一维树状数组入门

个人觉得非常棒的博客：https://www.cnblogs.com/xenny/p/9739600.html

第一类：单点更新，区间查询

　　　　例题：http://acm.hdu.edu.cn/showproblem.php?pid=1166

　　　　　AC代码：

/* */
# include <iostream>
# include <cstdio>
# include <cstring>
# include <string>
# include <cstdlib>
# include <queue>
# include <stack>
# include <vector>
# include <map>
# include <set>
# include <cmath>
# include <bitset>
# include <functional>
using namespace std;

int n, m;
int a[50005], c[50005];///对应原数组和树状数组
int lowbit(int x)
{
    return x&(-x);///当x为0时结果为0,当x为奇数时,结果为1;
    ///当x为偶数时,结果为x中2的最大次方的因子
    ///2^k=i&(-i)
}

void updata(int i, int k)///在第i个位置上加上k
{
    while( i<=n )///a[i]包含于c[i+2^k], c[i+2^k+2^k], c[i+2^k+2^k+2^k], ,,,
    {
        c[i] += k;
        i += lowbit(i);
    }
}

int getsum(int i)
{
    int res=0;
    while( i>0 )
    {
        res += c[i];
        i -= lowbit(i);
    }
    return res;
}

int main()
{
    int t;
    cin>>t;
    for(int tot=1; tot<=t; tot++ )
    {
        cout<<"Case "<<tot<<":"<<endl;
        memset(a, 0, sizeof(a));
        memset(c, 0, sizeof(c));
        cin>>n;
        for(int i=1; i<=n; i++ )
        {
            cin>>a[i];
            updata(i, a[i]);
        }

        string s;
        int x, y;
        while( cin>>s && s[0]!='E' )
        {
            cin>>x>>y;
            if( s[0]=='Q')
            {
                int sum=getsum(y)-getsum(x-1);
                cout<<sum<<endl;
            }
            else if( s[0]=='A' )
            {
                updata(x, y);
            }
            else if( s[0]=='S' )
            {
                updata(x, -y);
            }
        }
    }
    return 0;
}

第二类：区间修改，单点查询

　　　　例题：http://acm.hdu.edu.cn/showproblem.php?pid=1556

　　　　AC代码：

/* 一位数状数组：区间修改,单点查询 */
# include <iostream>
# include <stdio.h>
# include <string.h>
# include <string>
# include <algorithm>
# include <cmath>
# include <cstdlib>
# include <cctype>
# include <deque>
# include <climits>
# include <queue>
# include <stack>
# include <set>
# include <bitset>
# include <list>
# include <map>
using namespace std;

# define LL long long
# define lowbit(x)(x&(-x))
# define gcd(a, b) __gcd(a, b)
# define INF 0x3f3f3f3f
# define N 100010

int c[N];///树状数组不一定是求和

void updata(int x, int val)
{
    while( x<=N )
    {
        c[x] += val;
        x += lowbit(x);
    }
}

int getsum(int x)
{
    int res=0;
    while( x>0 )
    {
        res += c[x];
        x -= lowbit(x);
    }
    return res;
}

int main()
{
    int n, x, y, i;
    while( ~ scanf("%d", &n) && n )
    {
        memset(c, 0, sizeof(c));
        for(i=0; i<n; i++ )
        {
            scanf("%d %d", &x, &y);
            updata(x, 1);
            updata(y+1, -1);
        }

        for(i=1; i<=n-1; i++ )
            printf("%d ", getsum(i));
        printf("%d
", getsum(n));
    }
    return 0;
}

第三类：区间修改，区间查询

　　　　例题：http://poj.org/problem?id=3468

　　　　　AC代码：

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
typedef long long ll;
const int maxn=100010;
ll sum1[maxn];
ll sum2[maxn];
ll a[maxn];
int n,m;
int lowbit(int i){
    return i&(-i);
}

void updata(int i,ll k){
    int x=i;
    while(i<=n){
        sum1[i]+=k;
        sum2[i]+=k*(x-1);
        i+=lowbit(i);
    }
}

ll getsum(int i){
    ll res=0;
    int x=i;
    while(i>0){
        res+=x*sum1[i]-sum2[i];
        i-=lowbit(i);
    }
    return res;
}

int main()
{
    while(~scanf("%d%d",&n,&m)){
        memset(sum1,0,sizeof(sum1));
        memset(sum2,0,sizeof(sum2));
        for(int i=1;i<=n;i++){
            scanf("%lld",&a[i]);
            updata(i,a[i]-a[i-1]);
        }
        char s[10];
        while( m-- ){
            scanf("%s",s);
            if( s[0]=='C'){
                int x,y,c;
                scanf("%d%d%d",&x,&y,&c);
                updata(x,c);
                updata(y+1,-c);
            }
            else{
                int x,y;
                scanf("%d%d",&x,&y);
                ll sum=getsum(y)-getsum(x-1);
                cout<<sum<<endl;
            }
        }
    }
    return 0;
}