each of the n sports offered at the camp (like baseball, volleyball, etc.). There are m potential counselors who have applied, and for each sport, only a subset of these applicants is qualified. The question is: For a specified number k < m, is it possible to hire at most k counselors such that every one of the n sports has at least one qualified counselor? This scenario is referred to as the Efficient Recruiting Problem." + ], + "metadata": { + "id": "xm8QzOsuxcuX" + } + }, + { + "cell_type": "markdown", + "source": [ + "**Answer 7:**\n", + "\n", + "The Efficient Recruiting Problem, in the context of organizing a summer sports camp, involves finding the minimum number of counselors who can cover all the required sports. Let's break it down with an example for better understanding.\n", + "\n", + "Example Scenario:\n", + "\n", + "Sports at Camp: Baseball, Volleyball, Swimming, Archery (i.e., n=4 sports).\n", + "Applicants (Counselors):\n", + "Counselor A: Skilled in Baseball, Volleyball.\n", + "Counselor B: Skilled in Swimming.\n", + "Counselor C: Skilled in Archery, Baseball.\n", + "Counselor D: Skilled in Volleyball, Swimming, Archery.\n", + "(Thus, m=4 potential counselors).\n", + "\n", + "Problem Statement:\n", + "\n", + "Is it possible to hire at most k counselors (where k