树状数组的区间修改和区间查询

c是差分数组
a是c的前缀和数组
${\sum }_{i=1}^{n}a[i]$=a[1]+a[2]+a[3]+···+a[n]

=c[1]+c[1]+c[2]+c[1]+c[2]+c[3]+···+c[1]+c[2]+···+c[n−1]+c[n]

=n*c[1]+(n-1)*c[2]+(n-2)*c[3]+···+1*c[n]

=${\sum }_{i=1}^{n}c[i]\ast (n+1-i)$

=$(n+1)\ast {\sum }_{i=1}^{n}c[i]-{\sum }_{i=1}^{n}c[i]\ast i$

$设c1[i]=c[i]，c2[i]=c[i]\ast i$

=$(n+1)\ast {\sum }_{i=1}^{n}c1[i]-{\sum }_{i=1}^{n}c2[i]$

// 区间修改 update(l,num),update(r+1,-num)
// 区间查询 query(r) - query(l-1)
int query(int num){ //查询
   int ans=0,p=num;
   while(num>0){
   	ans+=(p+1)*c1[num]-c2[num];
   	num-=lowbit(num);
   }
   return ans;
}
void update(int num,int val){ //更新
   int p=num;
   while(num<=n){
   	c1[num]+=val;
   	c2[num]+=val*p
   	num+=lowbit(num);
   }
}