【数据结构】线段树-区间更新最值

仔细想想这个并不是什么正常的线段树，因为它除了PushDow有一部分信息是从上往下传递的。

http://acm.hdu.edu.cn/showproblem.php?pid=5306

1.区间更新min
2.区间查询max
3.区间查询sum

struct SegmentTreeBeats {

#define ls (u << 1)
#define rs (u << 1 | 1)
#define mid ((l + r) >> 1)

    static const int MAXN = 2e5 + 10;
    static const int INF = 0x3f3f3f3f;

    int tmi[MAXN << 2];

    ll sum[MAXN << 2];
    int mx1[MAXN << 2], cmx[MAXN << 2], mx2[MAXN << 2];

    void PushUp(int u) {
        sum[u] = sum[ls] + sum[rs];
        if(mx1[ls] < mx1[rs]) {
            mx1[u] = mx1[rs], cmx[u] = cmx[rs];
            mx2[u] = max(mx1[ls], mx2[rs]);
        } else if (mx1[ls] > mx1[rs]) {
            mx1[u] = mx1[ls], cmx[u] = cmx[ls];
            mx2[u] = max(mx2[ls], mx1[rs]);
        } else {
            mx1[u] = mx1[ls], cmx[u] = cmx[ls] + cmx[rs];
            mx2[u] = max(mx2[ls], mx2[rs]);
        }
    }

    void PushTagMin(int u, int t) {
        if(mx1[u] <= t)
            return;
        sum[u] += 1LL * (t - mx1[u]) * cmx[u];
        mx1[u] = tmi[u] = t;
    }

    void PushDown(int u, int l, int r) {
        int t = tmi[u];
        if(t != INF) {
            PushTagMin(ls, t);
            PushTagMin(rs, t);
            tmi[u] = INF;
        }
    }

    void Build(int u, int l, int r) {
        tmi[u] = INF;
        if(l == r) {
            sum[u] = mx1[u] = a[l];
            cmx[u] = 1, mx2[u] = -INF;
            return;
        }
        Build(ls, l, mid);
        Build(rs, mid + 1, r);
        PushUp(u);
    }

    void UpdateMin(int u, int l, int r, int L, int R, int v) {
        if(mx1[u] <= v)
            return;
        if(L <= l && r <= R && mx2[u] < v) {
            PushTagMin(u, v);
            return;
        }
        PushDown(u, l, r);
        if(L <= mid) UpdateMin(ls, l, mid, L, R, v);
        if(R >= mid + 1) UpdateMin(rs, mid + 1, r, L, R, v);
        PushUp(u);
    }

    ll QuerySum(int u, int l, int r, int L, int R) {
        if (L <= l && r <= R)
            return sum[u];
        PushDown(u, l, r);
        ll res = 0;
        if(L <= mid) res += QuerySum(ls, l, mid, L, R);
        if(R >= mid + 1) res += QuerySum(rs, mid + 1, r, L, R);
        return res;
    }

    int QueryMax(int u, int l, int r, int L, int R) {
        if(L <= l && r <= R)
            return mx1[u];
        PushDown(u, l, r);
        int res = -INF;
        if(L <= mid) res = max(res, QueryMax(ls, l, mid, L, R));
        if(R >= mid + 1) res = max(res, QueryMax(rs, mid + 1, r, L, R));
        return res;
    }

#undef ls
#undef rs
#undef mid

} stb;

用势能分析法可以得到m次操作总共是 \(O(m\log n)\) ？吉老师似乎说这个有问题，但是构造不出卡掉他的数据。

混合标记：
1.区间加法
2.区间取min
3.区间取max
4.区间查询sum
5.区间查询min
6.区间查询max

没有在OJ上面验证过哦，只能和另一个暴力程序对拍了。

struct SegmentTreeBeats {

#define ls (u << 1)
#define rs (u << 1 | 1)
#define mid ((l + r) >> 1)

    static const int MAXN = 2e5 + 10;
    static const int INF = 0x3f3f3f3f;

    int tad[MAXN << 2], tmi[MAXN << 2], tmx[MAXN << 2];

    ll sum[MAXN << 2];
    int mi1[MAXN << 2], cmi[MAXN << 2], mi2[MAXN << 2];
    int mx1[MAXN << 2], cmx[MAXN << 2], mx2[MAXN << 2];

    void PushUp(int u) {
        sum[u] = sum[ls] + sum[rs];
        if(mi1[ls] < mi1[rs]) {
            mi1[u] = mi1[ls], cmi[u] = cmi[ls];
            mi2[u] = min(mi2[ls], mi1[rs]);
        } else if(mi1[ls] > mi1[rs]) {
            mi1[u] = mi1[rs], cmi[u] = cmi[rs];
            mi2[u] = min(mi1[ls], mi2[rs]);
        }  else {
            mi1[u] = mi1[ls], cmi[u] = cmi[ls] + cmi[rs];
            mi2[u] = min(mi2[ls], mi2[rs]);
        }
        if(mx1[ls] < mx1[rs]) {
            mx1[u] = mx1[rs], cmx[u] = cmx[rs];
            mx2[u] = max(mx1[ls], mx2[rs]);
        } else if (mx1[ls] > mx1[rs]) {
            mx1[u] = mx1[ls], cmx[u] = cmx[ls];
            mx2[u] = max(mx2[ls], mx1[rs]);
        } else {
            mx1[u] = mx1[ls], cmx[u] = cmx[ls] + cmx[rs];
            mx2[u] = max(mx2[ls], mx2[rs]);
        }
    }

