BFS vs DFS

    public UndirectedGraphNode cloneGraph(UndirectedGraphNode node) 
    {
        if (node == null) {
            return node;
        }
        
        List<UndirectedGraphNode> nodes = new ArrayList<>();
        Map<UndirectedGraphNode, UndirectedGraphNode> map = new HashMap<>();
        nodes.add(node);
        map.put(node, new UndirectedGraphNode(node.label));
        
        int start = 0;
        while (start < nodes.size()) {
            UndirectedGraphNode head = nodes.get(start++);
            for (int i = 0; i < head.neighbors.size(); i++) {
                UndirectedGraphNode neighbor = head.neighbors.get(i);
                if (!map.containsKey(neighbor)) {
                    nodes.add(neighbor);
                    map.put(neighbor, new UndirectedGraphNode(neighbor.label));
                }
            }
        }
        
        for (int i = 0; i < nodes.size(); i++) {
            UndirectedGraphNode newNode = map.get(nodes.get(i));
            for (int j = 0; j < nodes.get(i).neighbors.size(); j++) {
                newNode.neighbors.add(map.get(nodes.get(i).neighbors.get(j)));
            }
        }
        
        return map.get(node);
    }

    public ArrayList<DirectedGraphNode> topSort(ArrayList<DirectedGraphNode> graph) {
        // write your code here
        ArrayList<DirectedGraphNode> result = new ArrayList<>();
        Map<DirectedGraphNode, Integer> map = new HashMap<>();
        
        for (DirectedGraphNode node : graph) {
            for (DirectedGraphNode neighbor : node.neighbors) {
                if (map.containsKey(neighbor)) {
                    map.put(neighbor, map.get(neighbor) + 1);
                } else {
                    map.put(neighbor, 1);
                }
            }
        }
        
        for (DirectedGraphNode node : graph) {
            if (!map.containsKey(node)) {
                result.add(node);
            }
        }
        
        int start = 0;
        while (start < result.size()) {
            DirectedGraphNode node = result.get(start++);
            for (DirectedGraphNode neighbor : node.neighbors) {
                map.put(neighbor, map.get(neighbor) - 1);
                if (map.get(neighbor) == 0) {
                    result.add(neighbor);
                }
            }
        }
        
        return result;
    }

    public boolean hasRoute(ArrayList<DirectedGraphNode> graph, 
                            DirectedGraphNode s, DirectedGraphNode t) {
        if (s == t) {
            return true;
        }
        
        Queue<DirectedGraphNode> queue = new LinkedList<>();
        Set<DirectedGraphNode> visited = new HashSet<>();
        queue.add(s);
        visited.add(s);
        
        while (!queue.isEmpty()){
            DirectedGraphNode node = queue.poll();
            for (DirectedGraphNode neighbor : node.neighbors) {
                if (visited.contains(neighbor)) {
                    continue;
                }
                queue.add(neighbor);
                visited.add(neighbor);
                if (neighbor == t) {
                    return true;
                }
            }
        }
        
        return false;
    }

    public ArrayList<ArrayList<String>> solveNQueens(int n) 
    {
        // write your code here
        ArrayList<ArrayList<String>> res = new ArrayList<>();
        search(res, new ArrayList<Integer>(), n);
        return res;
    }
    void search(ArrayList<ArrayList<String>> res, ArrayList<Integer> cols, int n) {
        if (cols.size() == n) {
            res.add(drawChessboard(cols));
            return;
        }
        
        for (int i = 0; i < n; i++) {
            if (!isValid(cols, i)) {
                continue;
            }
            cols.add(i);
            search(res, cols, n);
            cols.remove(cols.size() - 1);
        }
    }
    
    ArrayList<String> drawChessboard(List<Integer> cols) {
        ArrayList<String> result = new ArrayList<>();
        for (int i = 0; i < cols.size(); i++) {
            StringBuilder sb = new StringBuilder();
            for (int j = 0; j < cols.size(); j++) {
                sb.append(cols.get(i) == j ? "Q" : ".");
            }
            result.add(sb.toString());
        }
        return result;
    }
    
    boolean isValid(List<Integer> cols, int colIndex) {
        int row = cols.size();
        for (int i = 0; i < cols.size(); i++) {
            if (cols.get(i) == colIndex) {
                return false;
            }
            
            if (i + cols.get(i) == row + colIndex) {
                return false;
            }
            
            if (i - cols.get(i) == row - colIndex) {
                return false;
            }
        }
        return true;
    }

   public int ladderLength(String start, String end, Set<String> dict) 
    {
        if (dict == null) {
            return 0;
        }
        
