AI: Missionaries and Cannibals Problem

Study Notes

Artificial Intelligence (AI) is the field of computer science dedicated to creating systems that can perform tasks that typically require human intelligence
These tasks include learning, problem-solving, perception, understanding natural language, and logical reasoning
AI aims to develop machines that can think, learn, and act autonomously

The Missionaries and Cannibals problem is a classic state-space search problem often used to illustrate AI problem-solving techniques
Three missionaries and three cannibals must cross a river using a boat that can carry at most two people
The constraint is that if the cannibals ever outnumber the missionaries on either bank of the river, the missionaries will be eaten
The problem is to find a sequence of boat trips that transports everyone safely across the river

State: The state of the problem can be represented by a tuple (M, C, B), where
- M is the number of missionaries on the starting bank
- C is the number of cannibals on the starting bank
- B indicates the location of the boat (0 for the starting bank, 1 for the destination bank)
Initial State: The initial state is (3, 3, 0), meaning all three missionaries and three cannibals are on the starting bank, and the boat is also on the starting bank
Goal State: The goal state is (0, 0, 1), meaning all missionaries and cannibals have crossed to the destination bank and the boat is on the destination bank
Actions: The possible actions are the different ways to transport people across the river using the boat
- Two missionaries
- Two cannibals
- One missionary and one cannibal
- One missionary
- One cannibal
Transition Model: The transition model describes how each action changes the state
For example, if the current state is (3, 3, 0) and the action is to send one missionary and one cannibal across the river, the new state becomes (2, 2, 1)
Cost Function: The cost function typically assigns a cost of 1 to each action, as the objective is to minimize the number of crossings

The state space consists of all possible states reachable from the initial state through valid actions
States can be visualized as nodes in a graph
Actions are the edges connecting the nodes
The state space must be explored to find the path from the initial state to the goal state

The primary constraint is that on either bank of the river, the number of cannibals must never exceed the number of missionaries
This constraint ensures the missionaries' safety

The Missionaries and Cannibals problem can be solved using various search algorithms
These search algorithms include Breadth-First Search (BFS), Depth-First Search (DFS), and A* search
BFS explores all possible paths of a given length before moving to longer paths
DFS explores one path as deeply as possible before backtracking
A* search uses a heuristic to estimate the cost of reaching the goal from a given state, guiding the search towards promising paths

One possible solution involves the following steps:
- Send two cannibals across
- Return one cannibal
- Send two cannibals across
- Return one cannibal
- Send two missionaries across
- Return one missionary and one cannibal
- Send two missionaries across
- Return one cannibal
- Send two cannibals across
- Return one cannibal
- Send two cannibals across
This sequence of actions ensures that the constraint regarding the number of cannibals and missionaries on each bank is always satisfied

The Missionaries and Cannibals problem is important for several reasons
It serves as an understandable example of state-space search, which is a fundamental concept in AI
It demonstrates the use of constraints in problem-solving
It illustrates how different search algorithms can be applied to solve the same problem
It provides a framework for modeling and solving other similar problems involving resource transfer and constraints