[LeetCode] Minimum Window Substring

转载于 2015-03-11 15:04:00 发布 · 55 阅读

本文提供了一种算法，在O(n)时间内找到字符串中包含所有指定子串的最短窗口。通过使用双指针技巧，动态维护一个窗口来匹配目标子串，确保高效解决问题。

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Given a string S and a string T, find the minimum window in S which will contain all the characters in T in complexity O(n).

For example,
S = "ADOBECODEBANC"
T = "ABC"

Minimum window is "BANC".

Note:
If there is no such window in S that covers all characters in T, return the emtpy string "".

If there are multiple such windows, you are guaranteed that there will always be only one unique minimum window in S.

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Hash Table Two Pointers String

思路：

双指针，动态维护一个区间。尾指针不断往后扫，当扫到有一个窗口包含了所有 T 的字符后，
然后再收缩头指针，直到不能再收缩为止。最后记录所有可能的情况中窗口最小的

时间复杂度 O(n)，空间复杂度 O(1)

class Solution {
    public:
        string minWindow(string S, string T)
        {
            if(S.empty() || T.empty() || S.size() < T.size())
                return string();

            vector<int> expect(256, 0);
            vector<int> appear(256, 0);

            for(int i = 0; i < T.size(); i++)
            {   
                expect[T[i]] ++; 
            }   

            int minWidth = INT_MAX, min_start = 0; //
            int win_start = 0;
            int appearCharCnt = 0;
            for(int win_end = 0; win_end < S.size(); win_end++)
            {   
                if(expect[S[win_end]] > 0) // this char is part of T
                {   
                    appear[S[win_end]]++;
                    if(appear[S[win_end]] <= expect[S[win_end]])
                        appearCharCnt ++; 
                }   
                //cout << "appearCharCnt\t" <<appearCharCnt<< endl;
                if(appearCharCnt == T.size())
                {   
                    // shrink the start
                    while (appear[S[win_start]] > expect[S[win_start]]
                            || expect[S[win_start]] == 0) {
                        appear[S[win_start]]--;
                        win_start++;
                    }
                    if ((win_end - win_start + 1) < minWidth) {
                        minWidth = win_end - win_start + 1;
                        min_start = win_start;
                        //cout << "min_start\t" <<min_start << endl;
                        //cout << "min_width\t" <<minWidth<< endl;
                    }
                }
            }

            if (minWidth == INT_MAX)
                return "";
            else
                return S.substr(min_start, minWidth);


        }
};

精简一下条件判断

class Solution {
    public:
        string minWindow(string S, string T)
        {
            if(S.empty() || T.empty() || S.size() < T.size())
                return string();

            vector<int> expect(256, 0);
            vector<int> appear(256, 0);

            for(int i = 0; i < T.size(); i++)
            {
                expect[T[i]] ++;
            }

            int minWidth = INT_MAX, min_start = 0; 
            int win_start = 0;
            int appearCharCnt = 0;
            for(int win_end = 0; win_end < S.size(); win_end++)
            {   
                appear[S[win_end]]++;
                if(appear[S[win_end]] <= expect[S[win_end]])
                    appearCharCnt ++; 
                //cout << "appearCharCnt\t" <<appearCharCnt<< endl;
                if(appearCharCnt == T.size())
                {   
                    // shrink the win start
                    while (appear[S[win_start]] > expect[S[win_start]]
                          ) { 
                        appear[S[win_start]]--;
                        win_start++;
                    }   
                    if ((win_end - win_start + 1) < minWidth) {
                        minWidth = win_end - win_start + 1;
                        min_start = win_start;
                        //cout << "min_start\t" <<min_start << endl;
                        //cout << "min_width\t" <<minWidth<< endl;
                    }
                }
            }

            if (minWidth == INT_MAX)
                return "";
            else
                return S.substr(min_start, minWidth);


        }
};