https://reverseengineering.stackexchange.com/questions/18719/how-can-i-reverse-this-recursive-function/19287#19287

given.dot

strict digraph "" {
	graph [ordering="out"];
	null[label=""];
	C -> G;
	C -> H;
	G -> M;
	G -> N;
	F -> S;
	F -> U;
	H -> null;
	H -> W;
	J -> Z;
	J -> A;
	L -> P;
	L -> Y;
	O -> J;
	O -> K;
	P -> O;
	P -> E;
	S -> L;
	T -> F;
	T -> V;
	W -> X;
	W -> I;
	Z -> C;
	Z -> D;
}

given.svg

solve.py

debug = False


def the_process(stored, inp, size, fs):
    if debug:
        print '\t' * fs + \
            "the_process({}, {}, {})".format(stored, "".join(inp), size)
    idx = 0
    global thstr
    idx = stored.index(inp[0])
    if idx:
        the_process(stored[:idx], inp[1:], idx, fs + 1)
    if size - 1 != idx:
        the_process(stored[1 + idx:1 + idx + size - idx - 1],
                    inp[idx + 1:], size - idx - 1, fs + 1)
    thstr.append(inp[0])


def rev_process(stored, inp, size, fs):
    if debug:
        print '\t' * fs + \
            "rev_process({}, {}, {})".format(stored, "".join(inp), size)
    if not size:
        return
    global thstr
    mp = {stored[i]: i for i in xrange(len(stored))}
    idx = mp[inp[-1]]
    thstr.append(inp[-1])
    if size == 1:
        return
    try:
        less_part = max(
            loc for loc,
            val in enumerate(inp) if mp[val] < idx) + 1
    except ValueError:
        less_part = 0
    rev_process(stored[:idx], inp[:less_part], less_part, fs + 1)
    if less_part != size - 1:
        rev_process(stored[idx + 1:], inp[less_part:-1],
                    size - less_part - 1, fs + 1)


if __name__ == "__main__":
    thstr = []
    stored = "MGNCHXWIZDJAOKPELYSFUTV"
    input1 = "TFSLPOJZCGMNHWXIDAKEYUV"
    target = "MNGHCWZIJDXOPKLESUVTFYA"
    print "sample input  : " + input1
    the_process(stored, input1, 23, 0)
    output1 = "".join(thstr)
    print "sample output : " + output1
    thstr = []
    rev_process(stored, output1, 23, 0)
    input1_rev = "".join(thstr)
    assert input1 == input1_rev
    thstr = []
    print "target output : " + target
    rev_process(stored, target, 23, 0)
    target_rev = "".join(thstr)
    print "target input  : " + target_rev
    thstr = []
    the_process(stored, target_rev, 23, 0)
    target_out = "".join(thstr)
    assert target_out == target

target.dot

strict digraph "" {
	graph [ordering="out"];
    A -> X;
    X -> C;
    C -> G;
    G -> M;
    G -> N;
    C -> H;
    X -> D;
    D -> I;
    I -> W;
    I -> Z;
    D -> J;
    A -> Y;
    Y -> E;
    E -> K;
    E -> L;
    K -> O;
    K -> P;
    Y -> F;
    F -> S;
    F -> T;
    T -> U;
    T -> V;
}

target.svg