這道 題是leetcode 上面的 一道題。常規解法需要兩層循環。這種解法不僅代碼簡潔,而且只需要一層循環。降低了複雜度。一起欣賞一下作者的代碼。
原題:
Given a string, find the length of the longest substring without repeating characters.
Examples:
Given "abcabcbb"
, the answer is "abc"
, which the length is 3.
Given "bbbbb"
, the answer is "b"
, with the length of 1.
Given "pwwkew"
, the answer is "wke"
, with the length of 3. Note that the answer must be a
substring, "pwke"
is a subsequence and not a substring.
解法:
/**
* Solution (DP, O(n)):
*
* Assume L[i] = s[m...i], denotes the longest substring without repeating
* characters that ends up at s[i], and we keep a hashmap for every
* characters between m ... i, while storing <character, index> in the
* hashmap.
* We know that each character will appear only once.
* Then to find s[i+1]:
* 1) if s[i+1] does not appear in hashmap
* we can just add s[i+1] to hash map. and L[i+1] = s[m...i+1]
* 2) if s[i+1] exists in hashmap, and the hashmap value (the index) is k
* let m = max(m, k), then L[i+1] = s[m...i+1], we also need to update
* entry in hashmap to mark the latest occurency of s[i+1].
*
* Since we scan the string for only once, and the 'm' will also move from
* beginning to end for at most once. Overall complexity is O(n).
*
* If characters are all in ASCII, we could use array to mimic hashmap.
*/
實現代碼:簡直簡潔有木有!!!
/**
* Solution (DP, O(n)):
*
* Assume L[i] = s[m...i], denotes the longest substring without repeating
* characters that ends up at s[i], and we keep a hashmap for every
* characters between m ... i, while storing <character, index> in the
* hashmap.
* We know that each character will appear only once.
* Then to find s[i+1]:
* 1) if s[i+1] does not appear in hashmap
* we can just add s[i+1] to hash map. and L[i+1] = s[m...i+1]
* 2) if s[i+1] exists in hashmap, and the hashmap value (the index) is k
* let m = max(m, k), then L[i+1] = s[m...i+1], we also need to update
* entry in hashmap to mark the latest occurency of s[i+1].
*
* Since we scan the string for only once, and the 'm' will also move from
* beginning to end for at most once. Overall complexity is O(n).
*
* If characters are all in ASCII, we could use array to mimic hashmap.
*/
int lengthOfLongestSubstring(string s) {
// for ASCII char sequence, use this as a hashmap
vector<int> charIndex(256, -1);
int longest = 0, m = 0;
for (int i = 0; i < s.length(); i++) {
m = max(charIndex[s[i]] + 1, m); // automatically takes care of -1 case
charIndex[s[i]] = i;
longest = max(longest, i - m + 1);
}
return longest;
}