    void PushTagAdd(int u, int l, int r, int t) {
        sum[u] += 1LL * (r - l + 1) * t;
        tad[u] += t, mi1[u] += t, mx1[u] += t;
        if(mi2[u] != INF) mi2[u] += t;
        if(tmi[u] != INF) tmi[u] += t;
        if(mx2[u] != -INF) mx2[u] += t;
        if(tmx[u] != -INF) tmx[u] += t;
    }

    void PushTagMin(int u, int t) {
        if(mx1[u] <= t)
            return;
        sum[u] += 1LL * (t - mx1[u]) * cmx[u];
        if(mi1[u] == mx1[u]) mi1[u] = t;
        if(mi2[u] == mx1[u]) mi2[u] = t;
        if(tmx[u] > t) tmx[u] = t;
        mx1[u] = tmi[u] = t;
    }

    void PushTagMax(int u, int t) {
        if(mi1[u] >= t)
            return;
        sum[u] += 1LL * (t - mi1[u]) * cmi[u];
        if(mx1[u] == mi1[u]) mx1[u] = t;
        if(mx2[u] == mi1[u]) mx2[u] = t;
        if(tmi[u] < t) tmi[u] = t;
        mi1[u] = tmx[u] = t;
    }

    void PushDown(int u, int l, int r) {
        int t = tad[u];
        if(t != 0) {
            PushTagAdd(ls, l, mid, t);
            PushTagAdd(rs, mid + 1, r, t);
            tad[u] = 0;
        }
        t = tmi[u];
        if(t != INF) {
            PushTagMin(ls, t);
            PushTagMin(rs, t);
            tmi[u] = INF;
        }
        t = tmx[u];
        if(t != -INF) {
            PushTagMax(ls, t);
            PushTagMax(rs, t);
            tmx[u] = -INF;
        }
    }

    void Build(int u, int l, int r) {
        tad[u] = 0, tmi[u] = INF, tmx[u] = -INF;
        if(l == r) {
            sum[u] = mi1[u] = mx1[u] = a[l];
            cmi[u] = 1, mi2[u] = INF;
            cmx[u] = 1, mx2[u] = -INF;
            return;
        }
        Build(ls, l, mid);
        Build(rs, mid + 1, r);
        PushUp(u);
    }

    void UpdateAdd(int u, int l, int r, int L, int R, int v) {
        if(L <= l && r <= R) {
            PushTagAdd(u, l, r, v);
            return;
        }
        PushDown(u, l, r);
        if(L <= mid) UpdateAdd(ls, l, mid, L, R, v);
        if(R >= mid + 1) UpdateAdd(rs, mid + 1, r, L, R, v);
        PushUp(u);
    }

    void UpdateMin(int u, int l, int r, int L, int R, int v) {
        if(mx1[u] <= v)
            return;
        if(L <= l && r <= R && mx2[u] < v) {
            PushTagMin(u, v);
            return;
        }
        PushDown(u, l, r);
        if(L <= mid) UpdateMin(ls, l, mid, L, R, v);
        if(R >= mid + 1) UpdateMin(rs, mid + 1, r, L, R, v);
        PushUp(u);
    }

    void UpdateMax(int u, int l, int r, int L, int R, int v) {
        if(mi1[u] >= v)
            return;
        if(L <= l && r <= R && mi2[u] > v) {
            PushTagMax(u, v);
            return;
        }
        PushDown(u, l, r);
        if(L <= mid) UpdateMax(ls, l, mid, L, R, v);
        if(R >= mid + 1) UpdateMax(rs, mid + 1, r, L, R, v);
        PushUp(u);
    }

    ll QuerySum(int u, int l, int r, int L, int R) {
        if (L <= l && r <= R)
            return sum[u];
        PushDown(u, l, r);
        ll res = 0;
        if(L <= mid) res += QuerySum(ls, l, mid, L, R);
        if(R >= mid + 1) res += QuerySum(rs, mid + 1, r, L, R);
        return res;
    }

    int QueryMin(int u, int l, int r, int L, int R) {
        if(L <= l && r <= R)
            return mi1[u];
        PushDown(u, l, r);
        int res = INF;
        if(L <= mid) res = min(res, QueryMin(ls, l, mid, L, R));
        if(R >= mid + 1) res = min(res, QueryMin(rs, mid + 1, r, L, R));
        return res;
    }

    int QueryMax(int u, int l, int r, int L, int R) {
        if(L <= l && r <= R)
            return mx1[u];
        PushDown(u, l, r);
        int res = -INF;
        if(L <= mid) res = max(res, QueryMax(ls, l, mid, L, R));
        if(R >= mid + 1) res = max(res, QueryMax(rs, mid + 1, r, L, R));
        return res;
    }

#undef ls
#undef rs
#undef mid

} stb;

吉老师说 \(O(m\log^2 n)\)。