98 lines
2.6 KiB
Julia
98 lines
2.6 KiB
Julia
# Math Problem Solving - MCTS Example
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This example demonstrates using MCTS to solve a math problem by exploring different solution strategies.
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```julia
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using LLMMCTS
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# State represents the current state of problem solving
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# It contains the problem statement and the steps taken so far
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function math_problem_transition(state::Dict, args::NamedTuple)
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current_step = get(state, :step, 0)
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problem = state[:problem]
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# Example problem: Solve x^2 = 16
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if current_step == 0
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# First step: analyze the problem
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newstate = Dict(
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:step => 1,
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:thought => "This is a quadratic equation x^2 = 16",
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:action => "Take square root of both sides",
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:reward => 2.0,
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:isterminal => false
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)
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progressvalue = 5.0
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elseif current_step == 1
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# Second step: solve
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newstate = Dict(
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:step => 2,
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:thought => "Taking square root gives x = ±4",
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:action => "x = sqrt(16) or x = -sqrt(16)",
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:reward => 3.0,
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:isterminal => false
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)
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progressvalue = 7.0
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elseif current_step == 2
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# Third step: verify
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newstate = Dict(
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:step => 3,
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:thought => "Verify both solutions work",
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:action => "Check x=4: 4^2=16 ✓, Check x=-4: (-4)^2=16 ✓",
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:reward => 5.0,
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:isterminal => true # Problem solved!
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)
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progressvalue = 10.0
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else
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# Terminal state
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newstate = Dict(
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:step => current_step,
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:thought => "Problem solved",
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:action => "Solution complete",
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:reward => 10.0,
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:isterminal => true
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)
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progressvalue = 10.0
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end
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return Dict(
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:newNodeKey => "step_$current_step",
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:newstate => newstate,
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:progressvalue => progressvalue
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)
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end
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# Initial state
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initialstate = Dict(
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:step => 0,
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:problem => "Solve x^2 = 16",
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:reward => 0,
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:isterminal => false
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)
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# Transition arguments
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transitionargs = ()
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# Run MCTS
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result = runMCTS(
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initialstate,
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math_problem_transition,
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transitionargs;
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maxiterations = 15,
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explorationweight = 1.0,
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maxSimulationDepth = 3,
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horizontalSampleExpansionPhase = 3
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)
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# Display results
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println("Problem: ", initialstate[:problem])
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println()
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println("Best solution trajectory:")
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println(" Step ", result.bestTerminalState[:step])
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println(" Thought: ", result.bestTerminalState[:thought])
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println(" Action: ", result.bestTerminalState[:action])
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println()
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println("Solution complete! ✓")
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println("Root node visits: ", result.root.visits)
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```
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