【模板】树状数组

【LG3374】已知一个数列，你需要进行下面两种操作：
1.将某一个数加上x
2.求出某区间每一个数的和

#include<bits/stdc++.h>

using namespace std;

const int N = 500010;

int n, m;
int c[N];

int lowbit(int x){ return x & -x; }

void add(int x, int y){
    while(x <= n){
        c[x] += y;
        x += lowbit(x);
    }
}

int query(int x){
    int sum = 0;
    while(x){
        sum += c[x];
        x -= lowbit(x);
    }
    return sum;
}

int main(){
    scanf("%d%d", &n, &m);
    for(int i = 1; i <= n; i++){
        int x;
        scanf("%d", &x);
        add(i, x);
    }

    for(int i = 1; i <= m; i++){
        int x, y, z;
        scanf("%d%d%d", &z, &x, &y);
        if(z == 1){
            add(x, y);
        }
        else{
            printf("%d\n", query(y)-query(x-1));
        }
    }
    
    return 0;
}

【LG3368】已知一个数列，你需要进行下面两种操作：
1.将某区间每一个数数加上x
2.求出某一个数的和

#include<bits/stdc++.h>

using namespace std;

const int N = 500010;

int n, m, last;
int c[N];

int lowbit(int x){ return x & -x; }

void add(int x, int y){
    while(x <= n){
        c[x] += y;
        x += lowbit(x);
    }
}

int query(int x){
    int sum = 0;
    while(x){
        sum += c[x];
        x -= lowbit(x);
    }
    return sum;
}

int main(){
    scanf("%d%d", &n, &m);
    for(int i = 1; i <= n; i++){
        int x;
        scanf("%d", &x);
        add(i, x-last);
        last = x;
    }

    for(int i = 1; i <= m; i++){
        int x, y, z, k;
        scanf("%d", &z);
        if(z == 1){
            scanf("%d%d%d", &x, &y, &k);
            add(x, k);
            add(y+1, -k);
        }
        else{
            scanf("%d", &x);
            printf("%d\n", query(x));
        }
    }
    
    return 0;
}

【POJ2155】二维树状数组（本质：区间修改+单点查询）
输入：'C', x1, y1, x2, y2 将子矩阵(x1, y1)-(x2, y2)全部取反
输出：'Q', x1, y1 查询单点(x1, y1)

只有0和1两个状态，所以和一维一样的思路，但可以不用-1，这里+1-1不改变奇偶性，结果&1即可。（当然你-1也不是问题）

#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<algorithm>
#include<iostream>

using namespace std;

const int N = 1010;

int t, n, m;
int c[N][N];

template <typename T>
T read(){
	T N(0), F(1);
	char C = getchar();
	for(; !isdigit(C); C = getchar()) if(C == '-') F = -1;
	for(; isdigit(C); C = getchar()) N = N*10 + C-48;
	return N*F;
}

int lowbit(int x){
	return x & -x;
}

void modify(int x, int y, int add){
	int tmp = y;
	while(x <= n){
		y = tmp;
		while(y <= n){
			c[x][y] += add;
			y += lowbit(y);
		}
		x += lowbit(x);
	}
}

int query(int x, int y){
	int tmp = y, ans = 0;
	while(x){
		y = tmp;
		while(y){
			ans += c[x][y];
			y -= lowbit(y);
		}
		x -= lowbit(x);
	}
	return ans;
}

int main(){
	freopen("matrix.in", "r", stdin);
	freopen("matrix.out","w",stdout);

	int x1, y1, x2, y2;

	t = read<int>();
	while(t--){
		memset(c, 0, sizeof(c));

		n = read<int>(); m = read<int>();
		
		char cs;

		for(int i = 1; i <= m; i++){
			scanf("%c", &cs);
			if(cs == 'C'){
				x1 = read<int>(); y1 = read<int>(); x2 = read<int>(); y2 = read<int>();
				modify(x1, y1, 1);
				modify(x1, y2+1, 1);
				modify(x2+1, y1, 1);
				modify(x2+1, y2+1, 1);
			}
			else{
				x1 = read<int>(); y1 = read<int>();
				printf("%d\n", query(x1, y1)&1);
			}
		}
		printf("\n");
	}

	return 0;
}