Align two trees in TiKZ (states/nodes)

Question

In the following graph, i would like to align the tree with the states 11,12, 13, 14 such that 11-14 is a vertical chain, with state 11 being right of state 1, state 12 being right of state 3, state 13 being right of 6 and state 14 being right of state 10. How can I do this?
documentclass{article}

usepackage{tikz}
usepackage{amsmath}
usetikzlibrary{automata}
usetikzlibrary{calc,arrows.meta,positioning}

newcommand{iddots}{reflectbox{$ddots$}}
begin{document}

resizebox{textwidth}{!}{
begin{tikzpicture}[->,-latex,shorten >=1pt,auto,node distance=40mm,semithick, state/.style={circle, draw, minimum size=2cm}]
node[state](1)                  {$S_0$};
node[state](2)[below left  of=1] {$dcdot S_0$};
node[state](3)[below right of=1]{$u cdot S_0$};
node[state](4)[below left  of=2] {$d^2 cdot S_0$};
node[state](5)[below right of=2]{$du cdot S_0$};
node[state](6)[below right of=3]{$u^2 cdot S_0$};
node[state](7)[below left of=4]{$d^N cdot S_0$};
node[state](8)[below right of=4]{$d^k u^{N-k} cdot S_0$};
node[state](9)[below right of=5]{$d^{N-k}u^{k}cdot S_0$};
node[state](10)[below right of=6]{$u^N cdot S_0$};
node[state](14)[right of=10]{$S_1$};
node[state](13)[above of=14, right of=6]{$S_1$};
node[state](12)[above of=13, right of=3]{$S_1$};
node[state](11)[above of=12, right of=1]{$S_1$};

path (1) edge [swap] node {$1-p$}(2)
      (1) edge        node {$p$}(3)
      (2) edge [swap] node {$1-p$}(4)
      (2) edge        node {$p$}(5)
      (3) edge [swap] node {$1-p$}(5)
      (3) edge        node {$p$}(6);
       node at ($(7)!.5!(8)$) {$hdots$};
       node at ($(8)!.5!(9)$) {$hdots$};
       node at ($(9)!.5!(10)$) {$hdots$};
       
       node at ($(4)!.5!(7)$) {iddots};
       node at ($(5)!.5!(8)$) {iddots};
       node at ($(6)!.5!(9)$) {iddots};
       
       node at ($(4)!.5!(8)$) {$ddots$};
       node at ($(5)!.5!(9)$) {$ddots$};
       node at ($(6)!.5!(10)$) {$ddots$};
end{tikzpicture}
}
end{document}

What I want (more or less):

Excelsior · Accepted Answer

Like I mentioned in the comments, if you have two nodes, you can 'calculate' the corner of an imaginary rectangle using -| to place a node at this position. In your case, you have nodes (14) and (1), (3), (6), where you can align the other nodes at the desired positions.

documentclass[border=5pt]{standalone}

usepackage{tikz}
usepackage{amsmath}
usetikzlibrary{automata}
usetikzlibrary{calc,arrows.meta,positioning}

newcommand{iddots}{reflectbox{$ddots$}}
begin{document}
    
    resizebox{textwidth}{!}{
        begin{tikzpicture}[->,-latex,shorten >=1pt,auto,node distance=40mm,semithick, state/.style={circle, draw, minimum size=2cm}]
            node[state](1)                  {$S_0$};
            node[state](2)[below left  of=1] {$dcdot S_0$};
            node[state](3)[below right of=1]{$u cdot S_0$};
            node[state](4)[below left  of=2] {$d^2 cdot S_0$};
            node[state](5)[below right of=2]{$du cdot S_0$};
            node[state](6)[below right of=3]{$u^2 cdot S_0$};
            node[state](7)[below left of=4]{$d^N cdot S_0$};
            node[state](8)[below right of=4]{$d^k u^{N-k} cdot S_0$};
            node[state](9)[below right of=5]{$d^{N-k}u^{k}cdot S_0$};
            node[state](10)[below right of=6]{$u^N cdot S_0$};
            node[state](14)[right of=10]{$S_1$};
            node[state](13) at (6-|14) {$S_1$};
            node[state](12) at (3-|14) {$S_1$};
            node[state](11) at (1-|14) {$S_1$};
            
            path (1) edge [swap] node {$1-p$}(2)
            (1) edge        node {$p$}(3)
            (2) edge [swap] node {$1-p$}(4)
            (2) edge        node {$p$}(5)
            (3) edge [swap] node {$1-p$}(5)
            (3) edge        node {$p$}(6);
            node at ($(7)!.5!(8)$) {$hdots$};
            node at ($(8)!.5!(9)$) {$hdots$};
            node at ($(9)!.5!(10)$) {$hdots$};
            
            node at ($(4)!.5!(7)$) {iddots};
            node at ($(5)!.5!(8)$) {iddots};
            node at ($(6)!.5!(9)$) {iddots};
            
            node at ($(4)!.5!(8)$) {$ddots$};
            node at ($(5)!.5!(9)$) {$ddots$};
            node at ($(6)!.5!(10)$) {$ddots$};
        end{tikzpicture}
    }
end{document}

Align two trees in TiKZ (states/nodes)

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