Competitive-Programming-Templates/Lazy_Prop_Segment_Tree.cpp at master · rishu110067/Competitive-Programming-Templates · GitHub

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//to inc. use +=, to set use = while updating in lazy prop.

// Lazy Propgation Segment Tree for and Range sum/max/min query and Range update (inc. all values in range by x)
// type = 1 for sum, type = 2 for max, type = 3 for min
struct SegTree {
public:
    ll N;
    vll seg, upd;
    ll type;
    SegTree(ll n, ll T)
    {
        N = n+1;
        seg.resize(4*N,0);
        upd.resize(4*N,0);
        type = T;
    }

    void update(ll L,ll R,ll x,ll nd=1,ll l=1,ll r=-1)
    {
        if(r==-1) r=N;
        ll m=(l+r)/2, lnd=2*nd, rnd=2*nd+1;

        if(type==1)
        {
            seg[nd]+=upd[nd]*(r-l+1);
            if(l!=r)
            {
                upd[lnd]+=upd[nd];
                upd[rnd]+=upd[nd];
            }
        }
        else
        {
            seg[nd]+=upd[nd];
            if(l!=r)
            {
                upd[lnd]+=upd[nd];
                upd[rnd]+=upd[nd];
            }
        }
        upd[nd]=0;

        if(r<L || R<l) return;
        if(r==l)
        {
            if(type==1) seg[nd]+=x*(r-l+1);
            else seg[nd]+=x;
            return;
        }
        if(L<=l && r<=R)
        {
            if(type==1)
            {
                seg[nd]+=x*(r-l+1);
                upd[lnd]+=x;
                upd[rnd]+=x;
            }
            else
            {
                seg[nd]+=x;
                upd[lnd]+=x;
                upd[rnd]+=x;
            }
        }
        else
        {
            update(L,R,x,lnd,l,m);
            update(L,R,x,rnd,m+1,r);
            if(type == 1) seg[nd] = seg[lnd] + seg[rnd];
            else if(type == 2) seg[nd] = max(seg[lnd],seg[rnd]);
            else seg[nd] = min(seg[lnd],seg[rnd]);
        }
    }

    ll query(ll L,ll R,ll nd=1,ll l=1,ll r=-1)
    {
        if(r==-1) r=N;
        ll m=(l+r)/2, lnd=2*nd, rnd=2*nd+1;

        if(type==1)
        {
            seg[nd]+=upd[nd]*(r-l+1);
            if(l!=r)
            {
                upd[lnd]+=upd[nd];
                upd[rnd]+=upd[nd];
            }
        }
        else
        {
            seg[nd]+=upd[nd];
            if(l!=r)
            {
                upd[lnd]+=upd[nd];
                upd[rnd]+=upd[nd];
            }
        }
        upd[nd]=0;

        if(r<L || R<l) return (type<=2)?0:1e18;
        if(r==l) return seg[nd];
        if(L<=l && r<=R) return seg[nd];
        else
        {
            ll q1=query(L,R,lnd,l,m);
            ll q2=query(L,R,rnd,m+1,r);

            if(type == 1) seg[nd] = seg[lnd] + seg[rnd];
            else if(type == 2) seg[nd] = max(seg[lnd],seg[rnd]);
            else seg[nd] = min(seg[lnd],seg[rnd]);

            if(type == 1) return q1+q2;
            else if(type == 2) return max(q1,q2);
            else return min(q1,q2);

        }
    }

};


//1-indexed
//Lazy Propgation Segment Tree for and Range min query and Range update (inc. all values in range by x)
ll n;
const ll N=2e5+1;
ll seg[4*N], upd[4*N];
void update(ll L,ll R,ll x,ll nd=1,ll l=1,ll r=n)
{
    ll m=(l+r)/2, lnd=2*nd, rnd=2*nd+1;

    seg[nd]+=upd[nd];
    if(l!=r)
    {
        upd[lnd]+=upd[nd];
        upd[rnd]+=upd[nd];
    }
    upd[nd]=0;

    if(r<L || R<l) return;
    if(r==l)
    {
        seg[nd]+=x;
        return;
    }
    if(L<=l && r<=R)
    {
        seg[nd]+=x;
        upd[lnd]+=x;
        upd[rnd]+=x;
    }
    else
    {
        update(L,R,x,lnd,l,m);
        update(L,R,x,rnd,m+1,r);
        seg[nd]=min(seg[lnd],seg[rnd]);
    }
}
ll query(ll L,ll R,ll nd=1,ll l=1,ll r=n)
{
    ll m=(l+r)/2, lnd=2*nd, rnd=2*nd+1;

    seg[nd]+=upd[nd];
    if(l!=r)
    {
        upd[lnd]+=upd[nd];
        upd[rnd]+=upd[nd];
    }
    upd[nd]=0;

    if(r<L || R<l) return 1e18; //-1e18 for max
    if(r==l) return seg[nd];
    if(L<=l && r<=R) return seg[nd];
    else
    {
        ll q1=query(L,R,lnd,l,m);
        ll q2=query(L,R,rnd,m+1,r);
        seg[nd]=min(seg[lnd],seg[rnd]);
        return min(q1,q2);
    }
}


