从一道Hard学习滑动窗口

滑动窗口

　　滑动窗口（sliding windows algorithm）这种方法，专门用于解决区间解的问题。它在运算的时候，将解集放在窗口中，结束的时候比对是否符合预期。在运算的过程中，会对窗口的左右边缘进行操作（扩大、缩小）。特别针对于线性输入解决，滑动窗口就很形象了。

30. Substring with Concatenation of All Words

　　You are given a string, s, and a list of words, words, that are all of the same length. Find all starting indices of substring(s) in s that is a concatenation of each word in words exactly once and without any intervening characters.

　　题意是从一串输入字符串s中，找到能全包含words数组的起点（数组元素等长），这个起点可能有多个，而且不需要关心顺序。

Input:
  s = "barfoothefoobarman",
  words = ["foo","bar"]
Output: [0,9]
Explanation: Substrings starting at index 0 and 9 are "barfoo" and "foobar" respectively.
The output order does not matter, returning [9,0] is fine too.

　　比如这个例子，他在第0个位置和第9个位置可以包含words数组，也就是0位置和9位置各有一个长度为6的窗口可以囊括words数组。

 

 

Template = "foo","bar"

i=0

[b a r] f o o t h e f o o b a r m a n 

[b a r f o o] t h e f o o b a r m a n 

SAVE

b a r f o o[] t h e f o o b a r m a n 

b a r f o o [t h e] f o o b a r m a n 

b a r f o o t h e [f o o] b a r m a n 

b a r f o o t h e [f o o b a r] m a n 

SAVE

b a r f o o t h e f o o b a r[] m a n 

b a r f o o t h e f o o b a r [m a n] 

i=1

b [a r f] o o t h e f o o b a r m a n 
....

i=2

b a [r f o] o t h e f o o b a r m a n 
....

 

 　　每次扩展使用单词列表中的词长，如果扩展过程中不符合预期则清除窗口，窗口左端在当前词总数大于词组总数的时候，计算总数是单词的长度（因为s除以单词长度余数是0到单词长度之间，覆盖了余数就能覆盖整个场景）。

public class FindSubstring {
    public void test(){
        // [0,9]
        String s1 = "barfoothefoobarman";
        String[] words1 = {"foo","bar"};
        System.out.println(findSubstring(s1,words1));
        // []
        String s2 = "wordgoodgoodgoodbestword";
        String[] words2  = {"word","good","best","word"};
        System.out.println(findSubstring(s2,words2));
    }
    /**
     *  单词等长
     */
    public List<Integer> findSubstring(String s, String[] words) {
        List<Integer> result = new ArrayList<>();
        if(s == null || words.length == 0){
            return result;
        }
        int step = words[0].length();
        Map<String,Integer> counter = new HashMap<>();
        for(String word :words){
            counter.merge(word, 1, (a, b) -> a + b);
        }

        for(int i=0;i<step;++i){
            Map<String,Integer> window = new HashMap<>();
            int left = i;
            int right = i;
            while (right <= s.length() - step && left <= s.length() - step*words.length){
                String sub = s.substring(right,right + step);
                window.merge(sub,1,(a , b)->a + b);
                if(!counter.containsKey(sub)){
                    window.clear();
                    right += step;
                    left = right;
                    continue;
                }
                while (window.get(sub) > counter.get(sub)){
                    String drop = s.substring(left,left+step);
                    Integer dec = window.get(drop);
                    if(dec != null){
                        if(dec<=1){
                            window.remove(drop);
                        }else {
                            window.put(drop,dec-1);
                        }
                    }
                    left += step;
                }
                right += step;
                if(right - left == step * words.length){
                    result.add(left);
                }
            }
        }
        return result;
    }

}

 

 

 

 76. Minimum Window Substring

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"

题意是将s子串中包含T的所有字母的最短子串找出来，例子中BANC是包含ABC的最短子串。

Template = "ABC"

[]A D O B E C O D E B A N C

[A] D O B E C O D E B A N C

[A D] O B E C O D E B A N C

[A D O] B E C O D E B A N C

[A D O B] E C O D E B A N C

[A D O B E] C O D E B A N C

[A D O B E C] O D E B A N C
CONTAINS ABC mark substring A D O B E C
...

[A D O B E C O D E B] A N C
B now 2 > 1 so moving left but A is compliance
...

[A D O B E C O D E B A] N C
A 2 > 1 moving left

A D O [B E C O D E B A] N C
B 2 > 1 moving left

A D O B E [C O D E B A] N C
C O D E B A is not shorter than A D O B E C
...

