Palindrome Pairs

Given a list of unique words, find all pairs of distinct indices (i, j) in the given list, so that the concatenation of the two words, i.e. words[i] + words[j] is a palindrome.

Example 1:

Input: ["abcd","dcba","lls","s","sssll"]
Output: [[0,1],[1,0],[3,2],[2,4]] 
Explanation: The palindromes are ["dcbaabcd","abcddcba","slls","llssssll"]Example 2:
Input: ["bat","tab","cat"]
Output: [[0,1],[1,0]] 
Explanation: The palindromes are ["battab","tabbat"]

思路：跟two sum类似，就是存下每个word的index到hashmap里面，然后每次把word劈开两半，str1 + str2.

如果str1是palindrome，那么我们可以以str1为中间word，看有没有reverse(str2)存在，str2rvs + str1 + str2 = str2rvs + word必定是palindrome.

[i, j] , word[i] + word[j] is palindrome, 那么就加入[hashmap.get(str2rvs), i] 进入result；

如果str2 是panlindrome, 那么我们可以以str2为中间word，看有没有reverse(str1)存在，str1 + str2 + str1rvs = word + str1rvs必定是palindrome。

[i, j], , word[i] + word[j] is palindrome, 那么就加入[i, hashmap.get(str1rvs)] 进入result；

Time : O(n * wlen ^ 2); 注意：str2要判断不为空，去掉重复，因为判断str1palindrome的时候，已经把str2等于空的情况计算过了。

/** 
 * Step 1: store every word with its index into a hash map.
 * Step 2: For each word in the array, split into two parts str1 and str2. Check whether str1 and str2 is palindrome
 * If str1 is palindrome, we can use str1 as middle part, str2 as right part, and find if map contains reversed str2.
 * If contains, then we can use that string as left part, combine with middle part, right part, it will form a correct
 * palindrome string. 
 * Step 3: do all same operations for str2 (set str2 as middle part) 
 * */

class Solution {
    public List<List<Integer>> palindromePairs(String[] words) {
        List<List<Integer>> lists = new ArrayList<List<Integer>>();
        HashMap<String, Integer> hashmap = new HashMap<>();
        for(int i = 0; i < words.length; i++) {
            hashmap.put(words[i], i);
        }
        
        // YYYYY    YY YYYYY
        for(int i = 0; i < words.length; i++) {
            String word = words[i];
            for(int j = 0; j <= word.length(); j++) {
                String str1 = word.substring(0, j);
                String str2 = word.substring(j);
                
                if(isPalindrome(str1)) {
                    // reverseStr2 + str1 + str2;
                    String revstr2 = reverse(str2);
                    if(hashmap.containsKey(revstr2) && hashmap.get(revstr2) != i) {
                        List<Integer> list = new ArrayList<>();
                        list.add(hashmap.get(revstr2));
                        list.add(i);
                        lists.add(list);
                    }
                } 
                if(str2.length() != 0 && isPalindrome(str2)) {
                    // str1 + str2 + revstr1;
                    String revstr1 = reverse(str1);
                    if(hashmap.containsKey(revstr1) && hashmap.get(revstr1) != i) {
                        List<Integer> list = new ArrayList<>();
                        list.add(i);
                        list.add(hashmap.get(revstr1));
                        lists.add(list);
                    }
                }
            }
        }
        return lists;
    }
    
    private boolean isPalindrome(String str) {
        int i = 0; int j = str.length() - 1;
        while(i <= j) {
            if(str.charAt(i) != str.charAt(j)) {
                return false;
            }
            i++;
            j--;
        }
        return true;
    }
    
    private String reverse(String str) {
        StringBuilder sb = new StringBuilder();
        for(int i = str.length() - 1; i >= 0; i--) {
            sb.append(str.charAt(i));
        }
        return sb.toString();
    }
}

HashMap，如果速度不行，那么就用trie来存word，然后searchWord

class Solution {
    class TrieNode {
        public TrieNode[] children;
        public int index;
        public String word;
        public boolean isword;
        public TrieNode() {
            this.children = new TrieNode[26];
            this.index = -1;
            this.word = null;
            this.isword = false;
        }
    }
    
    class Trie {
        public TrieNode root;
        public Trie () {
            this.root = new TrieNode();
        }
        
        public void insertWord(String word, int index) {
            TrieNode cur = root;
            for(int i = 0; i < word.length(); i++) {
                char c = word.charAt(i);
                if(cur.children[c - 'a'] == null) {
                    cur.children[c - 'a'] = new TrieNode();
                }
                cur = cur.children[c - 'a'];
            }
            cur.word = word;
            cur.isword = true;
            cur.index = index;
        }
        
        public int searchWord(String word) {
            TrieNode cur = root;
            for(int i = 0; i < word.length(); i++) {
                char c = word.charAt(i);
                if(cur.children[c - 'a'] == null) {
                    return -1;
                }
                cur = cur.children[c - 'a'];
            }
            return cur.index;
        }
    }
    
    public List<List<Integer>> palindromePairs(String[] words) {
        List<List<Integer>> lists = new ArrayList<List<Integer>>();
        Trie trie = new Trie();
        for(int i = 0; i < words.length; i++) {
            // save word;
            trie.insertWord(words[i], i);
        }
        
        // YYYYY    YY YYYYY
        for(int i = 0; i < words.length; i++) {
            String word = words[i];
            for(int j = 0; j <= word.length(); j++) {
                String str1 = word.substring(0, j);
                String str2 = word.substring(j);
                
                if(isPalindrome(str1)) {
                    // reverseStr2 + str1 + str2;
                    String revstr2 = reverse(str2);
                    int index = trie.searchWord(revstr2);
                    if(index != -1 && index != i) {
                        List<Integer> list = new ArrayList<>();
                        list.add(index);
                        list.add(i);
                        lists.add(list);
                    }
                } 
                if(str2.length() != 0 && isPalindrome(str2)) {
                    // str1 + str2 + revstr1;
                    String revstr1 = reverse(str1);
                    int index = trie.searchWord(revstr1);
                    if(index != -1 && index != i) {
                        List<Integer> list = new ArrayList<>();
                        list.add(i);
                        list.add(index);
                        lists.add(list);
                    }
                }
            }
        }
        return lists;
    }
    
    private boolean isPalindrome(String str) {
        int i = 0; int j = str.length() - 1;
        while(i <= j) {
            if(str.charAt(i) != str.charAt(j)) {
                return false;
            }
            i++;
            j--;
        }
        return true;
    }
    
    private String reverse(String str) {
        StringBuilder sb = new StringBuilder();
        for(int i = str.length() - 1; i >= 0; i--) {
            sb.append(str.charAt(i));
        }
        return sb.toString();
    }
}