Vjudgian Decomposition

Revision en1, by vjudge38, 2024-05-19 13:51:14

Hello Codeforces! I got jealous of moemen_pro of writing educational bloggs and getting all the upvotes out there andd as an apprentice of the great vjudge36 I decided to write a blog abput a new topic i created on my own!!!! Let's say we have an array $a$ of length $n$ and we have $q$ queries of the form "what is the sum of elements in the range $[l,r]$ ????????????? Well of course the anive way is to build a sqet decpmpoistion but it is way too slow. Let's tiko of something faster. YeS! Lqoopijng!!! but how to loop ? it's $O(n)$. Well here wa can decompose the array into negative sized imaginary blocks, so we can loop through them in $O(iq)$ where $i=\sqrt{-1}$. Now is this complexity really faster? Well it's imaginary so it doesn't even exist!!!!!!!!!!!! Code:

#include <bits/stdc++.h>
using namespace std;
int main(){
int n,q;
cin>>n>>q;
int a[n],q,b[-n];
for (int i=1;i<=n;i++) b[-i]=a[i];
while (q--){
int l,r,ans=0;cin>>l>>r;
for (int i=r;i>=l;i--) ans+=b[i];
cout<<ans<<endl;
}return 0;
}

You can also update using this technique simply by updating the array $b$ and can answer many types of queriers.

pLEASE upvote for more lbof slile this!

#### History

Revisions

Rev. Lang. By When Δ Comment
en2 vjudge38 2024-05-19 13:52:03 1 Tiny change: 'em in $O(iq)$ where ' -> 'em in $O(inq)$ where '
en1 vjudge38 2024-05-19 13:51:14 1291 Initial revision (published)