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127. 单词接龙

English Version

题目描述

字典 wordList 中从单词 beginWord 和 endWord 的 转换序列 是一个按下述规格形成的序列 beginWord -> s1 -> s2 -> ... -> sk：

  • 每一对相邻的单词只差一个字母。
  •  对于 1 <= i <= k 时，每个 si 都在 wordList 中。注意， beginWord 不需要在 wordList 中。
  • sk == endWord

给你两个单词 beginWord 和 endWord 和一个字典 wordList ，返回 从 beginWord 到 endWord 的 最短转换序列 中的 单词数目 。如果不存在这样的转换序列，返回 0 。

 

示例 1：

输入：beginWord = "hit", endWord = "cog", wordList = ["hot","dot","dog","lot","log","cog"]
输出：5
解释：一个最短转换序列是 "hit" -> "hot" -> "dot" -> "dog" -> "cog", 返回它的长度 5。

示例 2：

输入：beginWord = "hit", endWord = "cog", wordList = ["hot","dot","dog","lot","log"]
输出：0
解释：endWord "cog" 不在字典中，所以无法进行转换。

 

提示：

  • 1 <= beginWord.length <= 10
  • endWord.length == beginWord.length
  • 1 <= wordList.length <= 5000
  • wordList[i].length == beginWord.length
  • beginWord、endWord 和 wordList[i] 由小写英文字母组成
  • beginWord != endWord
  • wordList 中的所有字符串 互不相同

解法

BFS 最小步数模型。本题可以用朴素 BFS，也可以用双向 BFS 优化搜索空间，从而提升效率。

双向 BFS 是 BFS 常见的一个优化方法，主要实现思路如下：

  1. 创建两个队列 q1, q2 分别用于“起点 -> 终点”、“终点 -> 起点”两个方向的搜索；
  2. 创建两个哈希表 m1, m2 分别记录访问过的节点以及对应的扩展次数（步数）；
  3. 每次搜索时，优先选择元素数量较少的队列进行搜索扩展，如果在扩展过程中，搜索到另一个方向已经访问过的节点，说明找到了最短路径；
  4. 只要其中一个队列为空，说明当前方向的搜索已经进行不下去了，说明起点到终点不连通，无需继续搜索。
while q1 and q2:
    if len(q1) <= len(q2):
        # 优先选择较少元素的队列进行扩展
        extend(m1, m2, q1)
    else:
        extend(m2, m1, q2)

def extend(m1, m2, q):
    # 新一轮扩展
    for _ in range(len(q)):
        p = q.popleft()
        step = m1[p]
        for t in next(p):
            if t in m1:
                # 此前已经访问过
                continue
            if t in m2:
                # 另一个方向已经搜索过，说明找到了一条最短的连通路径
                return step + 1 + m2[t]
            q.append(t)
            m1[t] = step + 1

Python3

朴素 BFS：

class Solution:
    def ladderLength(self, beginWord: str, endWord: str, wordList: List[str]) -> int:
        words = set(wordList)
        q = deque([beginWord])
        ans = 1
        while q:
            ans += 1
            for _ in range(len(q)):
                s = q.popleft()
                s = list(s)
                for i in range(len(s)):
                    ch = s[i]
                    for j in range(26):
                        s[i] = chr(ord('a') + j)
                        t = ''.join(s)
                        if t not in words:
                            continue
                        if t == endWord:
                            return ans
                        q.append(t)
                        words.remove(t)
                    s[i] = ch
        return 0

双向 BFS：

class Solution:
    def ladderLength(self, beginWord: str, endWord: str, wordList: List[str]) -> int:
        def extend(m1, m2, q):
            for _ in range(len(q)):
                s = q.popleft()
                step = m1[s]
                s = list(s)
                for i in range(len(s)):
                    ch = s[i]
                    for j in range(26):
                        s[i] = chr(ord('a') + j)
                        t = ''.join(s)
                        if t in m1 or t not in words:
                            continue
                        if t in m2:
                            return step + 1 + m2[t]
                        m1[t] = step + 1
                        q.append(t)
                    s[i] = ch
            return -1

        words = set(wordList)
        if endWord not in words:
            return 0
        q1, q2 = deque([beginWord]), deque([endWord])
        m1, m2 = {beginWord: 0}, {endWord: 0}
        while q1 and q2:
            t = extend(m1, m2, q1) if len(q1) <= len(
                q2) else extend(m2, m1, q2)
            if t != -1:
                return t + 1
        return 0

Java

朴素 BFS：

class Solution {
    public int ladderLength(String beginWord, String endWord, List<String> wordList) {
        Set<String> words = new HashSet<>(wordList);
        Queue<String> q = new ArrayDeque<>();
        q.offer(beginWord);
        int ans = 1;
        while (!q.isEmpty()) {
            ++ans;
            for (int i = q.size(); i > 0; --i) {
                String s = q.poll();
                char[] chars = s.toCharArray();
                for (int j = 0; j < chars.length; ++j) {
                    char ch = chars[j];
                    for (char k = 'a'; k <= 'z'; ++k) {
                        chars[j] = k;
                        String t = new String(chars);
                        if (!words.contains(t)) {
                            continue;
                        }
                        if (endWord.equals(t)) {
                            return ans;
                        }
                        q.offer(t);
                        words.remove(t);
                    }
                    chars[j] = ch;
                }
            }
        }
        return 0;
    }
}