A D O B E [C O D E B A N C]
C 2 > 1 moving left

A D O B E C O D E [B A N C]
B A N C is shorter than A D O B E C mark substring B A N C

 

import java.util.HashMap;
import java.util.Map;

public class MinimumWindowSubstring {
    public void test(){
        String s1 = "ADOBECODEBANC";
        String t1 = "ABC";
        // BANC
        System.out.println(minWindow(s1,t1));

        String s2 = "a";
        String t2 = "aa";
        // ""
        System.out.println(minWindow(s2,t2));

        String s3 = "a";
        String t3 = "b";
        // ""
        System.out.println(minWindow(s3,t3));

        String s4 = "a";
        String t4 = "a";
        // a
        System.out.println(minWindow(s4,t4));

        String s5 = "ab";
        String t5 = "b";
        // b
        System.out.println(minWindow(s5,t5));

        String s6 = "aa";
        String t6 = "aa";
        // aa
        System.out.println(minWindow(s6,t6));

        String s7 = "acbbaca";
        String t7 = "aba";
        // baca
        System.out.println(minWindow(s7,t7));

        String s8 = "aaaaaaaaaaaabbbbbcdd";
        String t8 = "abcdd";

        System.out.println(minWindow(s8,t8));


    }
    public String minWindow(String s, String t) {
        if(s == null || t == null || s.isEmpty() || t.isEmpty() || s.length() < t.length()){
            return "";
        }
        Map<Character,Integer> counter = new HashMap<>();
        char[] sArray = s.toCharArray();
        for(char c :t.toCharArray()){
            counter.merge(c,1,(a,b)->a+b);
        }
        int left = 0;
        int right ;
        int[] ans = {-1 , 0 , 0};
        Map<Character,Integer> window = new HashMap<>();
        for(int i=0;i<sArray.length;i++){
            char c = sArray[i];
            right = i;
            if(counter.containsKey(c)){
                window.merge(c,1,(a,b)->a+b);
                if(window.keySet().size() == counter.keySet().size()){
                    while (true){
                        Integer dec = window.get(sArray[left]);
                        Integer standard = counter.get(sArray[left]);
                        if(dec != null && standard != null){
                            if(dec <= standard){
                                break;
                            }
                            if(dec > standard){
                                window.merge(sArray[left],-1,(a,b)->a+b);
                            }
                        }
                        left ++;
                    }
                    boolean valid = true;
                    for(char v : counter.keySet()){
                        if(window.get(v) < counter.get(v)){
                            valid = false;
                        }
                    }
                    // mark if initial or shorter sequence
                    if(valid && (ans[0] == -1 || right - left + 1 < ans[0])){
                        ans[0] = right - left + 1;
                        ans[1] = left;
                        ans[2] = right;
                    }
                }
            }
        }
        return ans[0] == -1?"":s.substring(ans[1],ans[2]+1);
    }
}

 239. Sliding Window Maximum

Given an array nums, there is a sliding window of size k which is moving from the very left of the array to the very right. You can only see the k numbers in the window. Each time the sliding window moves right by one position. Return the max sliding window.

 

Input: nums = [1,3,-1,-3,5,3,6,7], and k = 3
Output: [3,3,5,5,6,7] 
Explanation: 

Window position                Max
---------------               -----
[1  3  -1] -3  5  3  6  7       3
 1 [3  -1  -3] 5  3  6  7       3
 1  3 [-1  -3  5] 3  6  7       5
 1  3  -1 [-3  5  3] 6  7       5
 1  3  -1  -3 [5  3  6] 7       6
 1  3  -1  -3  5 [3  6  7]      7

 

class Solution {
    public int[] maxSlidingWindow(int[] nums, int k) {
        List<Integer> result = new ArrayList<>();
        if(nums == null || nums.length == 0){
            return new int[]{};
        }
        int left = 0;
        int windowMax = Integer.MIN_VALUE;
        for(int i=0;i<nums.length;i++){
            if(i - left + 1 > k){
                int rv = nums[i];
                int currentMax = windowMax;
                if(nums[left] == windowMax){
                    currentMax = nums[left+1];
                    for(int t = left+1 ; t <= i ; t ++){
                        currentMax = Math.max(nums[t],currentMax);
                    }
                }
                windowMax = Math.max(currentMax,rv);
                result.add(windowMax);
                left ++ ;
            }  else {
                windowMax = Math.max(nums[i],windowMax);
                if(i - left + 1 == k){
                    result.add(windowMax);
                }
            }
        }
        int[] copyRes = new int[result.size()];
        for(int index = 0 ; index < result.size() ; index ++){
            copyRes[index] = result.get(index);
        }
        return copyRes;
    }
}