# Problem Formulation & Method Solving in Artificial Intelligence

Before an agent can start searching for solutions, it must formulate a goal and then use that goal to formulate a problem.

Problem Formulation & Method Solving in Artificial Intelligence (AI) organizes several steps to formulate a target/goals which require a specific action to achieve the goal.

Hence, today, Problem Formulation & Method Solving in Artificial Intelligence is in use in various domains to formulate the goal based on AI agents.

##### 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.

• Examples:

– Family tree;

– Tournament tree for a football game;

– Organization tree of a company; and

– Directory tree of a file management system.

## Useful terminologies

• 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 the 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, a 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 full, and nodes in the last level are as far left as possible.

## Graphical Analysis

• 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.

– N=|V|：number of nodes 