Create Second tree with tikz-trees where it shares some node with the first tree

Question

I'm working on a paper with several operations on Binary Tree, and I make a lot of posts related to the tree in the last weeks. At the moment I'm stuck because I need to customize one of the tree template proposed in one of the previous answers, In particular this answer

I result that I want to achieve is the following tree effect.

This is the tree where I want to put the previous effect before

\documentclass[12pt, margin=3mm]{standalone}
\usepackage{forest}
\usetikzlibrary{arrows.meta,
                backgrounds,
                fit}

\begin{document}
    \begin{forest}
for tree = {
% nodes
    circle, draw, fill=gray!30,
    minimum size=1.5em, inner sep=0pt, outer sep=0pt,
/tikz/every label/.style = {font=\tiny},
/tikz/FIT/.style = {draw, very thick, rounded corners, fill=gray!30,
                    inner sep=4pt, inner ysep=8pt, yshift=-4pt,
                    fit=#1},
% tree
/tikz/every edge/.style={draw=gray, -Straight Barb, 
                         -Straight Barb, shorten >=3pt, shorten <=3pt,
                         bend angle = 15},% style for bended arrows
    edge=semithick,
    l sep=4mm,
    s sep=12mm,
    where level=3{l sep=11mm}{},% at level 3 increase l sep
    where level=4{no edge, very thick, fill=white}{},
            }% level 4 is the lowest
[11, label=below:{1:[0,7]},  name=t0
    [13, label=below:{2:[0,3]},  name=t11
        [17, label=below:{4:[0,1]},  name=t21
            [18, thick, label=below:{8:[0,0]}
                [18, label=below:0]
            ]
            [17, draw=none, fill=gray,thick, label=below:{9:[1,1]},  name=t31
                [17, label=below:1, name=n1]
            ]
        ]
        [13, draw=none,fill=gray, label=below:{5:[2,3]}
            [13, very thick, label=below:{10:[2,2]}
                [13, draw=none, fill=gray, label=below:2]
            ]
            [19, very thick, label=below:{11:[3,3]}
                [19, label=below:3, name=n3]
            ]
        ]
    ]
    [11, very thick,edge=thick, label=below:{3:[4,7]}
        [11, thick,edge=thick,
            [15, thick,edge=thick,
                [15, label=below:4]
            ]
            [11, very thick,edge=thick,
                [13, label=below:5]
            ]
        ]
        [20, very thick,edge=thick,
            [20, very thick,edge=thick,
                [13, label=below:6]
            ]
            [99, very thick,edge=thick,,
                [13, label=below:7]
            ]
        ]
     ]
]
\end{forest}
\end{document}

In other words, I need to make a separate tree (yellow) tree in the picture that gives me the possibility to attach some nodes to some nodes of the previous tree (blue).

I'm trying to simulate a persistent data structure, and this data structure reuse some node of the old tree to make a new tree (partially new tree)

My idea is to make one single tree and join the node as an arch but it looks very bad with my actual code and I have difficulties to customize to active my object.

Answer 1

• What is the problem? How to reproduce showed image?
• Do you like that MWE (which is from answer on your previous question) would serve as starting point? if so, than you need to do the following:
  • remove all labels of nodes
  • remove definition for every label style
  • remove definition for FIT style
  • remove definition for every edge style
  • remove nodes in the lowest (4) levels
  • remove definition for 4 level
  • existing root node replace with [,phantom
• After above taken measures obtained MWE should produce the following result:

• The next step let be redesign of the left tree:
  • in the left branch replace numbers 13, 17 18 with 1', 2' and 3', which are in yellow nodes on your images.
  • add new fill color to this nodes
  • After this the first four lines of tree body are:

[,phantom
    [1', fill=yellow, name=t11
        [2', fill=yellow, name=t21
            [3',fill=yellow]

• remove nodes with numbers 13 and 19 at bottom of tree. Now tree should looks as:
• for finish redesign of left tree you need to make nodes with number 17 and 13 as phantom nodes:

[,phantom
    [1', fill=yellow, name=t11
        [2', fill=yellow, name=t21
            [3',fill=yellow]
            [,phantom]
        ]
        [,phantom]
    ]% end of left tree

• Now tree should looks as:

• for right tree you only need to do the following:
  • replace existing contents with new, showed on your image
  • give names to node with number 5 and number 3:

    ]% end of left tree
    [1
        [2
            [4]
            [5,name=t32]
        ]
        [3, name=t22
            [6]
            [7]
        ]
     ]% end of right tree

• On the end you need first to draw lines between left and right tree:

]% end of tree
\draw[very thick, orange]   (t11) -- (t22)
                            (t21) -- (t32);

• After all described actions you should obtain the following result:

• If the result obtained is satisfactory, the you are done with the work. Of course, you can beautify the resulting tree a wee bit by following changes in the preamble \for tree:
  • changing s sep=12 to for example to s sep=3 (that horizontal (sibling) distances between nodes become smaller)
  • to right tree add option fit=band (for increasing distances between trees)
• Considering aforementioned changes, the the complete MWE is:

\documentclass[12pt, margin=3mm]{standalone}
\usepackage{forest}
\usetikzlibrary{arrows.meta,
                backgrounds,
                fit}

\begin{document}
    \begin{forest}
for tree = {
% nodes
    circle, draw, fill=gray!30,
    minimum size=1.5em, inner sep=0pt, outer sep=0pt,
% tree
    edge=semithick,
    l sep=4mm,
    s sep=3mm,      % <------- changed
            }
[,phantom
    [1', fill=yellow, name=t11
        [2', fill=yellow, name=t21
            [3',fill=yellow]
            [,phantom]
        ]
        [,phantom]
    ]% end of left tree
    [1,fit=band     % <------- added
        [2, 
            [4]
            [5,name=t32]
        ]
        [3, name=t22, 
            [6]
            [7]
        ]
     ]% end of right tree
]% end of tree
% connection between left and right tree
\draw[very thick, orange]   (t11) -- (t22)
                            (t21) -- (t32); 
\end{forest}
\end{document}