leetcode 3 Longest Substring Without Repeating Characters最长无重复子串

Given a string, find the length of the longest substring without repeating characters. For example, the longest substring without
repeating letters for "abcabcbb" is "abc", which the length is 3. For "bbbbb" the longest substring is "b", with the length of 1.

这个应该是一个典型的动态规划问题：http://bbs.csdn.net/topics/310174805

直观地得到一个思路，表达起来真够难的，直接写代码要更容易



以abcbef这个串为例

用一个数据结构pos记录每个元素曾出现的下标，初始为-1

从s[0]开始，pos['a'] == -1，说明a还未出现过，令pos['a'] = 0，视为将a"加入当前串"，同时长度++

同理令pos['b'] = 1,pos['c'] = 2

到s[3]时，pos['b'] != -1，说明'b'在前面已经出现过了，此时可得到一个不重复串"abc"，刷新当前的最大长度，然后做如下处理：

pos[s[0~2]] = -1，亦即将"ab""移出当前串"，同时当前长度减去3



重复以上过程

int lengthOfLongestSubstring(string s) {
        vector<int> dict(256, -1);
        int maxLen = 0, start = -1;
        for (int i = 0; i != s.length(); i++) {
            if (dict[s[i]] > start)
                start = dict[s[i]];
            dict[s[i]] = i;
            maxLen = max(maxLen, i - start);
        }
        return maxLen;
    }

/**
 * 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;
}

下面给出python代码：

class Solution:
    # @return an integer
    def lengthOfLongestSubstring(self, s):
        start = maxLength = 0
        usedChar = {}

        for i in range(len(s)):
            if s[i] in usedChar and start <= usedChar[s[i]]:
                start = usedChar[s[i]] + 1
            else:
                maxLength = max(maxLength, i - start + 1)

            usedChar[s[i]] = i

        return maxLength

下面是c语言的版本：

// testlongsetString.cpp : 定义控制台应用程序的入口点。
//

#include "stdafx.h"
#include <stdio.h>
#include<iostream>

using namespace std;

void GetMaxUnRepeatSubStr(char *str)
{
	//global var
	int hashTable[256] ={0};
	char* pMS = str;
	int mLen = 0;

	//temp var
	char* pStart = pMS;
	int len = mLen;
	char* p = pStart;
	while(*p != '\0')
	{
		if(hashTable[*p] == 1)
		{
			if(len > mLen)
			{
				pMS = pStart;
				mLen = len;
			}

			while(*pStart != *p)
			{
				hashTable[*pStart] = 0;
				pStart++;
				len--;
			}
			pStart++;
		}
		else
		{
			hashTable[*p] = 1;
			len++;
		}
		p++;
	}
	// check the last time
	if(len > mLen)
	{
		pMS = pStart;
		mLen = len;
	}
	//print the longest substring
	while(mLen>0)
	{
		cout<<*pMS<<" ";
		mLen--;
		pMS++;
	}
	cout<<endl;
}

int main()
{
	char* str1="bdabcdcf";
	GetMaxUnRepeatSubStr(str1);
	char* str2="abcdefb";
	GetMaxUnRepeatSubStr(str2);
	char* str3="abcbef";
	GetMaxUnRepeatSubStr(str3);

	return 0;
}

参考文献：

http://bbs.csdn.net/topics/310174805

http://www.cnblogs.com/luxiaoxun/archive/2012/10/02/2710471.html

http://dsqiu.iteye.com/blog/1701324

http://www.ahathinking.com/archives/123.html