Sliding Window
Author: Benjamin Qi
Contributors: Darren Yao, Andrew Wang
Maintaining data over consecutive subarrays.
Sliding Window
From CPH:
A sliding window is a constant-size subarray that moves from left to right through the array.
For each position of the window, we want to compute some information.
Focus Problem – read through this problem before continuing!
Implementation
The most straightforward way to do this is to store an sorted set of integers representing the integers inside the window. If the window currently spans the range , we observe that moving the range forward to only removes and adds to the window. We can support these two operations and query for the minimum / maximum in the set in .
Time Complexity:
C++
vector<int> maxSlidingWindow(vector<int>& nums, int k) {multiset<int> s;vector<int> ret;for(int i = 0; i < k; i++){s.insert(nums[i]);}for(int i = k; i < nums.size(); i++){ret.push_back(*s.rbegin());s.erase(s.find(nums[i-k]));s.insert(nums[i]);}ret.push_back(*s.rbegin());return ret;}
Java
static TreeMap<Integer, Integer> multiset = new TreeMap<Integer, Integer>();static void add(int x) {if(multiset.containsKey(x)) {multiset.put(x, multiset.get(x) + 1);} else {multiset.put(x, 1);}}static void remove(int x) {multiset.put(x, multiset.get(x) - 1);
Problems
Status | Source | Problem Name | Difficulty | Tags | |
---|---|---|---|---|---|
CSES | Normal | Show TagsPrefix Sums, Sliding Window | |||
CSES | Normal | Show TagsSet, Sliding Window | |||
CSES | Hard | Show TagsSet, Sliding Window |
With Two Pointers
In general, it is not required for the subarray to have constant size as long as both the left and right endpoints of the subarray only move to the right.
Focus Problem – read through this problem before continuing!
Solution
C++
int n;set<int> s;int a[200000], ans;int main() {int r = -1;cin >> n; F0R(i,n) cin >> a[i];F0R(i,n) {while (r < n-1 && !s.count(a[r+1])) s.insert(a[++r]);ans = max(ans,r-i+1);s.erase(a[i]);}cout << ans;}
Java
public class test{public static void main(String[] args) throws Exception {BufferedReader br = new BufferedReader(new InputStreamReader(System.in));int n = Integer.parseInt(br.readLine());StringTokenizer st = new StringTokenizer(br.readLine());int a[] = new int[n];for (int i = 0; i < n; i++) a[i] = Integer.parseInt(st.nextToken());int r = -1;HashSet<Integer> s = new HashSet<Integer>();int ans = 0;
Problems
Status | Source | Problem Name | Difficulty | Tags | |
---|---|---|---|---|---|
CF | Easy | ||||
Gold | Easy | Show TagsSet, Sliding Window | |||
AC | Easy | Show TagsSliding Window | |||
CSES | Easy | Show Tags2P, Sliding Window | |||
APIO | Normal | Show TagsMedian, Sliding Window | |||
Gold | Normal | Show TagsSliding Window | |||
Plat | Normal | Show TagsSliding Window | |||
APIO | Hard | Show TagsDP, Sliding Window | |||
IOI | Hard | Show TagsBinary Search, DP, Sliding Window | |||
IOI | Hard | Show TagsDP, Sliding Window |
Sliding Window Minimum in
Focus Problem – read through this problem before continuing!
Resources
Resources | ||||
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cp-algo | multiple ways to solve this |
Method 1 - Deque
Method 2 from cp-algo.
Resources | ||||
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CPH |
C++
vector<int> maxSlidingWindow(vector<int>& nums, int k) {deque<int> d;vector<int> ret;for(int i = 0; i < k; i++){while(!d.empty() && nums[i] > nums[d.back()]){d.pop_back();}d.push_back(i);}for(int i = k; i < nums.size(); i++){
Java
static ArrayList<Integer> maxSlidingWindow(int[] nums, int k) {ArrayList<Integer> ret = new ArrayList<Integer>();ArrayDeque<Integer> d = new ArrayDeque<Integer>();for (int i = 0; i < k; i++) {while(!d.isEmpty() && nums[i] > nums[d.peekLast()]) {d.pollLast();}d.addLast(i);}for (int i = k; i < nums.length; i++) {
Python
def maxSlidingWindow(self, nums: List[int], k: int) -> List[int]:d = collections.deque()def enqueue(i: int) -> None:while d and nums[d[-1]] <= nums[i]:d.pop()d.append(i)while d and (i - d[0]) >= k:d.popleft()
Method 2 - Two Stacks
Method 3 from cp-algo. Not as common but nice to know!
This section is not complete.
Problems
Status | Source | Problem Name | Difficulty | Tags | |
---|---|---|---|---|---|
YS | Hard | ||||
Baltic OI | Hard |