missionaries games missionaries and cannibals problem in ai

This is the goal state, and the path from the root of the tree to this node represents a sequence of actions that solves the problem. The algorithm continues alternating subtraction and addition for each level of the tree until a node is generated with the vector as its value. For each of these remaining nodes, children nodes are generated by adding each of the possible action vectors. The valid children nodes generated would be, , and. Any node that has more cannibals than missionaries on either bank is in an invalid state, and is therefore removed from further consideration. The five possible actions (,, ,, and ) are then subtracted from the initial state, with the result forming children nodes of the root. To fully solve the problem, a simple tree is formed with the initial state as the root. The state would reflect that there are still three missionaries and two cannibals on the wrong side, and that the boat is now on the opposite bank. For instance, if a lone cannibal crossed the river, the vector would be subtracted from the state to yield. Actions are represented using vector subtraction/addition to manipulate the state vector. Since the boat and all of the missionaries and cannibals start on the wrong side, the vector is initialized to. The vector's elements represent the number of missionaries on the wrong side, the number of cannibals on the wrong side, and the number of boats on the wrong side, respectively.

SolvingĪmarel devised a system for solving the Missionaries and Cannibals problem whereby the current state is represented by a simple vector. Therefore, upon changing women to cannibals and men to missionaries, any solution to the jealous husbands problem will also become a solution to the missionaries and cannibals problem.

Under this constraint, there cannot be both women and men present on a bank with women outnumbering men, since if there were, some woman would be husbandless.

In the jealous husbands problem, the missionaries and cannibals become three married couples, with the constraint that no woman can be in the presence of another man unless her husband is also present. In the missionaries and cannibals problem, three missionaries and three cannibals must cross a river using a boat which can carry at most two people, under the constraint that, for both banks, if there are missionaries present on the bank, they cannot be outnumbered by cannibals (if they were, the cannibals would eat the missionaries.) The boat cannot cross the river by itself with no people on board.

Missionaries games missionaries and cannibals problem in ai