Problem Formulation & Method Solving in Artificial Intelligence (AI) organizes a number of steps to formulate a target/goals which require specific action to achieve the goal.
Hence, some methods used in Problem Formulation are :-
• Tree structure
• Graphical model
• Implementation of graph
The Tree Structure
• Connected list, stack, and queue are 1-D data structures.
• Hence, tree is a 2-D data structure.
– Family tree;
– Tournament tree for a football game;
– Organization tree of a company; and
– Directory tree of a file management system.
• The nodes that have the same parent are known as Siblings.
• Path is a sequence of nodes(no. of nodes) connected by edges
• Level of a node refers to the number of edges contained in the path hence from the root to this node
• Height of the tree indicates maximum distance from the root to the terminal nodes
Multi-way tree and binary tree
• Multi-way tree or multi-branch tree
– Hence, an internal node having more than 2 child nodes is known as a Multi-way tree or multi-branch tree.
– Hence, binary tree is useful both for information retrieval (binary search tree) and for pattern classification (e.g. decision tree).
• Complete binary tree：
– A binary tree is the one in which every node has 2 children. Hence, a binary tree is completely full, and nodes in the last level are as far left as possible.
• A graph is in use as 2-tuple where 𝑉 is a set of vertices or nodes; and 𝐸 is a set of edges, arcs, or connections.
𝐺 = (𝑉, 𝐸)
where 𝑉 is a set of vertices or nodes; and 𝐸 is a set of edges, arcs, or connections.
• Hence, Tree is a special graph without cycles.
– Hence, the path which the root forms is unique.
• Adjacency-list representation：
– N=|V|：number of nodes
– Hence, we define N lists Adj, Adj, …, Adj[N-1]
– Adj[i] is the list for the ith node, which basically contains all nodes connected to this node by an edge.
– That is, for any node j contained in Adj[i], (i,j) belongs to the set E of edges.
The above fig. explains the Adjacency-list representation.