Array and Queries


Problem Statement :


Given an array, you are asked to perform a number of queries and divide the array into what are called, beautiful subsequences.

The array A has length n. A function f(A)  is defined to be a minimal possible , such that it's possible to divide array A into x  beautiful subsequences. Note that each element of an array should belong to exactly one subsequence, and subsequence does not necessarily need to be consecutive.

A subsequence S with length len  is called beautiful if and only if:

len = 1

 or
Let S'  be a sorted version of S. It must hold that  for every 

You need to find  modulo .

Input Format

The first line contains a single integer , representing the length of array .
The next line contains the array  given as space-separated integers.
The next line contains a single integer , representing the number of queries.
Each of the  lines contain two integers  and , which is described above.



Output Format

Print the required answer in one line.

Sample Input 0

5
2 2 1 1 1
2
3 2
5 5


Sample Output 0

11


Solution :



title-img 




                        Solution in C++ :

special credits to  : 

Tara Mehta
startreckker@gmail.com





#include <bits/stdc++.h>
using namespace std;
long int mod=1000000007 ;
int main(){
    int n;
    cin>>n;
    multiset<int> set1;
    int arr[n];
    for(int i=0;i<n;i++){
        cin>>arr[i];
        set1.insert(arr[i]);
    }
    multiset<int> set2=set1;
    int count=0;
    while(set2.size()){
        count++;
        int cur=*(set2.begin());
        set2.erase(set2.find(cur));
        while((set2.find(cur+1))!=set2.end()){
            cur++;
            set2.erase(set2.find(cur));
        }
    }
   long long int q;
    cin>>q;
    long long int ans=0;
    for(long long int i=0;i<q;i++){
        int id,val;
        cin>>id>>val;
        id--;
        int curr=set1.count(arr[id]);
        int prev=set1.count(arr[id]-1);
          int next=set1.count(arr[id]+1);
          //cout<<'\t'<<curr<<'\t'<<prev<<'\t'<<next<<'\n';
          if(prev==0 && next==0)
          count--;
          else if(curr>max(prev,next))
          count--;
          else if(curr<=min(prev,next))
          count++;
          set1.erase(set1.find(arr[id]));
          arr[id]=val;
          curr=set1.count(arr[id]);
          prev=set1.count(arr[id]-1);
          next=set1.count(arr[id]+1);
          //cout<<'\t'<<curr<<'\t'<<prev<<'\t'<<next<<'\n';
         if(prev==0 && next==0)
          count++;
           else if((curr+1)>max(prev,next))
          count++;
           else if((curr+1)<=min(prev,next))
          count--;
          set1.insert(val);
          ans=(ans+((i+1)*(count))%mod)%mod;
    }
    cout<<ans;
    return 0;
}






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