Word Pattern

Given a pattern and a string str, find if str follows the same pattern.

Examples:
pattern = "abba", str = "dog cat cat dog" should return true.
pattern = "abba", str = "dog cat cat fish" should return false.
pattern = "aaaa", str = "dog cat cat dog" should return false.
pattern = "abba", str = "dog dog dog dog" should return false.

Notes: patterncontains only lowercase alphabetical letters, and str contains words separated by a single space. Each word in str contains only lowercase alphabetical letters. Both pattern and str do not have leading or trailing spaces. Each letter in pattern must map to a word with length that is at least 1.

哈希表法

复杂度

时间 O(N) 空间 O(N)

思路

这题几乎和Isomorphic Strings一模一样，不同的就是之前是字母映射字母，现在是字母映射字符串而已。

代码

public class Solution {
    public boolean wordPattern(String pattern, String str) {
        Map<Character, String> map = new HashMap<Character, String>();
        Set<String> set = new HashSet<String>();
        String[] pieces = str.split(" ");
        if(pieces.length != pattern.length()) return false;
        int i = 0;
        for(String s : pieces){
            char p = pattern.charAt(i);
            System.out.println(p);
            // 如果该字符产生过映射
            if(map.containsKey(p)){
                // 且映射的字符串和当前字符串不一样
                if(!s.equals(map.get(p))) return false;
            } else {
            // 如果该字符没有产生过映射
                // 如果当前字符串已经被映射过了
                if(set.contains(s)) return false;
                // 否则新加一组映射
                map.put(p, s);
                set.add(s);
            }
            i++;
        }
        return true;
    }
}

Word Pattern II

Given a pattern and a string str, find if str follows the same pattern.

Here follow means a full match, such that there is a bijection between a letter in pattern and a non-empty substring in str.

Examples: pattern = "abab", str = "redblueredblue" should return true. pattern = "aaaa", str = "asdasdasdasd" should return true. pattern = "aabb", str = "xyzabcxzyabc" should return false. Notes: You may assume both pattern and str contains only lowercase letters.

回溯法

复杂度

时间 O(N) 空间 O(N)

思路

因为目标字符串可以任意划分，所以我们不得不尝试所有可能性。这里通过深度优先搜索的回溯法，对于pattern中每个字母，在str中尝试所有的划分方式，如果划分出来的子串可以用这个字母映射，或者可以建立一个新的字母和字符串的映射关系，我们就继续递归判断下一个pattern中的字母。

代码

public class Solution {
    
    Map<Character, String> map;
    Set<String> set;
    boolean res;
    
    public boolean wordPatternMatch(String pattern, String str) {
        // 和I中一样，Map用来记录字符和字符串的映射关系
        map = new HashMap<Character, String>();
        // Set用来记录哪些字符串被映射了，防止多对一映射
        set = new HashSet<String>();
        res = false;
        // 递归回溯
        helper(pattern, str, 0, 0);
        return res;
    }
    
    public void helper(String pattern, String str, int i, int j){
        // 如果pattern匹配完了而且str也正好匹配完了，说明有解
        if(i == pattern.length() && j == str.length()){
            res = true;
            return;
        }
        // 如果某个匹配超界了，则结束递归
        if(i >= pattern.length() || j >= str.length()){
            return;
        }
        char c = pattern.charAt(i);
        // 尝试从当前位置到结尾的所有划分方式
        for(int cut = j + 1; cut <= str.length(); cut++){
            // 拆出一个子串
            String substr = str.substring(j, cut);
            // 如果这个子串没有被映射过，而且当前pattern的字符也没有产生过映射
            // 则新建一对映射，并且继续递归求解
            if(!set.contains(substr) && !map.containsKey(c)){
                map.put(c, substr);
                set.add(substr);
                helper(pattern, str, i + 1, cut);
                map.remove(c);
                set.remove(substr);
            // 如果已经有映射了，但是是匹配的，也继续求解
            } else if(map.containsKey(c) && map.get(c).equals(substr)){
                helper(pattern, str, i + 1, cut);
            }
            // 否则跳过该子串，尝试下一种拆分
        }
    }
}