To use the algorithms you mention, you need to figure out what the state space of the problem is. A state is a complete description of a situation in the problem (be it the starting situation, the final situation, or an intermediate situation).
The deal is to include just enough information in a state to be able to determine whether the state is a solution to the problem, and, if not, what to do next.
In your case, one possible way of representing the state is to use three variables:
the integer m tells how many missionaries are on the opening side of the river
the integer c tells how many cannibals are on the opening side
the boolean b tells which side the boat is on
Given values for (m, c, b), you can determine which possible actions you can take, and which other states this will bring you to. The algorithms you mention are algorithms for searching through such a set of connected states.
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