树状数组

树状数组的区间修改区间查询

设差分数组\(c_i=a_i-a_{i-1}\)，

\[\because a_i= \sum_{1}^{i}c_i \]

\[\therefore\sum_{i=1}^x a_i=\sum_{i=1}^x\sum_{j=1}^ic_j =\sum_{i=1}^x (x-i+1)*c_i \]

\[\sum_{i=1}^x a_i=(x+1)\sum_{i=1}^x c_i-\sum_{i=1}^x c_i \times i \]

修改

void add(long long k,long long z)
{
	for(long long i=k;i<=n;i+=(i& -i)) c[i]+=z,c1[i]+=(k-1)*z;
}

前缀和查询

long long qsum(long long k)
{
	long long ans=0;
	for(long long i=k;i>0;i-=(i & -i)) ans+=(long long)c[i]*k-c1[i];
	return ans;
}

调用

add(x,y); add(x+1,-y);