# Define a serialization format for the symbolic equations:
mutable struct Node
    #Holds operators, variables, constants in a tree
    degree::Integer #0 for constant/variable, 1 for cos/sin, 2 for +/* etc.
    val::Union{Float32, Integer} #Either const value, or enumerates variable
    constant::Bool #false if variable
    op::Integer #enumerates operator (separately for degree=1,2)
    l::Union{Node, Nothing}
    r::Union{Node, Nothing}

    Node(val::Float32) = new(0, val, true, 1, nothing, nothing)
    Node(val::Integer) = new(0, val, false, 1, nothing, nothing)
    Node(op::Integer, l::Node) = new(1, 0.0f0, false, op, l, nothing)
    Node(op::Integer, l::Union{Float32, Integer}) = new(1, 0.0f0, false, op, Node(l), nothing)
    Node(op::Integer, l::Node, r::Node) = new(2, 0.0f0, false, op, l, r)

    #Allow to pass the leaf value without additional node call:
    Node(op::Integer, l::Union{Float32, Integer}, r::Node) = new(2, 0.0f0, false, op, Node(l), r)
    Node(op::Integer, l::Node, r::Union{Float32, Integer}) = new(2, 0.0f0, false, op, l, Node(r))
    Node(op::Integer, l::Union{Float32, Integer}, r::Union{Float32, Integer}) = new(2, 0.0f0, false, op, Node(l), Node(r))
end

# Copy an equation (faster than deepcopy)
function copyNode(tree::Node)::Node
   if tree.degree == 0
       return Node(tree.val)
   elseif tree.degree == 1
       return Node(tree.op, copyNode(tree.l))
    else
        return Node(tree.op, copyNode(tree.l), copyNode(tree.r))
   end
end

# Count the operators, constants, variables in an equation
function countNodes(tree::Node)::Integer
    if tree.degree == 0
        return 1
    elseif tree.degree == 1
        return 1 + countNodes(tree.l)
    else
        return 1 + countNodes(tree.l) + countNodes(tree.r)
    end
end

# Count the max depth of a tree
function countDepth(tree::Node)::Integer
    if tree.degree == 0
        return 1
    elseif tree.degree == 1
        return 1 + countDepth(tree.l)
    else
        return 1 + max(countDepth(tree.l), countDepth(tree.r))
    end
end

# Convert an equation to a string
function stringTree(tree::Node)::String
    if tree.degree == 0
        if tree.constant
            return string(tree.val)
        else
            if useVarMap
                return varMap[tree.val]
            else
                return "x$(tree.val - 1)"
            end
        end
    elseif tree.degree == 1
        return "$(unaops[tree.op])($(stringTree(tree.l)))"
    else
        return "$(binops[tree.op])($(stringTree(tree.l)), $(stringTree(tree.r)))"
    end
end

# Print an equation
function printTree(tree::Node)
    println(stringTree(tree))
end

# Return a random node from the tree
function randomNode(tree::Node)::Node
    if tree.degree == 0
        return tree
    end
    a = countNodes(tree)
    b = 0
    c = 0
    if tree.degree >= 1
        b = countNodes(tree.l)
    end
    if tree.degree == 2
        c = countNodes(tree.r)
    end

    i = rand(1:1+b+c)
    if i <= b
        return randomNode(tree.l)
    elseif i == b + 1
        return tree
    end

    return randomNode(tree.r)
end

# Count the number of unary operators in the equation
function countUnaryOperators(tree::Node)::Integer
    if tree.degree == 0
        return 0
    elseif tree.degree == 1
        return 1 + countUnaryOperators(tree.l)
    else
        return 0 + countUnaryOperators(tree.l) + countUnaryOperators(tree.r)
    end
end

# Count the number of binary operators in the equation
function countBinaryOperators(tree::Node)::Integer
    if tree.degree == 0
        return 0
    elseif tree.degree == 1
        return 0 + countBinaryOperators(tree.l)
    else
        return 1 + countBinaryOperators(tree.l) + countBinaryOperators(tree.r)
    end
end

# Count the number of operators in the equation
function countOperators(tree::Node)::Integer
    return countUnaryOperators(tree) + countBinaryOperators(tree)
end


# Count the number of constants in an equation
function countConstants(tree::Node)::Integer
    if tree.degree == 0
        return convert(Integer, tree.constant)
    elseif tree.degree == 1
        return 0 + countConstants(tree.l)
    else
        return 0 + countConstants(tree.l) + countConstants(tree.r)
    end
end