[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
",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;
}