[POJ 3468] A Simple Problem with Integers

A Simple Problem with Integers

Time Limit: 5000MS		Memory Limit: 131072K
Total Submissions: 64372		Accepted: 19813
Case Time Limit: 2000MS

Description

You have N integers, A₁, A₂, ... , A_N. You need to deal with two kinds of operations. One type of operation is to add some given number to each number in a given interval. The other is to ask for the sum of numbers in a given interval.

Input

The first line contains two numbers N and Q. 1 ≤ N,Q ≤ 100000. The second line contains N numbers, the initial values of A₁, A₂, ... , A_N. -1000000000 ≤ A_i ≤ 1000000000. Each of the next Q lines represents an operation. "C a b c" means adding c to each of A_a, A_a+1, ... , A_b. -10000 ≤ c ≤ 10000. "Q a b" means querying the sum of A_a, A_a+1, ... , A_b.

Output

You need to answer all Q commands in order. One answer in a line.

Sample Input

10 5

1 2 3 4 5 6 7 8 9 10

Q 4 4

Q 1 10

Q 2 4

C 3 6 3

Q 2 4

Sample Output

4

55

9

15

Hint

The sums may exceed the range of 32-bit integers.

 

这个题也可以用线段树做、而且更快、= =

注意用64位整数、

#include <iostream>

#include <cstdio>

#include <cstring>

using namespace std;

#define N 101000

#define ll __int64



ll num[N];

struct SplayTree

{

    ll ch[N][2],pre[N],val[N],add[N],sz[N],sum[N];

    ll root,top;



    inline void AddNode(ll x,ll c)

    {

        if(x==0) return;

        val[x]+=c;

        add[x]+=c;

        sum[x]+=c*sz[x];

    }

    inline void PushUp(ll x)

    {

        if(x==0) return;

        sz[x]=sz[ch[x][0]]+sz[ch[x][1]]+1;

        sum[x]=val[x]+sum[ch[x][0]]+sum[ch[x][1]];

    }

    inline void PushDown(ll x)

    {

        if(x==0) return;

        if(add[x])

        {

            AddNode(ch[x][0],add[x]);

            AddNode(ch[x][1],add[x]);

            add[x]=0;

        }

    }

    inline void Rotate(ll x,ll c) 

    {

        ll y=pre[x];

        PushDown(y);

        PushDown(x);

        ch[y][!c]=ch[x][c];

        if(ch[x][c]) pre[ch[x][c]]=y;

        pre[x]=pre[y];

        if(pre[y]) ch[pre[y]][ch[pre[y]][1]==y]=x;

        ch[x][c]=y;

        pre[y]=x;

        PushUp(y);

        if(y==root) root=x;

    }

    inline void Splay(ll x,ll f)

    { 

        PushDown(x);

        while(pre[x]!=f) 

        {

            PushDown(pre[pre[x]]); 

            PushDown(pre[x]);

            PushDown(x);

            if(pre[pre[x]]==f) Rotate(x,ch[pre[x]][0]==x);

            else

            {

                ll y=pre[x],z=pre[y];

                ll c=(ch[z][0]==y);

                if(ch[y][c]==x) Rotate(x,!c),Rotate(x,c);

                else Rotate(y,c),Rotate(x,c);

            }

        }

        PushUp(x);

        if(f==0) root=x;

    }

    inline void SplayKth(ll k,ll f)

    { 

        ll x=root;

        k+=1;

        while(1)

        {

            PushDown(x);

            if(k==sz[ch[x][0]]+1) break;

            else if(k<=sz[ch[x][0]]) x=ch[x][0];

            else k-=sz[ch[x][0]]+1,x=ch[x][1];

        }

        Splay(x,f);

    }

    inline void NewNode(ll &x,ll c)

    {

        x=++top;

        ch[x][0]=ch[x][1]=pre[x]=0;

        sz[x]=1;

        add[x]=0;

        sum[x]=val[x]=c;

    }

    inline void Build(ll &x,ll l,ll r,ll f)

    {

        if(l>r) return;

        ll m=(l+r)>>1;

        NewNode(x,num[m]);

        Build(ch[x][0],l,m-1,x);

        Build(ch[x][1],m+1,r,x);

        pre[x]=f;

        PushUp(x);

    }

    inline void Init(ll n)

    {

        ch[0][0]=ch[0][1]=pre[0]=val[0]=add[0]=sz[0]=sum[0]=0;

        root=top=0;

        for(ll i=1;i<=n;i++) scanf("%I64d",&num[i]);

        Build(root,0,n+1,0);

    }

    inline void Add(ll a,ll b,ll c)

    {

        SplayKth(a-1,0);

        SplayKth(b+1,root);

        AddNode(ch[ch[root][1]][0],c);

    }

    inline void GetSum(ll a,ll b)

    {

        SplayKth(a-1,0);

        SplayKth(b+1,root);

        printf("%I64d\n",sum[ch[ch[root][1]][0]]);

    }



}t;

int main()

{

    ll n,m;

    while(scanf("%I64d%I64d",&n,&m)!=EOF)

    {

        t.Init(n);

        while(m--)

        {

            char op;

            ll a,b,c;

            scanf(" %c",&op);

            if(op=='Q')

            {

                scanf("%I64d%I64d",&a,&b);

                t.GetSum(a,b);

            }

            else 

            {

                scanf("%I64d%I64d%I64d",&a,&b,&c);

                t.Add(a,b,c);

            }

        }

    }

    return 0;

}