#include <bits/stdc++.h> using namespace std; const int N = 1e5 + 7; // How to calculate subarray max for every subarray of size K in O(N) // A = [5, 7, 3, 4, 2], K = 3 // ans = [7, 7, 4] // HW 1 -> To try solve the same problem using SETS/MAPS/Priority_Queue in O(NlogN) // HW 2 -> To try solve the same problem in O(N) using prefix/suffix max arrays + partitioning idea // Alternate to DQ for the same problem meant to be done in O(N) int A[N]; deque<pair<int, int> > DQ; int cost = 0; void push(int x) { while(!DQ.empty()) { if(DQ.back().first < A[x]) { DQ.pop_back(); cost++; } else { cost++; break; } } DQ.push_back({A[x], x}); cost++; } // Conjecture -> cost <= 3n // Complexity -> O(N) int query(int l, int r) { while(!DQ.empty()) { if(DQ.front().second < l) { DQ.pop_front(); cost++; } else { cost++; break; } } return DQ.front().first; // Invariants: DQ is descending } int main() { int n, k; cin>>n>>k; for(int i = 1; i <= n; i++) cin>>A[i]; for(int i = 1; i <= k; i++) { push(i); } //l = 1, r = k int l = 1, r = k; cout<<query(l, r)<<" "; for(r = k + 1; r <= n; r++) { l++; push(r); cout<<query(l, r)<<" "; } cout<<endl; cout<<cost<<endl; // cost <= 2*n }
Standard input is empty
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