树状数组

#include<iostream>
#include<cstring>
#include<cstdlib>
#include<algorithm>
#include<cctype>
#include<cmath>
#include<ctime>
#include<string>
#include<stack>
#include<deque>
#include<queue>
#include<list>
#include<set>
#include<map>
#include<cstdio>
#include<limits.h>
#define MOD 1000000007
#define fir first
#define sec second
#define fin freopen("/home/ostreambaba/文档/input.txt", "r", stdin)
#define fout freopen("/home/ostreambaba/文档/output.txt", "w", stdout)
#define mes(x, m) memset(x, m, sizeof(x))
#define Pii pair<int, int>
#define Pll pair<ll, ll>
#define INF 1e9+7
#define Pi 4.0*atan(1.0)

#define lowbit(x) (x&(-x))
#define lson l,m,rt<<1
#define rson m+1,r,rt<<1|1

#define scini(n) scanf("%d", &n)
#define scinii(n, m) scanf("%d%d", &n, &m)
#define scout(n) printf("%d\n", n);

typedef long long ll;
typedef unsigned long long ull;
const double eps = 1e-6;
const int maxn = 50010;
using namespace std;

int res[maxn];

void update(int i, int add)  //更新，将第i个增加add大小
{
    while(i <= N){
        res[i] += add;  //跟新与之相关的点
        i += lowbit(i);
    }
}
int sum(int n)  //区间求和，求n项和
{
    int ret = 0;
    while(n > 0){
        ret += res[n];
        n -= lowbit(n);
    }
}

int main()
{
  //  fin;
    int N;
    scini(N);
    mes(res, 0);
    int num;
    for(int i = 1; i <= N; ++i){
       scini(num);
       update(i, num);
    }
    int n;
    scini(n);
    int ret = sum(n);
    cout << ret << endl;
}

树状数组主要的三个部分(优雅美丽)
第一部分：

int lowbit(int n)
{
    return n&(-n); //或者 return n&(n^(n-1));
}
作用： lowbit(n)是为了求出2^x(x为n的二进制表示的最右边的1的位置)，例如3，二进制为11，最右边的1的位置为0，则lowbit(3)= 2^0 = 1; 
例如6，二进制为110，，最右边的1的位置为1， 则lowbit(6)= 2^1 = 2; 

第二部分：

void update(int i, int add)  //更新，将第i个增加add大小
{
    while(i <= N){
        res[i] += add;  //跟新与之相关的点
        i += lowbit(i);
    }
}

第三部分：

int sum(int n)  //区间求和，求n项和
{
    int ret = 0;
    while(n > 0){
        ret += res[n];
        n -= lowbit(n);
    }
}

题目：hdu1166 士兵杀敌
区间求和，单点更新

#include<iostream>
#include<cstring>
#include<cstdlib>
#include<algorithm>
#include<cctype>
#include<cmath>
#include<ctime>
#include<string>
#include<stack>
#include<deque>
#include<queue>
#include<list>
#include<set>
#include<map>
#include<cstdio>
#include<limits.h>
#define MOD 1000000007
#define fir first
#define sec second
#define fin freopen("/home/ostreambaba/文档/input.txt", "r", stdin)
#define fout freopen("/home/ostreambaba/文档/output.txt", "w", stdout)
#define mes(x, m) memset(x, m, sizeof(x))
#define Pii pair<int, int>
#define Pll pair<ll, ll>
#define INF 1e9+7
#define Pi 4.0*atan(1.0)

#define lowbit(x) (x&(-x))
#define lson l,m,rt<<1
#define rson m+1,r,rt<<1|1

#define scini(n) scanf("%d", &n)
#define scinii(n, m) scanf("%d%d", &n, &m)
#define scout(n) printf("%d\n", n);

typedef long long ll;
typedef unsigned long long ull;
const double eps = 1e-6;
const int maxn = 50010;
using namespace std;

int res[maxn];
int N;
void update(int i, int add)
{
    while(i <= N){
        res[i] += add;
        i += lowbit(i);
    }
}
int getSum(int n)
{
    int ret = 0;
    while(n > 0){
        ret += res[n];
        n -= lowbit(n);
    }
    return ret;
}

int main()
{
   // fin;
    int Case;
    scini(Case);
    for(int i = 1; i <= Case; ++i){
        printf("Case %d:\n", i);
        int num;
        mes(res, 0);
        scini(N);
        for(int i = 1; i <= N; ++i){
            scini(num);
            update(i, num);
        }
        string op;
        int l, r;
        cin >> op;
        while(op != "End"){
            scinii(l, r);
            if(op == "Query"){
                int Sum = getSum(r) - getSum(l-1);
                scout(Sum);
            }
            else if(op == "Add"){
                update(l, r);
            }
            else{
                update(l, -r);
            }
            cin >> op;
        }
    }
    return 0;
}