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examples/simple_example.jl

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+# Simple MCTS Example
+
+This example demonstrates basic MCTS usage with a simple state transition function.
+
+```julia
+using LLMMCTS
+
+# Define a simple state transition function
+function simple_transition(state::Dict, args::NamedTuple)
+    # In a real scenario, this would call an LLM
+    # For this example, we'll just generate deterministic next states
+    
+    current_step = get(state, :step, 0)
+    new_step = current_step + 1
+    
+    # Create new state
+    newstate = Dict(
+        :step => new_step,
+        :reward => new_step * 2,  # Simple reward function
+        :isterminal => new_step >= args.max_steps
+    )
+    
+    # LLM would provide progressvalue estimate
+    progressvalue = (new_step / args.max_steps) * 10
+    
+    return Dict(
+        :newNodeKey => "step_$(new_step)",
+        :newstate => newstate,
+        :progressvalue => progressvalue
+    )
+end
+
+# Initial state
+initialstate = Dict(
+    :step => 0,
+    :reward => 0,
+    :isterminal => false
+)
+
+# Transition arguments
+transitionargs = (max_steps = 5,)
+
+# Run MCTS
+result = runMCTS(
+    initialstate,
+    simple_transition,
+    transitionargs;
+    maxiterations = 10,
+    explorationweight = 1.0,
+    maxSimulationDepth = 3,
+    horizontalSampleExpansionPhase = 3
+)
+
+# Access results
+println("Root node visits: ", result.root.visits)
+println("Best next state: ", result.bestNextState)
+println("Best terminal state: ", result.bestTerminalState)
+println("High value states: ", result.highValueStateList)
+```