线段树模板

向上回溯

void pushup(int rt){
	t[rt].sum = t[lc].sum + t[rc].sum;
	t[rt].mx = max(t[lc].mx, t[rc].mx);
} 

建树

void build(int rt, int l, int r){
	t[rt].l = l;
	t[rt].r = r;
	if(l == r){
		t[rt].mx = t[rt].sum = a[l];
		return;
	}
	int mid = (l + r) >> 1;
	build(lc, l, mid);
	build(rc, mid+1, r);
	
	pushup(rt);
}

单点更新

void update(int rt, int pos, int w){
	if(t[rt].l == t[rt].r){
		t[rt].mx = t[rt].sum = w;
		return;
	}
	int mid = (t[rt].l + t[rt].r) >> 1;
	if(pos <= mid) update(lc, pos, w);
	else update(rc, pos, w);
	
	pushup(rt);
}

区间查询

int query(int rt, int l, int r){
   if(l <= t[rt].l and t[rt].r <= r){
	   return t[rt].sum;
   }
   int mid = (t[rt].l + t[rt].r) >> 1;
   int val = 0;
   if(l <= mid) val += query(lc, l, r);
   if(r > mid) val += query(rc, l, r);
	
   return val;
}

延迟标记

void pushdown(int rt){
	if(t[rt].lz){
		int la = t[rt].lz;
		t[rt].lz = 0;
		t[lc].lz += la;
		t[rc].lz += la;
		t[lc].sum += la * (t[lc].r - t[lc].l + 1);
		t[rc].sum += la * (t[rc].r - t[rc].l + 1);
	}
}

区间更新

void update(int rt, int l, int r, int w){
	if(l <= t[rt].l and t[rt].r <= r){
		t[rt].lz += w;
		t[rt].sum += w * (t[rt].r - t[rt].l + 1);
		return;
	}
	pushdown(rt);
	int mid = (t[rt].l + t[rt].r) >> 1;
	if(l <= mid) update(lc, l, r, w);
	if(r >= mid) update(rc, l, r, w);
	
	pushup(rt);
}

带延迟标记区间查询

int query(int rt, int l, int r){
	if(l <=  t[rt].l and t[rt].r <= r){
		return t[rt].sum;
	}
	pushdown(rt);
	int mid = (t[rt].l + t[rt].r) >> 1;
	int val = 0;
	if(l <= mid) val += query(lc, l, r);
	if(r > mid) val += query(rc, l, r);
	
	return val;
}