76 Minimum Window Substring

本文介绍了一种在字符串S中寻找包含字符串T所有字符的最短子串的算法,复杂度为O(n)。通过使用双指针技术,动态维护一个包含T所有字符的最小子串区间。

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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).

Example:

Input: S = "ADOBECODEBANC", T = "ABC"
Output: "BANC"

Note:

  • If there is no such window in S that covers all characters in T, return the empty string "".
  • If there is such window, you are guaranteed that there will always be only one unique minimum window in S.


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

class Solution {
    public String minWindow(String s, String t) {
        if (s.isEmpty()) {
            return "";
        }
        
        if (s.length() < t.length()) {
            return "";
        }
        final int ASCII = 256;
        int[] expect_count = new int[ASCII];
        int[] appear_count = new int[ASCII];
        Arrays.fill(expect_count, 0);
        Arrays.fill(appear_count, 0);
        
        int appear = 0, wnd_start = 0, min_width = Integer.MAX_VALUE;
        int min_start = 0;
        
        for (int i = 0; i < t.length(); i++) {
            expect_count[t.charAt(i)]++;
        }
        
        for (int wnd_end = 0; wnd_end < s.length(); wnd_end++) {
            if (expect_count[s.charAt(wnd_end)] > 0) {
                appear_count[s.charAt(wnd_end)]++;
                if (appear_count[s.charAt(wnd_end)] <= 
                   expect_count[s.charAt(wnd_end)]) {
                    appear++;
                }
            }
            
            if (appear == t.length()) {
                while (appear_count[s.charAt(wnd_start)] > 
                      expect_count[s.charAt(wnd_start)] || 
                       expect_count[s.charAt(wnd_start)] == 0) {
                    appear_count[s.charAt(wnd_start)]--;
                    wnd_start++;
                }
                if (min_width > wnd_end - wnd_start + 1) {
                    min_width = wnd_end - wnd_start + 1;
                    min_start = wnd_start;
                }
            }
        }
        if (min_width == Integer.MAX_VALUE) {
            return "";
        } else {
            return s.substring(min_start, min_start + min_width);
        }
    }
}

To solve this problem, we can use the sliding window approach again. Here's the algorithm: 1. Initialize two dictionaries: need and window. need stores the count of each character in t, and window stores the count of each character in the current window. 2. Initialize two pointers left and right to mark the current window, and two variables match and required to track the number of matched characters and the number of required characters respectively. 3. Initialize a variable min_len to a large value and a variable start to 0 to store the start index of the minimum window substring. 4. While the right pointer is less than the length of the string s: - If the character at s[right] is in need, add it to window and update match and required accordingly. - While all characters in need are included in window, update min_len and start accordingly, and remove the character at s[left] from window and update match and required accordingly. - Move the left pointer to the right. - Move the right pointer to the right. 5. Return the minimum window substring starting from index start and having length min_len, or the empty string if no such substring exists. Here's the Python code for the algorithm: ``` def min_window(s, t): need = {} for c in t: need[c] = need.get(c, 0) + 1 window = {} left = right = 0 match = 0 required = len(need) min_len = float('inf') start = 0 while right < len(s): if s[right] in need: window[s[right]] = window.get(s[right], 0) + 1 if window[s[right]] == need[s[right]]: match += 1 while match == required: if right - left + 1 < min_len: min_len = right - left + 1 start = left if s[left] in need: window[s[left]] -= 1 if window[s[left]] < need[s[left]]: match -= 1 left += 1 right += 1 return s[start:start+min_len] if min_len != float('inf') else "" ``` Example usage: ``` s = "ADOBECODEBANC" t = "ABC" print(min_window(s, t)) # Output: "BANC" ```
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