30. Substring with Concatenation of All Words
题目：
You are given a string, s, and a list of words, words, that are all of the same length. Find all starting indices of substring(s) in s that is a concatenation of each word in wordsexactly once and without any intervening characters.
For example, given:
s: "barfoothefoobarman"
words: ["foo", "bar"]
You should return the indices: [0,9].
(order does not matter).
链接： http://leetcode.com/problems/substring-with-concatenation-of-all-words/
题解：
第一反应是用Trie，像spell checker一样，在Trie中检查这段text是不是word。 （待补充）
第二反应是做一个类似于DFA的状态机。 （待补充）
第三反应是看答案。默默看答案，看到大家都用HashMap，所以也写了用两个HashMap的， 提交就超时了。再想一想，还是要用sliding window， 比如text = abca， 单词为'a'，'b'和'c'，这样0和1都是有效index，要减少重复compare.
HashMap:
先把word以及word count放入一个wordMap中，然后对text进行遍历。遍历的时候，每次步长为wordLength，所以对于整个text我们只需要遍历wordLength次pass。 对于每次pass，由于要找到所有复合条件的index，所以我们进行sliding window。为此我们还需要一个current map用来记录当前的window，一个lo变量来记录window的左边界，以及一个。之后对于每次pass，先看当前的单词是否存在于wordMap里，假如不存在则reset curMap，count和lo。假如存在，则把当前单词加入现在的window里。加入完毕后还需要检查重复情况，假如当前window里这个单词的计数大于wordMap里的计数，则从window左边界逐个取出单词，直到当前单词的计数等于wordMap里的计数为止。 假如count == 单词总数，则 lo 是一个解，加入到结果list里，更新lo，count，并且window向右移动一个单词。 代码写得很拖沓，有空要好好refactor。
Time Complexity - O(n)， Space Complexity - O(m * l)， m为单词数量，l为单词长度。
public class Solution { HashMap<String, Integer> wordMap; public List<Integer> findSubstring(String s, String[] words) { List<Integer> res = new ArrayList<>(); if(s == null ||s.length() == 0 || words == null || words.length == 0) return res; wordMap = new HashMap<>(); fillWordMap(words); //put all words and their frequencey to wordMap int wordLen = words[0].length(), wordCount = words.length; HashMap<String, Integer> curMap = new HashMap<>(); //sliding window storing current word for(int i = 0; i < wordLen; i++) { //we are going to process s word by word, so totally we need "wordLen" passes int j = i, lo = i, count = 0; //lo is the index we need to record and add to result list curMap.clear(); while(j <= s.length() - wordLen) { String curWord = s.substring(j, j + wordLen); if(!wordMap.containsKey(curWord)) { // intervening characters found curMap.clear(); count = 0; lo = j + wordLen; } else { if(curMap.containsKey(curWord)) //put current word into current window curMap.put(curWord, curMap.get(curWord) + 1); else curMap.put(curWord, 1); count++; while(curMap.get(curWord) > wordMap.get(curWord)) { // remove words from left end of the window until valid String rmvWord = s.substring(lo, lo + wordLen); curMap.put(rmvWord, curMap.get(rmvWord) - 1); count--; lo += wordLen; } if(count == wordCount) { //if target string found res.add(lo); String loWord = s.substring(lo, lo + wordLen); curMap.put(loWord, curMap.get(loWord) - 1); count--; lo += wordLen; } } j += wordLen; } } return res; } private void fillWordMap(String[] words) { for(String word : words) { if(wordMap.containsKey(word)) wordMap.put(word, wordMap.get(word) + 1); else wordMap.put(word, 1); } } }
Trie:
DFA:
Histogram:
二刷：
