这是最近一次编程采访中提出的一个问题。
给定一个随机字符串S和另一个具有唯一元素的字符串T，找到S的最小连续子字符串，使其包含T中的所有元素。 说，
S='adobecodebanc'
T='abc'
Answer='banc'
我想出了一个解决方案，
public static String completeSubstring(String T, String S){
String minSub = T;
StringBuilder sb = new StringBuilder();
for (int i = 0; i <T.length()-1; i++) {
for (int j = i + 1; j <= T.length() ; j++) {
String sub = T.substring(i,j);
if(stringContains(sub, S)){
if(sub.length() < minSub.length()) minSub = sub;
}
}
}
return minSub;
}
private static boolean stringContains(String t, String s){
//if(t.length() <= s.length()) return false;
int[] arr = new int[256];
for (int i = 0; i <t.length() ; i++) {
char c = t.charAt(i);
arr[c -'a'] = 1;
}
boolean found = true;
for (int i = 0; i <s.length() ; i++) {
char c = s.charAt(i);
if(arr[c - 'a'] != 1){
found = false;
break;
}else continue;
}
return found;
}
该算法具有O（n3）复杂度，但自然不是很好。有人可以提出更好的算法。
答案 0 :(得分：7)
这是O（N）解决方案。
需要注意的重要事项：复杂性是每个工作单元都需要递增start或end，它们不会减少，算法会在它们结束之前停止。
public static String findSubString(String s, String t)
{
//algorithm moves a sliding "current substring" through s
//in this map, we keep track of the number of occurrences of
//each target character there are in the current substring
Map<Character,int[]> counts = new HashMap<>();
for (char c : t.toCharArray())
{
counts.put(c,new int[1]);
}
//how many target characters are missing from the current substring
//current substring is initially empty, so all of them
int missing = counts.size();
//don't waste my time
if (missing<1)
{
return "";
}
//best substring found
int bestStart = -1, bestEnd = -1;
//current substring
int start=0, end=0;
while (end<s.length())
{
//expand the current substring at the end
int[] cnt = counts.get(s.charAt(end++));
if (cnt!=null)
{
if (cnt[0]==0)
{
--missing;
}
cnt[0]+=1;
}
//while the current substring is valid, remove characters
//at the start to see if a shorter substring that ends at the
//same place is also valid
while(start<end && missing<=0)
{
//current substring is valid
if (end-start < bestEnd-bestStart || bestEnd<0)
{
bestStart = start;
bestEnd = end;
}
cnt = counts.get(s.charAt(start++));
if (cnt != null)
{
cnt[0]-=1;
if (cnt[0]==0)
{
++missing;
}
}
}
//current substring is no longer valid. we'll add characters
//at the end until we get another valid one
//note that we don't need to add back any start character that
//we just removed, since we already tried the shortest valid string
//that starts at start-1
}
return(bestStart<=bestEnd ? s.substring(bestStart,bestEnd) : null);
}
答案 1 :(得分：1)
我知道已经有足够的O（N）复杂性答案，但我试图在不抬头的情况下自行解决，只是因为它是一个有趣的问题需要解决并认为我会分享。这是我提出的O（N）解决方案：
public static String completeSubstring(String S, String T){
int min = S.length()+1, index1 = -1, index2 = -1;
ArrayList<ArrayList<Integer>> index = new ArrayList<ArrayList<Integer>>();
HashSet<Character> targetChars = new HashSet<Character>();
for(char c : T.toCharArray()) targetChars.add(c);
//reduce initial sequence to only target chars and keep track of index
//Note that the resultant string does not allow the same char to be consecutive
StringBuilder filterS = new StringBuilder();
for(int i = 0, s = 0 ; i < S.length() ; i++) {
char c = S.charAt(i);
if(targetChars.contains(c)) {
if(s > 0 && filterS.charAt(s-1) == c) {
index.get(s-1).add(i);
} else {
filterS.append(c);
index.add(new ArrayList<Integer>());
index.get(s).add(i);
s++;
}
}
}
//Not necessary to use regex, loops are fine, but for readability sake
String regex = "([abc])((?!\\1)[abc])((?!\\1)(?!\\2)[abc])";
Matcher m = Pattern.compile(regex).matcher(filterS.toString());
for(int i = 0, start = -1, p1, p2, tempMin, charSize = targetChars.size() ; m.find(i) ; i = start+1) {
start = m.start();
ArrayList<Integer> first = index.get(start);
p1 = first.get(first.size()-1);
p2 = index.get(start+charSize-1).get(0);
tempMin = p2-p1;
if(tempMin < min) {
min = tempMin;
index1 = p1;
index2 = p2;
}
}
return S.substring(index1, index2+1);
}
我很确定复杂性是O（N），如果我错了，请纠正
答案 2 :(得分：1)
@MattTimmermans提出的O（N）算法的替代实现，它使用Map<Integer, Integer>来计算出现次数，Set<Integer>来存储当前子字符串中存在的来自T的字符：
public static String completeSubstring(String s, String t) {
Map<Integer, Integer> occ
= t.chars().boxed().collect(Collectors.toMap(c -> c, c -> 0));
Set<Integer> found = new HashSet<>(); // characters from T found in current match
int start = 0; // current match
int bestStart = Integer.MIN_VALUE, bestEnd = -1;
for (int i = 0; i < s.length(); i++) {
int ci = s.charAt(i); // current char
if (!occ.containsKey(ci)) // not from T
continue;
occ.put(ci, occ.get(ci) + 1); // add occurrence
found.add(ci);
for (int j = start; j < i; j++) { // try to reduce current match
int cj = s.charAt(j);
Integer c = occ.get(cj);
if (c != null) {
if (c == 1) { // cannot reduce anymore
start = j;
break;
} else
occ.put(cj, c - 1); // remove occurrence
}
}
if (found.size() == occ.size() // all chars found
&& (i - start < bestEnd - bestStart)) {
bestStart = start;
bestEnd = i;
}
}
return bestStart < 0 ? null : s.substring(bestStart, bestEnd + 1);
}