Missionaries and Cannibals

Aight. Assume that there are three missionaries and three cannibals on one side of a river. They need to cross the river using a boat that can carry at most two people. If the cannibals ever outnumber the missionaries on either side of the river, the missionaries will be eaten. How can they all cross the river safely?

This, is the Missionaries and Cannibals problem. It is a classic river-crossing puzzle that is often used to demonstrate the capabilities of search algorithms in artificial intelligence.

In this post, we will discuss the problem in detail and explore how it can be solved using a search algorithm.

Problem Statement

The Missionaries and Cannibals problem can be defined as follows:

• There are three missionaries and three cannibals on one side of a river.
• They need to cross the river to the other side.
• They have a boat that can carry at most two people.
• If the cannibals ever outnumber the missionaries on either side of the river, the missionaries will be eaten.

The goal is to find a sequence of boat trips that will safely transport all the missionaries and cannibals to the other side of the river without violating the constraints of the problem.

Modeling the Problem

State Representation

If you dont know what a state is, here is a quick refresher:

State is a representation of the problem at a given point in time. For instance, in the Missionaries and Cannibals problem, a state could represent the number of missionaries and cannibals on each side of the river, as well as the position of the boat.

The initial state of the problem is:

• 3 missionaries and 3 cannibals on the left side of the river. (3, 3, L)
• 0 missionaries and 0 cannibals on the right side of the river. (0, 0, R)

The goal state of the problem is:

• 0 missionaries and 0 cannibals on the left side of the river. (0, 0, L)

Transitions

Transitions represent the actions that can be taken to move from one state to another.

In the Missionaries and Cannibals problem, the possible actions are:

• Move 1 missionary from left to right.
• Move 2 missionaries from left to right.
• Move 1 cannibal from left to right.
• Move 2 cannibals from left to right.
• Move 1 missionary and 1 cannibal from left to right.

Each action will result in a new state of the problem.

Solving the Problem

To solve the Missionaries and Cannibals problem, we can use a search algorithm to explore the state space and find a sequence of actions that will lead us from the initial state to the goal state.

One common search algorithm that can be used to solve this problem is the state-space search algorithm.

The state-space search algorithm works by exploring the state space of the problem, starting from the initial state and moving through the possible actions to reach the goal state.

In the case of the Missionaries and Cannibals problem, the state-space search algorithm will explore the possible actions that can be taken to move from one state to another, making sure to avoid any states that violate the constraints

Solution

A simple simulation

Here is a simple simulation of the Missionaries and Cannibals:

Code Implementation

The below python code demonstrates how the Missionaries and Cannibals problem can be solved using a state-space search and the breadth-first search algorithm. It systemetically explores all valid states and transitions between them.

The code is self explanatory and should be easy to understand. If you have any questions, feel free to ask me in either of my social media handles or in the comments section below.

from collections import deque

# Define the initial state
INITIAL_STATE = (3, 3, 0, 0, 'left')  # (M_left, C_left, M_right, C_right, boat_position)
GOAL_STATE = (0, 0, 3, 3, 'right')    # (M_left, C_left, M_right, C_right, boat_position)

def is_valid_state(state):
    """
    Checks if a given state is valid (no more cannibals than missionaries on either side).
    """
    M_left, C_left, M_right, C_right, _ = state
    # Ensure non-negative values
    if M_left < 0 or C_left < 0 or M_right < 0 or C_right < 0:
        return False
    # Missionaries must not be outnumbered by cannibals on either side
    if (M_left > 0 and M_left < C_left) or (M_right > 0 and M_right < C_right):
        return False
    return True

def get_next_states(state):
    """
    Generates all possible valid next states from the current state.
    """
    M_left, C_left, M_right, C_right, boat_position = state
    next_states = []

    # Define all possible moves
    moves = [
        (1, 0),  # 1 Missionary
        (0, 1),  # 1 Cannibal
        (2, 0),  # 2 Missionaries
        (0, 2),  # 2 Cannibals
        (1, 1),  # 1 Missionary and 1 Cannibal
    ]

    for M, C in moves:
        if boat_position == 'left':
            new_state = (M_left - M, C_left - C, M_right + M, C_right + C, 'right')
        else:
            new_state = (M_left + M, C_left + C, M_right - M, C_right - C, 'left')

        if is_valid_state(new_state):
            next_states.append(new_state)

    return next_states

def bfs_search(initial_state, goal_state):
    """
    Solves the Missionaries and Cannibals problem using Breadth-First Search (BFS).
    """
    queue = deque([(initial_state, [])])  # Queue of (current_state, path_to_state)
    visited = set()                       # Keep track of visited states

    while queue:
        current_state, path = queue.popleft()

        # Check if goal state is reached
        if current_state == goal_state:
            return path + [current_state]

        if current_state in visited:
            continue
        visited.add(current_state)

        # Generate next states
        for next_state in get_next_states(current_state):
            queue.append((next_state, path + [current_state]))

    return None  # No solution found

# Run the solution
solution = bfs_search(INITIAL_STATE, GOAL_STATE)

# Print the solution path
if solution:
    print("Solution found!")
    for step, state in enumerate(solution):
        print(f"Step {step}: {state}")
else:
    print("No solution found.")

Conclusion

In this post, we discussed the Missionaries and Cannibals problem and how it can be solved using a search algorithm, along with a simple simulation of the problem, and a code implementation in Python. I hope you found this post helpful and that it gave you a better understanding of how search algorithms can be used to solve complex problems in artificial intelligence.

If you have any questions or feedback, feel free to leave a comment below. I'd love to hear from you!

Until next time, happy coding! 🚀