这里主要还是跟第一遍相同。先建立一个global的wordMap，里面还有单词以及个数。接下来做双重循环，外循环是从0 到 单词的长度，每次递增一个字符，内循环开始前我们clear curMap。内循环是从j = i开始，每次递增一个单词长度L。同时我们维护一个滑动窗口的左边界lo，以及当前复合条件的单词数目 count。 每次我们先求出当前的单词 - s.substring(j, j + wordLen)，先判断其是否在wordMap里，假如不在，我们可以直接跳过L - 当前单词，从下一个单词其实为止开始查找 (这里我们要清空curMap以及count，更新lo)。假若当前单词在wordMap里， 那么我们把它加入到curMap中，之后再拿curMap中这个单词的value与wordMap中这个单词的value进行比较。假如curMap.value小，那么我们继续下面的计算。假如curMap.get(curWord) > wordMap.get(curWord)，说明我们加入了多余的单词，这里我们要用类似"Sliding Window Maximum"中的方法，使用一个while循环，将这个window前部的单词一个一个poll出去。poll的过程就是先求出前部单词 s.substring(lo, lo + wordLen)，然后在curMap中将其value - 1，并且count--，之后再更新lo = lo + wordLen来比较下一个首部单词。直到我们把多加入的单词去掉，使得curMap.get(curWord) <= wordMap.get(curWord)为止。 最后当count == words.length时，这时我们找到了一个解，把这个解的开头index lo加入到结果集中。然后我们要把window首部单词去掉，count--，并且增加lo = lo + wordLen，来继续进行下面的判断。
Java:
假如不考虑substring的话，应该是L次遍历，每次遍历 n / L个字符，这样应该算是 Time Complexity: O(n)， Space Complexity - O(L * m)， L为单词的长度，m为单词个数。
public class Solution { public List<Integer> findSubstring(String s, String[] words) { List<Integer> res = new ArrayList<>(); if (s == null || s.length() == 0 || words == null || words.length == 0) { return res; } Map<String, Integer> wordMap = new HashMap<>(); for (String word : words) { if (!wordMap.containsKey(word)) { wordMap.put(word, 1); } else { wordMap.put(word, wordMap.get(word) + 1); } } int wordLen = words[0].length(); Map<String, Integer> curMap = new HashMap<>(); for (int i = 0; i < wordLen; i++) { // start from each char int lo = i, count = 0; curMap.clear(); for (int j = i; j <= s.length() - wordLen; j += wordLen) { String curWord = s.substring(j, j + wordLen); if (!wordMap.containsKey(curWord)) { curMap.clear(); count = 0; lo = j + wordLen; } else { if (!curMap.containsKey(curWord)) { curMap.put(curWord, 1); } else { curMap.put(curWord, curMap.get(curWord) + 1); } count++; while (curMap.get(curWord) > wordMap.get(curWord)) { // poll from front String wordToRemove = s.substring(lo, lo + wordLen); curMap.put(wordToRemove, curMap.get(wordToRemove) - 1); lo += wordLen; count--; } if (count == words.length) { // found one solution res.add(lo); String loWord = s.substring(lo, lo + wordLen); curMap.put(loWord, curMap.get(loWord) - 1); lo += wordLen; count--; } } } } return res; } }
有的时候HashMap的操作也可以简写，比如
curMap.put(curWord, curMap.get(curWord) == null ? 1 : curMap.get(curWord) + 1);
三刷:
跟二刷基本相同。
要注意的是 j的范围是 [i, s.length() - wordLen]，前后都是闭合的。
Java：
public class Solution { public List<Integer> findSubstring(String s, String[] words) { List<Integer> res = new ArrayList<>(); if (s == null || words == null || words.length == 0) return res; Map<String, Integer> wordsMap = new HashMap<>(); for (String word : words) { if (!wordsMap.containsKey(word)) wordsMap.put(word, 1); else wordsMap.put(word, wordsMap.get(word) + 1); } int wordLen = words[0].length(); for (int i = 0; i < wordLen; i++) { Map<String, Integer> curMap = new HashMap<>(); int lo = i; int count = 0; for (int j = i; j <= s.length() - wordLen; j += wordLen) { String word = s.substring(j, j + wordLen); if (!wordsMap.containsKey(word)) { count = 0; curMap.clear(); lo = j + wordLen; continue; } if (!curMap.containsKey(word)) curMap.put(word, 1); else curMap.put(word, curMap.get(word) + 1); count++; while (curMap.get(word) > wordsMap.get(word)) { String loWord = s.substring(lo, lo + wordLen); curMap.put(loWord, curMap.get(loWord) - 1); lo += wordLen; count--; } if (count == words.length) { res.add(lo); String loWord = s.substring(lo, lo + wordLen); curMap.put(loWord, curMap.get(loWord) - 1); lo += wordLen; count--; } } } return res; } }
