LeetCode: 76. Minimum Window Substring

题目描述

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 empty string "".

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

题目大意：在 S 串中找到一段子串 s (窗口)， 使其含有 T 串的所有字母。要求算法复杂度为 O(n)。

解题思路 —— 步步为营，庖丁解牛

• 找到第一个窗口。
• 根据第一个窗口，求出下一个窗口。
• 以此类推，计算出最小窗口。

AC 代码

class Solution {
private:
    // find the first window, [first, second).
    // the second of return value is 0, if there is no window in s.
    pair<size_t, size_t> findFirstWnd(string s, string t, map<char, int>& tCharNumMap)
    {
        if(t.empty() && !s.empty()) return {0, 1};

        pair<size_t, size_t> firstWnd{0, 0};
        size_t count = t.size();

        for(size_t i = 0; i < s.size() && count > 0; ++i)
        {
            if(tCharNumMap.find(s[i]) == tCharNumMap.end())
            {
                continue;
            }

            if(count == s.size()) firstWnd.first = i;
            if(tCharNumMap[s[i]] > 0)
            {
                --count;
            }
            --tCharNumMap[s[i]];

            // there are enough times of the first char aka s[i] in firstWnd.
            while(tCharNumMap.find(s[firstWnd.first]) == tCharNumMap.end() || tCharNumMap[s[firstWnd.first]] < 0)
            {
                if(tCharNumMap.find(s[firstWnd.first]) != tCharNumMap.end()) ++tCharNumMap[s[firstWnd.first]];
                ++firstWnd.first; 
            }

            if(count == 0)
            {
                firstWnd.second = i+1;
                break;
            }
        }
        return firstWnd;
    }

    // find the next window.
    // the second of return value is 0, if there is no more window in s. 
    pair<size_t, size_t> findNextWnd(string s, string t, pair<size_t, size_t> lastWnd, map<char, int>& tCharNumMap)
    {
        pair<size_t, size_t> nextWnd{lastWnd.first+1, 0};
        ++tCharNumMap[s[lastWnd.first]];

        // there is enough times of the first char aka s[i] in firstWnd.
        while(tCharNumMap.find(s[nextWnd.first]) == tCharNumMap.end() || tCharNumMap[s[nextWnd.first]] < 0)
        {
            if(tCharNumMap.find(s[nextWnd.first]) != tCharNumMap.end()) ++tCharNumMap[s[nextWnd.first]];
            ++nextWnd.first; 
        }

        for(size_t i = lastWnd.second; i < s.size(); ++i)
        {
            if(s[i] == s[lastWnd.first])
            {
                nextWnd.second = i+1;
                --tCharNumMap[s[i]];
                break;
            }

            if(tCharNumMap.find(s[i]) == tCharNumMap.end()) continue;
            --tCharNumMap[s[i]];

            // there are enough times of the first char aka s[i] in firstWnd.
            while(tCharNumMap.find(s[nextWnd.first]) == tCharNumMap.end() || tCharNumMap[s[nextWnd.first]] < 0)
            {
                if(tCharNumMap.find(s[nextWnd.first]) != tCharNumMap.end()) ++tCharNumMap[s[nextWnd.first]];
                ++nextWnd.first; 
            }

        }

        return nextWnd;
    }
public:
    string minWindow(string s, string t) {
        // 0. calculate the apearing time of char in string t
        map<char, int> tCharNumMap;
        for(char ch : t)
        {
            ++tCharNumMap[ch];
        }

        // 1. find the first window
        pair<size_t, size_t> firstWnd = findFirstWnd(s, t, tCharNumMap);
        if(firstWnd.second == 0) return "";

        // 2. keep iterating the chars in string s, and find the minmum windows.
        pair<size_t, size_t> lastWnd = firstWnd;
        pair<size_t, size_t> minWnd = firstWnd;


        while(lastWnd.second != 0)
        {
            pair<size_t, size_t> nextWnd = findNextWnd(s, t, lastWnd, tCharNumMap);

            if(nextWnd.second != 0 && (int)nextWnd.second - (int)nextWnd.first < (int)minWnd.second - (int)minWnd.first)
            {
                minWnd = nextWnd;
            }
            lastWnd = nextWnd;
        }
        return s.substr(minWnd.first, minWnd.second-minWnd.first);
    }
};