From 43afdc3fb8bd88acd0e19f3e7325cea302dc56c5 Mon Sep 17 00:00:00 2001
From: Anshuman7080 <164294129+Anshuman7080@users.noreply.github.com>
Date: Sun, 13 Oct 2024 15:32:11 +0000
Subject: [PATCH] Deque for Efficient Window Management ( O(N) Time Complexity)

---
 Algorithms/binary_exponentiation.cpp | 54 ------------------------
 Algorithms/max_sliding_window.cpp    | 63 ++++++++++++----------------
 2 files changed, 26 insertions(+), 91 deletions(-)

diff --git a/Algorithms/binary_exponentiation.cpp b/Algorithms/binary_exponentiation.cpp
index 71ce2a6..e69de29 100644
--- a/Algorithms/binary_exponentiation.cpp
+++ b/Algorithms/binary_exponentiation.cpp
@@ -1,54 +0,0 @@
-#include<bits/stdc++.h>
-
-using namespace std;
-typedef long long int  ll;
-
-template <class T>
-class Algebra{
-    public:
-        // Iterative Approach
-        static T binExpIterative(T a,T b)  //a^b  
-        {
-            T ans=1;
-            do{
-                if (b & 1) // 'b' is odd
-                    ans*=a;
-                b>>=1;     //b/=2
-                a*=a;   //a^2
-            }while(b!=0);
-            return ans;
-        }
-        //Recursive Approach
-        static T   binExpRecursive(T a, T b) //a^b
-        {
-            if(b<1)
-                return 1;
-            if (b & 1) // 'b' is odd
-                return a * binExpRecursive(a * a, b / 2);
-            else
-                return binExpRecursive(a * a, b / 2);
-        };
-        
-        static T modExponentiation(T a,T b,T c)   // (a^b)%c
-        {
-            T ans=1;
-            do{
-                if(b&1)
-                    ans=(ans*a)%c;
-                b >>= 1; // b/=2
-                a=a*a%c;
-            }while(b!=0);
-            return ans;
-        }
-};
-
-
-int main()
-{
-    ll   a=603,b=1109;
-    cout<<Algebra<ll>::binExpIterative(a,b)<<endl;
-
-    cout << Algebra<ll>::binExpRecursive(a, b) << endl;
-
-    cout << Algebra<ll>::modExponentiation(a, b,2881) << endl;
-}
diff --git a/Algorithms/max_sliding_window.cpp b/Algorithms/max_sliding_window.cpp
index a4b5adb..47bccd0 100644
--- a/Algorithms/max_sliding_window.cpp
+++ b/Algorithms/max_sliding_window.cpp
@@ -1,50 +1,39 @@
-// Program for max sliding window
 #include <bits/stdc++.h>
 using namespace std;
-// Comparator to sort the vector of pair with increasing first and decreasing second values
-bool comparator(pair<int, int> a, pair<int, int> b)
-{
-    if (a.first == b.first)
-    {
-        return a.second > b.second;
-    }
-    return a.first < b.first;
-}
-// k-> size of the window
-vector<int> maxSlidingWindow(vector<int> &nums, int k)
-{
-    // Create a priority queue with comparator
-    priority_queue<pair<int, int>, vector<pair<int, int>>, function<bool(pair<int, int>, pair<int, int>)>> pq(comparator);
 
-    int n = nums.size();
+vector<int> maxSlidingWindow(vector<int>& nums, int k) {
+    deque<int> dq;
     vector<int> windowMax;
-    // Insert first K elements in priority queue
-    for (int i = 0; i < k; i++)
-    {
-        pq.push({nums[i], i});
-    }
-    windowMax.push_back(pq.top().first);
-    // Now slide over remaining elements
-    for (int i = k; i < n; i++)
-    {
+    int n = nums.size();
 
-        pq.push({nums[i], i});
-        // Loop until priority queue top element index comes undes the range
-        while (pq.top().second <= i - k)
-        {
-            pq.pop();
+    for (int i = 0; i < n; ++i) {
+        // Remove elements not within the sliding window
+        if (!dq.empty() && dq.front() == i - k) {
+            dq.pop_front();
+        }
+
+        // Remove elements smaller than the current element from the back of the deque
+        while (!dq.empty() && nums[dq.back()] < nums[i]) {
+            dq.pop_back();
+        }
+
+        // Add the current element index to the deque
+        dq.push_back(i);
+
+        // The front of the deque is the largest element in the current window
+        if (i >= k - 1) {
+            windowMax.push_back(nums[dq.front()]);
         }
-        windowMax.push_back(pq.top().first);
     }
+
     return windowMax;
 }
 
-int main()
-{
+int main() {
     vector<int> arr = {1, 1, 5, 2, 1, 0, 1, 3, 2, 1, 2, 1};
-    int k=4;
-    vector<int> max_arr =  maxSlidingWindow(arr,k);
-    for(auto e : max_arr){
-        cout<<e<<" ";
+    int k = 4;
+    vector<int> max_arr = maxSlidingWindow(arr, k);
+    for (auto e : max_arr) {
+        cout << e << " ";
     }
 }