双向 BFS：

class Solution {
    private Set<String> words;

    public int ladderLength(String beginWord, String endWord, List<String> wordList) {
        words = new HashSet<>(wordList);
        if (!words.contains(endWord)) {
            return 0;
        }
        Queue<String> q1 = new ArrayDeque<>();
        Queue<String> q2 = new ArrayDeque<>();
        Map<String, Integer> m1 = new HashMap<>();
        Map<String, Integer> m2 = new HashMap<>();
        q1.offer(beginWord);
        q2.offer(endWord);
        m1.put(beginWord, 0);
        m2.put(endWord, 0);
        while (!q1.isEmpty() && !q2.isEmpty()) {
            int t = q1.size() <= q2.size() ? extend(m1, m2, q1) : extend(m2, m1, q2);
            if (t != -1) {
                return t + 1;
            }
        }
        return 0;
    }

    private int extend(Map<String, Integer> m1, Map<String, Integer> m2, Queue<String> q) {
        for (int i = q.size(); i > 0; --i) {
            String s = q.poll();
            int step = m1.get(s);
            char[] chars = s.toCharArray();
            for (int j = 0; j < chars.length; ++j) {
                char ch = chars[j];
                for (char k = 'a'; k <= 'z'; ++k) {
                    chars[j] = k;
                    String t = new String(chars);
                    if (!words.contains(t) || m1.containsKey(t)) {
                        continue;
                    }
                    if (m2.containsKey(t)) {
                        return step + 1 + m2.get(t);
                    }
                    q.offer(t);
                    m1.put(t, step + 1);
                }
                chars[j] = ch;
            }
        }
        return -1;
    }
}

C++

朴素 BFS：

class Solution {
public:
    int ladderLength(string beginWord, string endWord, vector<string>& wordList) {
        unordered_set<string> words(wordList.begin(), wordList.end());
        queue<string> q{{beginWord}};
        int ans = 1;
        while (!q.empty())
        {
            ++ans;
            for (int i = q.size(); i > 0; --i)
            {
                string s = q.front();
                q.pop();
                for (int j = 0; j < s.size(); ++j)
                {
                    char ch = s[j];
                    for (char k = 'a'; k <= 'z'; ++k)
                    {
                        s[j] = k;
                        if (!words.count(s)) continue;
                        if (s == endWord) return ans;
                        q.push(s);
                        words.erase(s);
                    }
                    s[j] = ch;
                }
            }
        }
        return 0;
    }
};

双向 BFS：

class Solution {
public:
    int ladderLength(string beginWord, string endWord, vector<string>& wordList) {
        unordered_set<string> words(wordList.begin(), wordList.end());
        if (!words.count(endWord)) return 0;
        queue<string> q1{{beginWord}};
        queue<string> q2{{endWord}};
        unordered_map<string, int> m1;
        unordered_map<string, int> m2;
        m1[beginWord] = 0;
        m2[endWord] = 0;
        while (!q1.empty() && !q2.empty())
        {
            int t = q1.size() <= q2.size() ? extend(m1, m2, q1, words) : extend(m2, m1, q2, words);
            if (t != -1) return t + 1;
        }
        return 0;
    }

    int extend(unordered_map<string, int>& m1, unordered_map<string, int>& m2, queue<string>& q, unordered_set<string>& words) {
        for (int i = q.size(); i > 0; --i)
        {
            string s = q.front();
            int step = m1[s];
            q.pop();
            for (int j = 0; j < s.size(); ++j)
            {
                char ch = s[j];
                for (char k = 'a'; k <= 'z'; ++k)
                {
                    s[j] = k;
                    if (!words.count(s) || m1.count(s)) continue;
                    if (m2.count(s)) return step + 1 + m2[s];
                    m1[s] = step + 1;
                    q.push(s);
                }
                s[j] = ch;
            }
        }
        return -1;
    }
};

Go

朴素 BFS：

func ladderLength(beginWord string, endWord string, wordList []string) int {
	words := make(map[string]bool)
	for _, word := range wordList {
		words[word] = true
	}
	q := []string{beginWord}
	ans := 1
	for len(q) > 0 {
		ans++
		for i := len(q); i > 0; i-- {
			s := q[0]
			q = q[1:]
			chars := []byte(s)
			for j := 0; j < len(chars); j++ {
				ch := chars[j]
				for k := 'a'; k <= 'z'; k++ {
					chars[j] = byte(k)
					t := string(chars)
					if !words[t] {
						continue
					}
					if t == endWord {
						return ans
					}
					q = append(q, t)
					words[t] = false
				}
				chars[j] = ch
			}
		}
	}
	return 0
}

双向 BFS：

func ladderLength(beginWord string, endWord string, wordList []string) int {
	words := make(map[string]bool)
	for _, word := range wordList {
		words[word] = true
	}
	if !words[endWord] {
		return 0
	}

	q1, q2 := []string{beginWord}, []string{endWord}
	m1, m2 := map[string]int{beginWord: 0}, map[string]int{endWord: 0}
	extend := func() int {
		for i := len(q1); i > 0; i-- {
			s := q1[0]
			step, _ := m1[s]
			q1 = q1[1:]
			chars := []byte(s)
			for j := 0; j < len(chars); j++ {
				ch := chars[j]
				for k := 'a'; k <= 'z'; k++ {
					chars[j] = byte(k)
					t := string(chars)
					if !words[t] {
						continue
					}
					if _, ok := m1[t]; ok {
						continue
					}
					if v, ok := m2[t]; ok {
						return step + 1 + v
					}
					q1 = append(q1, t)
					m1[t] = step + 1
				}
				chars[j] = ch
			}
		}
		return -1
	}
	for len(q1) > 0 && len(q2) > 0 {
		if len(q1) > len(q2) {
			m1, m2 = m2, m1
			q1, q2 = q2, q1
		}
		t := extend()
		if t != -1 {
			return t + 1
		}
	}
	return 0
}

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