poj 3468 A Simple Problem with Integers

#include<stdio.h>
struct CNode
{
    int L,R;
    long long nSum;
    long long Inc;
    CNode *pLeft,*pRight;
};
CNode Tree[1000000];
int nCount;
int Mid(CNode *pRoot)
{
    return (pRoot->L+pRoot->R)/2;
}
void BuildTree(CNode *pRoot,int L,int R)
{
    pRoot->L=L;
    pRoot->R=R;
    pRoot->nSum=0;
    pRoot->Inc=0;
    if(L==R)
        return ;
    nCount++;
    pRoot->pLeft=Tree+nCount;
    nCount++;
    pRoot->pRight=Tree+nCount;
    BuildTree(pRoot->pLeft,L,(L+R)/2);
    BuildTree(pRoot->pRight,(L+R)/2+1,R);
}
void Insert(CNode *pRoot,int i,int v)
{
    if(pRoot->L==i&&pRoot->R==i)
    {
        pRoot->nSum=v;
        return ;
    }
    pRoot->nSum+=v;
    if(i<=Mid(pRoot))
        Insert(pRoot->pLeft,i,v);
    else
        Insert(pRoot->pRight,i,v);
}
void Add(CNode *pRoot,int a,int b,long long c)
{
    if(pRoot->L==a&&pRoot->R==b)
    {
        pRoot->Inc+=c;
        return ;
    }
    pRoot->nSum+=c*(b-a+1);
    if(b<=Mid(pRoot))
        Add(pRoot->pLeft,a,b,c);
    else if(a>Mid(pRoot))
        Add(pRoot->pRight,a,b,c);
    else
    {
        Add(pRoot->pLeft,a,Mid(pRoot),c);
        Add(pRoot->pRight,Mid(pRoot)+1,b,c);
    }
}
long long QuerySum(CNode *pRoot,int a,int b)
{
    if(pRoot->L==a&&pRoot->R==b)
    {
        return pRoot->nSum+(pRoot->R-pRoot->L+1)*pRoot->Inc;
    }
    pRoot->nSum+=(pRoot->R-pRoot->L+1)*pRoot->Inc;
    Add(pRoot->pLeft,pRoot->L,Mid(pRoot),pRoot->Inc);
    Add(pRoot->pRight,Mid(pRoot)+1,pRoot->R,pRoot->Inc);
    pRoot->Inc=0;
    if(b<=Mid(pRoot))
        return QuerySum(pRoot->pLeft,a,b);
    else if(a>Mid(pRoot))
        return QuerySum(pRoot->pRight,a,b);
    else
    {
        return QuerySum(pRoot->pLeft,a,Mid(pRoot))+
        QuerySum(pRoot->pRight,Mid(pRoot)+1,b);
    }
}
int main()
{
    int n,q,a,b,c;
    int i,j,k;
    char cmd[10];
    scanf("%d%d",&n,&q);
    nCount=0;
    BuildTree(Tree,1,n);
    for(i=1;i<=n;i++)
    {
        scanf("%d",&a);
        Insert(Tree,i,a);
    }
    for(i=0;i<q;i++)
    {
        scanf("%s",cmd);
        if(cmd[0]=='C')
        {
            scanf("%d%d%d",&a,&b,&c);
            Add(Tree,a,b,c);
        }
        else
        {
            scanf("%d%d",&a,&b);
            printf("%d\n",QuerySum(Tree,a,b));
        }
    }
    return 0;
}

在增加时，如果要加的区间正好覆盖一个
节点，则增加其节点的Inc值，不再往下走
，否则要更新nSum,再将增量往下传
这样更新的复杂度就是O(log(n))
在查询时，如果待查区间不是正好覆盖一
个节点，就将节点的Inc往下带，然后将Inc
代表的所有增量累加到nSum上后将Inc清0
，接下来再往下查询。 Inc往下带的过程也是
区间分解的过程，复杂度也是O(log(n))