regex/nfa.go

package main

const EPSILON int = 0

type State struct {
	content     int              // Contents of current state
	isEmpty     bool             // If it is empty - Union operator and Kleene star states will be empty
	isLast      bool             // If it is the last state (acept state)
	output      []*State         // The outputs of the current state ie. the 'outward arrows'. A union operator state will have more than one of these.
	transitions map[int][]*State // Transitions to different states (maps a character (int representation) to a _list of states. This is useful if one character can lead multiple states eg. ab|aa)
	isKleene    bool             // Identifies whether current node is a 0-state representing Kleene star
}

type NFA struct {
	start   State
	outputs []State
}

// verifyLastStatesHelper performs the depth-first recursion needed for verifyLastStates
func verifyLastStatesHelper(state *State, visited map[*State]bool) {
	if len(state.transitions) == 0 {
		state.isLast = true
		return
	}
	if len(state.transitions) == 1 && len(state.transitions[state.content]) == 1 && state.transitions[state.content][0] == state { // Eg. a*
		state.isLast = true
		return
	}

	if len(state.transitions) == 1 && state.isKleene { // A State representing a Kleene Star has a transition going out, which loops back to it. If that is the only transition (and it contains only one state), then it must be a last-state
		for _, v := range state.transitions { // Should only loop once
			if len(v) == 1 {
				state.isLast = true
				return
			}
		}
	}
	if visited[state] == true {
		return
	}
	visited[state] = true
	for _, states := range state.transitions {
		for i := range states {
			if states[i] != state {
				verifyLastStatesHelper(states[i], visited)
			}
		}
	}
}

// verifyLastStates enables the 'isLast' flag for the leaf nodes (last states)
func verifyLastStates(start []*State) {
	verifyLastStatesHelper(start[0], make(map[*State]bool))
}

func concatenate(s1 *State, s2 *State) *State {
	for i := range s1.output {
		s1.output[i].transitions[s2.content] = unique_append(s1.output[i].transitions[s2.content], s2)
	}
	s1.output = s2.output
	return s1
}

func kleene(s1 State) *State {
	toReturn := &State{}
	toReturn.transitions = make(map[int][]*State)
	toReturn.content = EPSILON
	toReturn.isEmpty = true
	toReturn.isKleene = true
	toReturn.output = append(toReturn.output, toReturn)
	for i := range s1.output {
		s1.output[i].transitions[toReturn.content] = unique_append(s1.output[i].transitions[toReturn.content], toReturn)
	}
	toReturn.transitions[s1.content] = unique_append(toReturn.transitions[s1.content], &s1)
	return toReturn
}

func alternate(s1 *State, s2 *State) *State {
	toReturn := &State{}
	toReturn.transitions = make(map[int][]*State)
	toReturn.output = append(toReturn.output, s1.output...)
	toReturn.output = append(toReturn.output, s2.output...)
	// Unique append is used here (and elsewhere) to ensure that,
	// for any given transition, a state can only be mentioned once.
	// For example, given the transition 'a', the state 's1' can only be mentioned once.
	// This would lead to multiple instances of the same set of match indices, since both
	// 's1' states would be considered to match.
	toReturn.transitions[s1.content] = unique_append(toReturn.transitions[s1.content], s1)
	toReturn.transitions[s2.content] = unique_append(toReturn.transitions[s2.content], s2)
	toReturn.content = EPSILON
	toReturn.isEmpty = true

	return toReturn
}