树状数组解决区间求和问题（模板）

1.改点求段模型

题目：HDU 1166 敌兵布阵

#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
const int MAXL=50000;
int tree[MAXL+50];
int a[MAXL+50];
char s[10];
int n;
int lowbit(int k)
{
return k&-k;
}
void update(int i,int value,int t)
{
value*=t;
while(i<=n)
{
tree[i]+=value;
i+=lowbit(i);
}
}
int getsum(int i)
{
int ans=0;
while(i>0)
{
ans+=tree[i];
i-=lowbit(i);
}
return ans;
}
int main()
{
int T;
int CASE=1;
scanf("%d",&T);
while(T--)
{
memset(tree,0,sizeof(tree));
scanf("%d",&n);
for(int i=1;i<=n;i++)
{
scanf("%d",a+i);
update(i,a[i],1);
}
int x,y;
cout<<"Case "<<CASE++<<":"<<endl;
while(scanf("%s",s))
{
if(!strcmp(s,"End"))
break;
else if(!strcmp(s,"Add"))
{
scanf("%d%d",&x,&y);
update(x,y,1);
}
else if(!strcmp(s,"Sub"))
{
scanf("%d%d",&x,&y);
update(x,y,-1);
}
else
{
scanf("%d%d",&x,&y);
int ans1=getsum(y);
int ans2=getsum(x-1);
cout<<ans1-ans2<<endl;
}
}
}
}

2.改段求段模型

题目：POJ 3468 A Simple Problem with Integers

#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
const int MAXL=100000;
typedef long long int LL;
LL b[MAXL+50],c[MAXL+50];
LL sum[MAXL+50];
int a[MAXL+50];
int n,m;
int lowbit(int k)
{
return k&-k;
}
void update(LL a[],int i,int value)
{
while(i<=n)
{
a[i]+=value;
i+=lowbit(i);
}
}

LL getsum(LL a[],int i)
{
LL ans=0;
while(i>0)
{
ans+=a[i];
i-=lowbit(i);
}
return ans;
}
int main()
{
memset(b,0,sizeof(b));
memset(c,0,sizeof(c));
memset(sum,0,sizeof(sum));
scanf("%d%d",&n,&m);
for(int i=1; i<=n; i++)
scanf("%d",a+i);
for(int i=0;i<=n;i++)
sum[i]=sum[i-1]+a[i];
int x,y,value;
char ch;
int T=m;
while(T--)
{
getchar();
scanf("%c",&ch);
if(ch=='C')
{
scanf("%d%d%d",&x,&y,&value);
update(b,x,value);
update(b,y+1,-value);
update(c,x,value*x);
update(c,y+1,-value*(y+1));
}
else if(ch=='Q')
{
scanf("%d%d",&x,&y);
LL ans=0;
ans=sum[y]-sum[x-1];
ans+=(y+1)*getsum(b,y)-getsum(c,y);
ans-=(x*getsum(b,x-1))-getsum(c,x-1);
cout<<ans<<endl;
}

}
}

3.改点求区间最大值

题目：HDU 1754 I Hate It

#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
const int MAXL(200000);
int tree[MAXL+50];
int a[MAXL+50];
int n,m;
int max(int a,int b)
{
return a>b?a:b;
}
int lowbit(int k)
{
return k&(-k);
}
void init()
{
for(int i=1; i<=n; i++)
{
tree[i]=a[i];
for(int j=1; j<lowbit(i); j<<=1)
tree[i]=max(tree[i],tree[i-j]);
}
}
void Update(int x)
{
for(int i=x; i<=n; i+=lowbit(i))
{
tree[i]=a[i];
for(int j=1; j<lowbit(i); j<<=1)
tree[i]=max(tree[i],tree[i-j]);
}
}
int Query(int x,int y)
{
int ans=0;
while(x<=y)
{
ans=max(a[y],ans);
for(y--; y-lowbit(y)>=x; y-=lowbit(y))
ans=max(tree[y],ans);
}
return ans;
}
int main()
{
while(~scanf("%d%d",&n,&m))
{
for(int i=1; i<=n; i++)
scanf("%d",a+i);
init();
char ch;
int x,y;
int T=m;
while(T--)
{
scanf("%c",&ch);
if(ch=='U')
{
scanf("%d%d",&x,&y);
a[x]=y;
Update(x);
}
if(ch=='Q')
{
scanf("%d%d",&x,&y);
int ans=Query(x,y);
printf("%d\n",ans);
}
}
}
}