线段树 （维护区间和）模板

const int MAX_LEN = ;
int seg_tree[MAX_LEN << 2];
int Lazy[MAX_LEN << 2];
int arr[MAX_LEN];
//从下往上更新 节点 
void push_up (int root) {
	seg_tree[root] = seg_tree[root << 1] + seg_tree[root << 1 | 1]; 
} 
//从上向下更新，左右孩子 
void push_down (int root, int L, int R) {
	if(Lazy[root]){
		Lazy[root << 1] += Lazy [root];
		Lazy[root << 1 | 1] += Lazy[root];
		int mid = (L + R) >> 1;
		seg_tree[root << 1] +=  Lazy[root] * (mid - L + 1);
		seg_tree[root << 1 | 1] += Lazy[root] * (R - mid); 
		Lazy[root] = 0;
	}
}
//建树
void build (int root, int L, int R) {
	Lazy[root] = 0;
	if(L == R) {
		seg_tree[root] = arr[L];
		return ;
	}
	int mid = (L + R) >> 1;
	build(root << 1, L, mid);
	build(root << 1 | 1, mid + 1, R);
	push_up(root);
}
//区间查询
int query (int root, int L, int R, int LL, int RR) {
	if (LL <= L && R <= RR) return seg_tree[root];
	push_down(root, L, R); 	//每次访问都去检查Lazy 标记 
	int Ans = 0;
	int mid = (L + R) >> 1;
	if(LL <= mid) Ans += query(root << 1, L, mid, LL, RR);
	if(RR > mid) Ans += query(root << 1 | 1, mid + 1, R, LL, RR);
	return Ans;
}
//区间修改
void update_Interval(int root, int L, int R, int LL, int RR, int val){
	 if (LL <= L && R <= RR) {
	 	Lazy[root] += val;
	 	seg_tree[root] += val * (R - L + 1);
		return ; 
	 }
	 push_down(root, L, R);
	 int mid = (L + R) >> 1;
	 if (LL <= mid) update_Interval(root << 1, L, mid, LL, RR, val);
	 if (RR > mid) update_Interval(root << 1 | 1, mid + 1, R, LL , RR, val);
	 push_up(root); 
} 
//单点修改 
void update(int root, int L, int R, int pos, int val) {
	if(L == R){
		seg_tree[root] += val;
		return ;
	} 
	int mid = (L + R) >> 1;
	if(pos <= mid) update(root << 1, L, mid, pos, val);
	else update(root << 1 | 1, mid + 1, R, pos, val);
	push_up(root); 
}
 

区间直接变为某值：

void push_down (int root, int L, int R) {
	if(Lazy[root]){
		Lazy[root << 1] = Lazy [root];
		Lazy[root << 1 | 1] = Lazy[root];
		int mid = (L + R) >> 1;
		seg_tree[root << 1] =  Lazy[root] * (mid - L + 1);
		seg_tree[root << 1 | 1] = Lazy[root] * (R - mid); 
		Lazy[root] = 0;
	}
}
void update_Interval(int root, int L, int R, int LL, int RR, int val){
	 if (LL <= L && R <= RR) {
	 	Lazy[root] = val;
	 	seg_tree[root] = val * (R - L + 1);
		return ; 
	 }
	 push_down(root, L, R);
	 int mid = (L + R) >> 1;
	 if (LL <= mid) update_Interval(root << 1, L, mid, LL, RR, val);
	 if (RR > mid) update_Interval(root << 1 | 1, mid + 1, R, LL , RR, val);
	 push_up(root); 
} 

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