[笔记]线段树 | 树状数组

线段树

最Simple的区间加码风样式模板

struct Segment_Tree {
	#define ls (p << 1)
	#define rs (p << 1 | 1)
	#define mid ((l + r) >> 1)
    ll ans[_ << 2], tag[_ << 2];
    inline void pushup(ll p) { ans[p] = ans[ls] + ans[rs]; }
    inline void pushdown(ll p, ll l, ll r) {
        ans[ls] += (mid - l + 1) * tag[p];
        tag[ls] += tag[p];
        ans[rs] += (r - mid) * tag[p];
        tag[rs] += tag[p];
        tag[p] = 0;
    }
    void build(ll p, ll l, ll r) {
        if(l == r) {
			ans[p] = a[l];
			return;
		}
        build(ls, l, mid);
        build(rs, mid + 1, r);
        pushup(p);
    }
    void update(ll p, ll l, ll r, ll ul, ll ur, ll k) {
        if(ul <= l && r <= ur) {
            ans[p] += (r - l + 1) * k;
            tag[p] += k;
            return;
        }
        if(tag[p]) pushdown(p, l, r);
        if(ul <= mid) update(ls, l, mid, ul, ur, k);
        if(ur > mid) update(rs, mid + 1, r, ul, ur, k);
        pushup(p);
    }
    ll query(ll p, ll l, ll r, ll ql, ll qr) {
        if(ql <= l && r <= qr) return ans[p];
        if(tag[p]) pushdown(p, l, r);
        ll res = 0;
        if(ql <= mid) res += query(ls, l, mid, ql, qr);
        if(qr > mid) res += query(rs, mid + 1, r, ql, qr);
        return res;
    }
    #undef ls
	#undef rs
	#undef mid
}T;

Problem

Tag的用法

区间01取反xor
区间翻转rev
区间最长连续1/0
区间min/max子段和
P2572 [SCOI2010]序列操作

扫描线

矩形面积并
P1502 窗口的星星
P1856 [USACO5.5]矩形周长Picture

二维线段树

树套树
P3437 [POI2006]TET-Tetris 3D