02 BIT (RANGE update , POINT query).cpp

/**

Fenwick Tree
============

Description
-----------

A data structure to quickly do the following -
1 . Point Update
2 . Prefix Sum Array Update

Operations
----------

- Add value to an index                 : O(logN)
- Calculate Prefix Sum upto an index    : O(logN)

Modification to do range updates
--------------------------------

This is the same trick as we do for arrays .
Imagine there are a lot of range updates and we only have to answer query after all updates .

Then , we can do as follows :
- Update a[l] = +value , a[r+1] = -value for each update
- After all update operation calculate Prefix Sum Array

The Prefix Sum Array will contain the value for each index after all update operations .

If there were any update after query we again would have to calculate the Prefix Sum Array again in O(N) .
Fenwick Tree allows us to do both this Point Update and Prefix Sum Array Update in O(logN) time .

**/

/** Which of the favors of your Lord will you deny ? **/

#include<bits/stdc++.h>
using namespace std;

#define LL long long
#define PII pair<int,int>
#define PLL pair<LL,LL>
#define F first
#define S second

#define ALL(x)      (x).begin(), (x).end()
#define READ        freopen("alu.txt", "r", stdin)
#define WRITE       freopen("vorta.txt", "w", stdout)

#ifndef ONLINE_JUDGE
#define DBG(x)      cout << __LINE__ << " says: " << #x << " = " << (x) << endl
#else
#define DBG(x)
#define endl "\n"
#endif

template<class T1, class T2>
ostream &operator <<(ostream &os, pair<T1,T2>&p);
template <class T>
ostream &operator <<(ostream &os, vector<T>&v);
template <class T>
ostream &operator <<(ostream &os, set<T>&v);

inline void optimizeIO()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
}

const int nmax = 2e5+7;

/** BIT / FENWICK TREE **/
/*** 1 based indexing ***/

struct Fenwick{

    vector<LL>BIT;
    int N;

    Fenwick (int n) : BIT(n+1,0) , N(n) {}

    inline int LSB(int x) {return x&(-x);} /// find the number with first bit set

    /// POINT update : adds val to index idx
    void add(int idx,LL val)
    {
        for(int i = idx ; i<=N ; i += LSB(i)) /// adding LSB , jumping to next segment covered by this index
            BIT[i] += val;
    }

    /// prefix sum upto index idx
    LL pref(int idx)
    {
        LL sum = 0;

        for(int i = idx ; i>0 ; i -= LSB(i)) /// removing LSB , jumping to next segment covering upto index
            sum += BIT[i];

        return sum;
    }

    /// RANGE update : adds val to [l,r]
    void update(int l,int r,LL val)
    {
        add(l,val);
        add(r+1,-val);
    }

    void debug()
    {
        cout<<"Prefix Sum Array : ";
        for(int i=1;i<=N;i++)
            cout<<pref(i)<<" ";
        cout<<endl;
    }
};

int main()
{
    optimizeIO();

    int n,q;
    cin>>n>>q;

    Fenwick f(n);

    vector<LL>ara(n+1);
    for(int i=1;i<=n;i++)
    {
        cin>>ara[i];
        f.update(i,i,ara[i]);
    }

    while(q--)
    {
        f.debug();

        int type;
        cin>>type;

        if(type==1) /** POINT Query **/
        {
            int idx;
            cin>>idx;

            cout<<f.pref(idx)<<endl;
        }
        else if(type==2) /** RANGE update **/
        {
            int l,r;
            LL val;
            cin>>l>>r>>val;

            f.update(l,r,val);
        }
    }

    return 0;
}

/**
10 10
3 4 0 0 0 0 1 2 3 3
2 5 7 12
1 4
**/

template<class T1, class T2>
ostream &operator <<(ostream &os, pair<T1,T2>&p)
{
    os<<"{"<<p.first<<", "<<p.second<<"} ";
    return os;
}
template <class T>
ostream &operator <<(ostream &os, vector<T>&v)
{
    os<<"[ ";
    for(T i:v)
    {
        os<<i<<" " ;
    }
    os<<" ]";
    return os;
}

template <class T>
ostream &operator <<(ostream &os, set<T>&v)
{
    os<<"[ ";
    for(T i:v)
    {
        os<<i<<" ";
    }
    os<<" ]";
    return os;
}