public int commonPrefixedPathNumber(String prefix) {
        int count = 0;
        PGridPath prefixPath = new PGridPath(prefix);
        for (String path : unsolvedPaths_.keySet()) {
            PGridPath otherPath = new PGridPath(path);
            if (otherPath.hasPrefix(prefixPath)) {
                ++count;
            }
        }
        return count;
    }