Map a function at a given level of a tree

In Julia, you can map a function at a given level of a tree in different ways. Here, we will explore three different options to achieve this.

Option 1: Using recursion

function map_tree(f, tree, level)
    if level == 1
        return f(tree)
    elseif level > 1
        return map(x -> map_tree(f, x, level-1), tree)
    else
        return tree
    end
end

In this option, we define a recursive function map_tree that takes a function f, a tree, and a level as input. If the level is 1, we apply the function f to the tree. If the level is greater than 1, we recursively apply map_tree to each element of the tree at the next lower level. If the level is less than or equal to 0, we return the tree as is. This option allows mapping a function at any level of the tree.

Option 2: Using a loop

function map_tree(f, tree, level)
    for i in 1:level
        tree = map(f, tree)
    end
    return tree
end

In this option, we define a function map_tree that takes a function f, a tree, and a level as input. We use a loop to repeatedly apply the map function to the tree for the specified number of levels. This option is simpler and more straightforward compared to the recursive approach.

Option 3: Using a combination of recursion and loop

function map_tree(f, tree, level)
    if level == 1
        return map(f, tree)
    elseif level > 1
        for i in 1:level
            tree = map(x -> map_tree(f, x, level-1), tree)
        end
        return tree
    else
        return tree
    end
end

In this option, we combine the recursive approach with a loop. If the level is 1, we directly apply the map function to the tree. If the level is greater than 1, we recursively apply map_tree to each element of the tree at the next lower level using a loop. This option provides flexibility and allows mapping a function at any level of the tree.

Among the three options, the best choice depends on the specific requirements and complexity of the tree structure. Option 1 (using recursion) is suitable when the tree has a known depth and the mapping needs to be performed at a specific level. Option 2 (using a loop) is preferable when the depth of the tree is not known in advance or when a simple and straightforward solution is desired. Option 3 (using a combination of recursion and loop) provides flexibility and can handle trees with varying depths. It is recommended to choose the option that best suits the specific use case.