Note:
Solution1:
维护一个窗口,每次关注窗口中的字符串,在每次判断中,左窗口和右窗口选择其一向前移动。同样是维护一个HashSet, 正常情况下移动右窗口,如果没有出现重复则继续移动右窗口,如果发现重复字符,则说明当前窗口中的串已经不满足要求,继续移动有窗口不可能得到更好的结果,此时移动左窗口,直到不再有重复字符为止,中间跳过的这些串中不会有更好的结果,因为他们不是重复就是更短。
因为左窗口和右窗口都只向前,所以两个窗口都对每个元素访问不超过一遍,因此时间复杂度为O(2*n)=O(n),是线性算法。空间复杂度为HashSet的size,也是O(n).
public class Solution { public int lengthOfLongestSubstring(String s) { if(s == null || s.length() == 0) return 0; HashSetset = new HashSet (); int left = 0; int right = 0; int max = 0; while(right < s.length()) { if(set.contains(s.charAt(right))) { if(max < right - left) { max = right - left; } while(s.charAt(left) != s.charAt(right)) { set.remove(s.charAt(left)); left++; } left++; }else { set.add(s.charAt(right)); } right++; } max = Math.max(max, right - left); return max; } }
Solution2:
O(n) runtime, O(1) space – Two iterations:
Need two indices to record the head and the tail of the current substring. Since i and j both traverse at most n steps, the worst case would be 2n steps, which the runtime complexity must be O(n).
Note that the space complexity is constant O(1), even though we are allocating an array. This is because no matter how long the string is, the size of the array stays the same at 256.
public class Solution { public int lengthOfLongestSubstring(String s) { boolean[] exist = new boolean[256]; int i = 0, maxLen = 0; for(int j = 0; j < s.length(); j++) { while(exist[s.charAt(j)]) { exist[s.charAt(i)] = false; i++; } exist[s.charAt(j)] = true; maxLen = Math.max(maxLen, j - i + 1); } return maxLen; } }Solution3:
O(n) runtime, O(1) space – Single iteration:
Instead of using a table to tell if a character exists or not, we could define a mapping of the characters to its index. Then we can skip the characters immediately when we found a repeated character.
public class Solution { public int lengthOfLongestSubstring(String s) { int[] charMap = new int[256]; Arrays.fill(charMap, -1); //Assigns -1 to each element of the specified array of ints int i = 0, maxLen = 0; for(int j = 0; j < s.length(); j++) { if(charMap[s.charAt(j)] >= i) { i = charMap[s.charAt(j)] + 1; } charMap[s.charAt(j)] = j; maxLen = Math.max(maxLen, j - i + 1); } return maxLen; } }
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