這裡只有模板，並不作講解，僅為路過的各位做一個參考以及用做自己複習的資料，轉載註明出處。

樹狀陣列（B.I.T）

單點修改區間查詢

/*Copyright: Copyright (c) 2018
*Created on 2018-11-02  
*Author: 十甫
*Version 1.0 
*Title: BIT-1
*Time: 5 mins
*/
#include<cstdio>
#include<iostream>
#include<cstring>
using namespace std;
const int size = 10005;

inline int lowbit(int x) {
	return x & (-x);
}
int n, arr[size];
inline void add(int a[], int i, int k) {
	while(i <= n) {
		a[i] += k;
		i += lowbit(i);
	}
}
inline int query(int a[], int i) {
	int res = 0;
	while(i) {
		res += a[i];
		i -= lowbit(i);
	}
	return res;
}

int main() {
	scanf("%d", &n);
	for(int i = 1;i <= n;i++) {
		int k;
		scanf("%d", &k);
		add(arr, i, k);
	}
	int q;
	scanf("%d", &q);
	while(q--) {
		int man;
		scanf("%d", &man);
		if(man) {
			int i, k;
			scanf("%d%d", &i, &k);
			add(arr, i, k);
		} else {
			int l, r;
			scanf("%d%d", &l, &r);
			printf("%d\n", query(arr, r) - query(arr, l - 1));
		}
	}
	return 0;
}
 

區間修改單點查詢

/*Copyright: Copyright (c) 2018
*Created on 2018-11-02  
*Author: 十甫
*Version 1.0 
*Title: BIT-2
*Time: 4.5 mins
*/
#include<cstdio>
#include<iostream>
#include<cstring>
using namespace std;
const int size = 10005;

inline int lowbit(int x) {
	return x & (-x);
}
int n, arr[size];
inline void add(int a[], int i, int k) {
	while(i <= n) {
		a[i] += k;
		i += lowbit(i);
	}
}
inline int query(int a[], int i) {
	int res = 0;
	while(i) {
		res += a[i];
		i -= lowbit(i);
	}
	return res;
}

int main() {
	scanf("%d", &n);
	int last = 0;
	for(int i = 1;i <= n;i++) {
		int k;
		scanf("%d", &k);
		add(arr, i, k - last);
		last = k;
	}
	int q;
	scanf("%d", &q);
	while(q--) {
		int man;
		scanf("%d", &man);
		if(man) {
			int l, r, k;
			scanf("%d%d%d", &l, &r, &k);
			add(arr, l, k), add(arr, r + 1, -k);
		} else {
			int i;
			scanf("%d", &i);
			printf("%d\n", query(arr, i));
		}
	}
	return 0;
}
 

區間修改區間查詢

/*Copyright: Copyright (c) 2018
*Created on 2018-11-02  
*Author: 十甫
*Version 1.0 
*Title: BIT-3
*Time: 7 mins
*/
#include<cstdio>
#include<iostream>
#include<cstring>
using namespace std;
const int size = 10005;

inline int lowbit(int x) {
	return x & (-x);
}
int n, num[size], d1[size], d2[size];
inline void add(int a[], int i, int k) {
	while(i <= n) {
		a[i] += k;
		i += lowbit(i);
	}
}
inline int query(int a[], int i) {
	int res = 0;
	while(i) {
		res += a[i];
		i -= lowbit(i);
	}
	return res;
}
inline void modify(int l, int r, int k) {
	add(d1, l, k), add(d1, r + 1, -k);
	add(d2, l, l * k), add(d2, r + 1, -k * (r + 1));
}
inline int enquiry(int l, int r) {
	int res = 0;
	res += query(num, r) - query(num, l - 1);
	res += (r + 1) * query(d1, r) - l * query(d1, l - 1);
	res -= query(d2, r) - query(d2, l - 1);
	return res;
}
int main() {
	scanf("%d", &n);
	for(int i = 1;i <= n;i++) {
		int k;
		scanf("%d", &k);
		add(num, i, k);
	}
	int q;
	scanf("%d", &q);
	while(q--) {
		int man;
		scanf("%d", &man);
		if(man) {
			int l, r, k;
			scanf("%d%d%d", &l, &r, &k);
			modify(l, r, k);
		} else {
			int l, r;
			scanf("%d%d", &l, &r);
			printf("%d\n", enquiry(l, r));
		}
	}
	return 0;
}