        if (start.equals(end)) {
            return 1;
        }
        
        dict.add(end);
        Set<String> visited = new HashSet<>();
        Queue<String> queue = new LinkedList<>();
        queue.add(start);
        int length = 1;
        
        while (!queue.isEmpty()) {
            length++;
            int size = queue.size();
            for (int i = 0; i < size; i++) {
                String word = queue.poll();
                for (String newWord: getNextWords(word, dict)) {
                    if (visited.contains(newWord)) {
                        continue;
                    }
                    
                    if (newWord.equals(end)) {
                        return length;
                    }
                    
                    visited.add(newWord);
                    queue.add(newWord);
                }
            }
        }
        return 0;
    }
    
    List<String> getNextWords(String word,  Set<String> dict) {
        List<String> result = new ArrayList<>();
        for (char c = ‘a‘; c <= ‘z‘; c++) {
            for (int i = 0; i < word.length(); i++) {
                if (c == word.charAt(i)) {
                    continue;
                }
                String newWord = replace(word, i, c);
                if (dict.contains(newWord)) {
                    result.add(newWord);
                }
            }
        }
        return result;
    }
    
    
    String replace(String word, int i, char c) {
        char[] arr = word.toCharArray();
        arr[i] = c;
        return new String(arr);
    }

public class Solution {
    /**
      * @param start, a string
      * @param end, a string
      * @param dict, a set of string
      * @return a list of lists of string
      */
    public List<List<String>> findLadders(String start, String end, Set<String> dict) {
        List<List<String>> result = new ArrayList<>();
        Map<String, Integer> distance = new HashMap<>();
        Map<String, List<String>> map = new HashMap<>();
        
        dict.add(start);
        dict.add(end);
        
        bfs(start, end, dict, distance, map);
        
        List<String> path = new ArrayList<>();
        
        dfs(start, end, result, distance, map, path);
        
        return result;
    }
    
    void dfs(String start, String cur, List<List<String>> result, Map<String, Integer> distance, 
             Map<String, List<String>> map, List<String> path) {
        path.add(cur);
        if (cur.equals(start)) {
            Collections.reverse(path);
            result.add(new ArrayList<>(path));
            Collections.reverse(path);
        } else {
        for (String word : map.get(cur)) {
            if (distance.containsKey(word) && distance.get(word) + 1 == distance.get(cur)) {
                dfs(start, word, result, distance, map, path);
            }
        }
        }
        path.remove(path.size() - 1);
    }
    
    void bfs(String start, String end, Set<String> dict, Map<String, Integer> distance, 
             Map<String, List<String>> map) {
             
        Queue<String> queue = new LinkedList<>();
        queue.offer(start);
        distance.put(start, 0);
        
        for(String word : dict) {
            map.put(word, new ArrayList<String>());
        }
        
        while (!queue.isEmpty()) {
            String word = queue.poll();
            for (String newWord: getNextWords(word, dict)) {
                map.get(newWord).add(word);
                if (!distance.containsKey(newWord)) {
                    distance.put(newWord, distance.get(word) + 1);
                    queue.offer(newWord);
                }
            }
        }
    }
    
        List<String> getNextWords(String word,  Set<String> dict) {
        List<String> result = new ArrayList<>();
        for (char c = ‘a‘; c <= ‘z‘; c++) {
            for (int i = 0; i < word.length(); i++) {
                if (c == word.charAt(i)) {
                    continue;
                }
                String newWord = replace(word, i, c);
                if (dict.contains(newWord)) {
                    result.add(newWord);
                }
            }
        }
        return result;
    }
    
    
    String replace(String word, int i, char c) {
        char[] arr = word.toCharArray();
        arr[i] = c;
        return new String(arr);
    }
}

     public ArrayList<ArrayList<String>> partition(String s) {
         ArrayList<ArrayList<String>> res = new ArrayList<>();
         ArrayList<String> path = new ArrayList<>();
         dfs(s, 0, path, res);
         return res;
     }
     void dfs(String s, int start, ArrayList<String> path, ArrayList<ArrayList<String>> res) {
         if (start == s.length()) {
             res.add(new ArrayList<>(path));
             return;
         }
         for (int i = start; i < s.length(); i++) {
             if (isValid(s, start, i)){
                 path.add(s.substring(start, i + 1));
                 dfs(s, i + 1, path, res);
                 path.remove(path.size() - 1);
             }
         }
     }
     boolean isValid(String s, int left, int right) {
         while (left < right) {
             if (s.charAt(left++) != s.charAt(right--)) {
                 return false;
             }
         }
         return true;
     }