Algorithm 1 Pseudocode for identifying independently folded nucleic acid substructures.

Input: Set of all subchains C, Set of interacting subchains $Y_x$ for each subchain x

Output: Independently folded $Substructures$

$Library$←C     ▹$Library$ records all subchains not assigned to substructures

forx in C do

if x in $Library$ then      ▹ Find the substructure containing subchain x

$S_x\leftarrow Y_x$

$S_{new}\leftarrow Y_x$      ▹$S_{new}$ records newly added subchains in each loop below

while $S_{new}$ not empty do

$S_{tmp}\leftarrow S_x$        ▹$S_{tmp}$ updates the substructure in each loop

for z in $S_{new}$ do

$S_{tmp}\leftarrow S_{tmp}\cup Y_z$  ▹ Include interacting subchains for each newly added subchain

end for

$S_{new}\leftarrow S_{tmp}\backslash S_x$

$S_x\leftarrow S_{tmp}$

end while

$Library$←$Library\backslash S_x$       ▹ Remove subchains in $S_x$ from $Library$

Add $S_x$ to $Substructures$

end if

end for