//1-indexed
//Lazy Propgation Segment Tree for and Range sum query and Range update (set all values in range to x)
const ll N=2e5+1;
ll seg[4*N], upd[4*N];
void update(ll L,ll R,ll x,ll nd=1,ll l=1,ll r=n)
{
    ll m=(l+r)/2, lnd=2*nd, rnd=2*nd+1;

    if(upd[nd]!=0)
    {
        seg[nd]=upd[nd]*(r-l+1);
        if(l!=r)
        {
            upd[lnd]=upd[nd];
            upd[rnd]=upd[nd];
        }
        upd[nd]=0;
    }

    if(r<L || R<l) return;
    if(r==l)
    {
        seg[nd]=x*(r-l+1);
        return;
    }
    if(L<=l && r<=R)
    {
        seg[nd]=x*(r-l+1);
        upd[lnd]=x;
        upd[rnd]=x;
    }
    else
    {
        update(L,R,x,lnd,l,m);
        update(L,R,x,rnd,m+1,r);
        seg[nd]=seg[lnd]+seg[rnd];
    }
}
ll query(ll L,ll R,ll nd=1,ll l=1,ll r=n)
{
    ll m=(l+r)/2, lnd=2*nd, rnd=2*nd+1;

    if(upd[nd]!=0)
    {
        seg[nd]=upd[nd]*(r-l+1);
        if(l!=r)
        {
            upd[lnd]=upd[nd];
            upd[rnd]=upd[nd];
        }
        upd[nd]=0;
    }

    if(r<L || R<l) return 0;
    if(r==l) return seg[nd];
    if(L<=l && r<=R) return seg[nd];
    else
    {
        ll q1=query(L,R,lnd,l,m);
        ll q2=query(L,R,rnd,m+1,r);
        seg[nd]=seg[lnd]+seg[rnd];
        return q1+q2;
    }
}


//1-indexed
//Lazy Propgation Segment Tree for Range sum query and Range AP update (inc. all values in range by AP)
const ll N=2e5+1;
ll seg[4*N], ft[4*N], cd[4*N];
void update(ll L,ll R,ll nd=1,ll l=1,ll r=n)
{
    ll m=(l+r)/2, lnd=2*nd, rnd=2*nd+1;

    seg[nd]+=sumAP(ft[nd],cd[nd],r-l+1);
    if(l!=r)
    {
        ft[lnd]+=ft[nd];
        cd[lnd]+=cd[nd];
        ft[rnd]+=AP(ft[nd],cd[nd],m+1-l+1);
        cd[rnd]+=cd[nd];
    }
    ft[nd]=0; cd[nd]=0;


    if(r<L || R<l) return;
    if(r==l)
    {
        seg[nd]+=l-L+1;
        return;
    }
    if(L<=l && r<=R)
    {
        seg[nd]+=segAP(l-L+1,1,r-l+1);
        ft[lnd]+=l-L+1;
        cd[lnd]++;
        ft[rnd]+=m+1-L+1;
        cd[rnd]++;
    }
    else
    {
        update(L,R,lnd,l,m);
        update(L,R,rnd,m+1,r);
        seg[nd]=seg[lnd]+seg[rnd];
    }
}
ll query(ll L,ll R,ll nd=1,ll l=1,ll r=n)
{
    ll m=(l+r)/2, lnd=2*nd, rnd=2*nd+1;

    seg[nd]+=segAP(ft[nd],cd[nd],r-l+1);
    if(l!=r)
    {
        ft[lnd]+=ft[nd];
        cd[lnd]+=cd[nd];
        ft[rnd]+=AP(ft[nd],cd[nd],m+1-l+1);
        cd[rnd]+=cd[nd];
    }
    ft[nd]=0; cd[nd]=0;

    if(r<L || R<l) return 0;
    if(r==l) return seg[nd];
    if(L<=l && r<=R) return seg[nd];
    else
    {
        ll q1=query(L,R,lnd,l,m);
        ll q2=query(L,R,rnd,m+1,r);
        seg[nd]=seg[lnd]+seg[rnd];
        return q1+q2;
    }
}


// Problem on Lazy Propagation Segment Tree (including mx,mn,sum range queries and update) and its beautiful implementation
// https://codeforces.com/contest/1439/problem/C
// https://codeforces.com/contest/1439/submission/120268200


// https://codedrills.io/contests/amrita-icpc-practice-session-7/problems/subarray-mex-sum
// https://codedrills.io/submissions/81644