[LeetCode] 126. Word Ladder II

最新推荐文章于 2022-02-07 22:27:20 发布

转载最新推荐文章于 2022-02-07 22:27:20 发布 · 54 阅读

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原文链接：https://segmentfault.com/a/1190000006210763

本文介绍了一种使用DFS和BFS结合的方法来寻找两个单词间最短转换路径的算法。通过改变一个字母的方式从起始单词逐步变为目标单词，每一步都必须确保中间状态存在于给定的词典中。

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Problem

Given two words (start and end), and a dictionary, find all shortest transformation sequence(s) from start to end, such that:

Only one letter can be changed at a time
Each intermediate word must exist in the dictionary

Notice

All words have the same length.
All words contain only lowercase alphabetic characters.

Example

Given:

start = "hit"
end = "cog"
dict = ["hot","dot","dog","lot","log"]

Return

[
    ["hit","hot","dot","dog","cog"],
    ["hit","hot","lot","log","cog"]
]

Solution DFS+BFS

Updated 2018-11

class Solution {
    public List<List<String>> findLadders(String start, String end, List<String> wordList) {
        List<List<String>> res = new ArrayList<>();
        Set<String> dict = new HashSet<>(wordList);
        if (!dict.contains(end)) return res;
        //save shortest distance from start to each node
        Map<String, Integer> distanceMap = new HashMap<>();
        //save all the nodes can be transformed from each node
        Map<String, List<String>> neighborMap = new HashMap<>();
        
        dict.add(start);
        //use bfs to: find the shortest distance; update neighborMap and distanceMap
        bfs(start, end, dict, neighborMap, distanceMap);
        //use dfs to: output all the paths with the shortest distance
        dfs(start, end, neighborMap, distanceMap, new ArrayList<>(), res);
        
        return res;
    }
    
    private void bfs(String start, String end, Set<String> dict, Map<String, List<String>> neighborMap, Map<String, Integer> distanceMap) {
        for (String str: dict) {
            neighborMap.put(str, new ArrayList<>());
        }
        
        Deque<String> queue = new ArrayDeque<>();
        queue.offer(start);
        distanceMap.put(start, 0);
        
        while (!queue.isEmpty()) {
            int size = queue.size();
            boolean foundEnd = false;
            for (int i = 0; i < size; i++) {
                String cur = queue.poll();
                int curDist = distanceMap.get(cur);
                List<String> neighbors = getNeighbors(dict, cur);
                
                for (String neighbor: neighbors) {
                    neighborMap.get(cur).add(neighbor);
                    if (!distanceMap.containsKey(neighbor)) {
                        distanceMap.put(neighbor, curDist+1);
                        if (neighbor.equals(end)) foundEnd = true;
                        else queue.offer(neighbor);
                    }
                }
            }
            if (foundEnd) break;
        }
    }
    
    private void dfs(String start, String end, Map<String, List<String>> neighborMap, Map<String, Integer> distanceMap, List<String> temp, List<List<String>> res) {
        if (start.equals(end)) {
            temp.add(start);
            res.add(new ArrayList<>(temp));
            temp.remove(temp.size()-1);
        }
        for (String neighbor: neighborMap.get(start)) {
            temp.add(start);
            if (distanceMap.get(neighbor) == distanceMap.get(start)+1) {
                dfs(neighbor, end, neighborMap, distanceMap, temp, res);
            }
            temp.remove(temp.size()-1);
        }
    }
    
    private List<String> getNeighbors(Set<String> dict, String str) {
        List<String> res = new ArrayList<>();
        for (int i = 0; i < str.length(); i++) {
            StringBuilder sb = new StringBuilder(str);
            for (char ch = 'a'; ch <= 'z'; ch++) {
                sb.setCharAt(i, ch);
                String neighbor = sb.toString();
                if (dict.contains(neighbor)) res.add(neighbor);
            }
        }
        return res;
    }
}

Solution

Note

result: 存放transformation过程中的所有List<String>集合
map: key为所有transformation的结尾String，value则顺序存放这个结尾String对应的transformation中的所有String
queue: 存放同一个循环level的新加入的String，在下一个循环再依次对其中元素进行进一步的BFS
preList: 把首个字符串start放入新List，再将List放入res，并将start-res键值对放入map，进行初始化

public class Solution {
    public List<List<String>> findLadders(String start, String end, Set<String> dict) {
        List<List<String>> res = new ArrayList<>();
        List<String> preList = new ArrayList<>();
        Queue<String> queue = new LinkedList<>();
        Map<String, List<List<String>>> map = new HashMap<>();
        preList.add(start);
        queue.offer(start);
        res.add(preList);
        map.put(start, res);
        while (!queue.isEmpty()) {
            String pre = queue.poll();
            if (pre.equals(end)) return map.get(pre);
            for (int i = 0; i < pre.length(); i++) {
                for (int j = 0; j < 26; j++) {
                    StringBuilder sb = new StringBuilder(pre);
                    sb.setCharAt(i,(char) ('a'+j));
                    String cur = sb.toString();
                    if (!cur.equals(pre) && dict.contains(cur) && (!map.containsKey(cur) || map.get(pre).get(0).size()+1 <= map.get(cur).get(0).size())) {
                        List<List<String>> temp = new ArrayList<>();
                        for (List<String> p: map.get(pre)) {
                            List<String> curList = new ArrayList<>(p);
                            curList.add(cur);
                            temp.add(curList);
                        }
                        if (!map.containsKey(cur)) {
                            map.put(cur, temp);
                            queue.offer(cur);
                        }
                        else if (map.get(pre).get(0).size()+1 < map.get(cur).get(0).size()) map.put(cur, temp);
                        else map.get(cur).addAll(temp);
                        
                    }
                }
            }
        }
        return res.get(0).size() > 1 ? res : new ArrayList<List<String>>();
    }
}