Given two strings s and t of lengths m and n respectively, return the minimum window

substring

of s such that every character in t (including duplicates) is included in the window. If there is no such substring, return the empty string "".

The testcases will be generated such that the answer is unique.

Example 1:

Input: s = "ADOBECODEBANC", t = "ABC"
Output: "BANC"
Explanation: The minimum window substring "BANC" includes 'A', 'B', and 'C' from string t.

Example 2:

Input: s = "a", t = "a"
Output: "a"
Explanation: The entire string s is the minimum window.

Example 3:

Input: s = "a", t = "aa"
Output: ""
Explanation: Both 'a's from t must be included in the window. Since the largest window of s only has one 'a', return empty string.

Constraints:

• m == s.length
• n == t.length
• 1 <= m, n <= 105
• s and t consist of uppercase and lowercase English letters.

Follow up: Could you find an algorithm that runs in O(m + n) time?

We will use a sliding window to find the minimum window. We wish to use a charmap to store the number of characters seen in s, and we will use two indices to represent an interval (left inclusive, right exclusive) of the window. To ensure that all characters in t is included, we can initialize charmap to negative counts for each character in t, so that when we iterate s and increase the counter for each c, we know that charmap[c] >= 0 means that s contains enough c to satisfy the condition. So the window is valid when every value in charmap is non-negative, thus we can find the smallest window.

Notice that our window interval is initialized with (-m, 0) which has a length m but will produce "" if we were to obtain s[-m:0].

Implementation

def minWindow(self, s: str, t: str) -> str:
    m, n = len(s), len(t)
    if m < n:
        return ""
    charmap = defaultdict(int)
    for c in t:
        charmap[c] -= 1
    window, l = (-m, 0), 0

    for r in range(m):
        charmap[s[r]] += 1
        r += 1
        while min(charmap.values()) >= 0:       # valid
            if window[1] - window[0] >= r - l:  # smaller than current
                window = (l, r)
            charmap[s[l]] -= 1
            l += 1
            
    return s[window[0] : window[1]]