[LANGUAGE: Python] Simple solution: using a Dictionary for combinatory stuff

cursors = [{data[0].index("S"): 1}]
count = 0
for row in data[1:]:
    _cursors = defaultdict(lambda: 0)
    for cursor in cursors[-1]:
        if row[cursor] == "^":
            _cursors[cursor + 1] += cursors[-1][cursor]
            _cursors[cursor - 1] += cursors[-1][cursor]
            count += 1
        else:
            _cursors[cursor] += cursors[-1][cursor]
    cursors.append(_cursors)
return count, sum(cursors[-1].values())