From 3ab0aac2778daed84fb97fa4f5e4db48bf513654 Mon Sep 17 00:00:00 2001 From: Baoshuo Date: Mon, 9 Jan 2023 08:03:43 +0800 Subject: [PATCH] =?UTF-8?q?P6242=20=E3=80=90=E6=A8=A1=E6=9D=BF=E3=80=91?= =?UTF-8?q?=E7=BA=BF=E6=AE=B5=E6=A0=91=203?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit https://www.luogu.com.cn/record/99085281 --- Luogu/P6242/P6242.cpp | 294 +++++++++++++++++++++++++++++++++++ Luogu/P6242/data/P6242_1.in | 3 + Luogu/P6242/data/P6242_1.out | 3 + Luogu/P6242/data/P6242_2.in | 3 + Luogu/P6242/data/P6242_2.out | 3 + 5 files changed, 306 insertions(+) create mode 100644 Luogu/P6242/P6242.cpp create mode 100644 Luogu/P6242/data/P6242_1.in create mode 100644 Luogu/P6242/data/P6242_1.out create mode 100644 Luogu/P6242/data/P6242_2.in create mode 100644 Luogu/P6242/data/P6242_2.out diff --git a/Luogu/P6242/P6242.cpp b/Luogu/P6242/P6242.cpp new file mode 100644 index 00000000..c901e4df --- /dev/null +++ b/Luogu/P6242/P6242.cpp @@ -0,0 +1,294 @@ +#include +#include + +using std::cin; +using std::cout; +const char endl = '\n'; + +const int N = 5e5 + 5; +const int INF = 0x3f3f3f3f; + +int n, m, a[N]; + +struct node { + int l, r; // 左右端点 + + int tag_add; // 懒标记：加减标记（最大值无关） + int tag_his_add; // 懒标记：历史最大的加减标记（最大值无关） + int tag_add_max; // 懒标记：最大值的加减标记 + int tag_his_add_max; // 懒标记：历史最大的最大值的加减标记 + + long long sum; // 区间和 + int max; // 区间最大值 + int max_2nd; // 区间严格次大值 + int his_max; // 历史区间最大值 + int max_cnt; // 区间最大值个数 + + node(const int &_l = 0, const int &_r = 0) + : l(_l), + r(_r), + tag_add(0), + tag_his_add(0), + tag_add_max(0), + tag_his_add_max(0), + sum(0), + max(0), + max_2nd(-INF), // -INF 表示不存在 + his_max(0), + max_cnt(1) {} +} tr[N << 2]; + +void pushup(int u) { + auto &p = tr[u], + &l = tr[u << 1], + &r = tr[u << 1 | 1]; + + p.sum = l.sum + r.sum; + p.his_max = std::max(l.his_max, r.his_max); + + if (l.max == r.max) { + p.max = l.max; + p.max_2nd = std::max(l.max_2nd, r.max_2nd); + p.max_cnt = l.max_cnt + r.max_cnt; + } else if (l.max > r.max) { + p.max = l.max; + p.max_2nd = std::max(l.max_2nd, r.max); + p.max_cnt = l.max_cnt; + } else { // l.max < r.max + p.max = r.max; + p.max_2nd = std::max(l.max, r.max_2nd); + p.max_cnt = r.max_cnt; + } +} + +void pushdown(int u) { + auto &p = tr[u]; + + std::function update = [&](node &ch) -> void { + ch.sum += static_cast(ch.r - ch.l + 1) * p.tag_add; + + ch.his_max = std::max(ch.his_max, ch.max + p.tag_his_add); + ch.max += p.tag_add; + + if (ch.max_2nd != -INF) ch.max_2nd += p.tag_add; + + ch.tag_his_add = std::max(ch.tag_his_add, ch.tag_add + p.tag_his_add); + ch.tag_add += p.tag_add; + + ch.tag_his_add_max = std::max(ch.tag_his_add_max, ch.tag_add_max + p.tag_his_add); + ch.tag_add_max += p.tag_add; + }; + + std::function update_with_max = [&](node &ch) -> void { + // 最大值相关部分 + ch.sum += static_cast(ch.max_cnt) * p.tag_add_max; + + ch.his_max = std::max(ch.his_max, ch.max + p.tag_his_add_max); + ch.max += p.tag_add_max; + + ch.tag_his_add_max = std::max(ch.tag_his_add_max, ch.tag_add_max + p.tag_his_add_max); + ch.tag_add_max += p.tag_add_max; + + // 最大值无关部分 + ch.sum += static_cast(ch.r - ch.l + 1 - ch.max_cnt) * p.tag_add; + + ch.tag_his_add = std::max(ch.tag_his_add, ch.tag_add + p.tag_his_add); + ch.tag_add += p.tag_add; + + if (ch.max_2nd != -INF) ch.max_2nd += p.tag_add; + }; + + if (tr[u << 1].max == tr[u << 1 | 1].max) { + update_with_max(tr[u << 1]); // 左子树：最大值相关 + update_with_max(tr[u << 1 | 1]); // 右子树：最大值相关 + } else if (tr[u << 1].max > tr[u << 1 | 1].max) { + update_with_max(tr[u << 1]); // 左子树：最大值相关 + update(tr[u << 1 | 1]); // 右子树：最大值无关 + } else { + update(tr[u << 1]); // 左子树：最大值无关 + update_with_max(tr[u << 1 | 1]); // 右子树：最大值相关 + } + + p.tag_add = p.tag_add_max = p.tag_his_add = p.tag_his_add_max = 0; +} + +void build(int u, int l, int r) { + tr[u] = node(l, r); + + if (l == r) { + tr[u].sum = tr[u].max = tr[u].his_max = a[l]; + + return; + } + + int mid = (l + r) >> 1; + + build(u << 1, l, mid); + build(u << 1 | 1, mid + 1, r); + + pushup(u); +} + +/** + * 对于所有的 i ∈ [l, r]，将 a[i] 加上 k + */ +void modify_add(int u, int l, int r, int k) { + if (l <= tr[u].l && tr[u].r <= r) { + tr[u].sum += static_cast(k) * (tr[u].r - tr[u].l + 1); + + tr[u].max += k; + tr[u].his_max = std::max(tr[u].his_max, tr[u].max); + if (tr[u].max_2nd != -INF) tr[u].max_2nd += k; + + tr[u].tag_add += k; + tr[u].tag_his_add = std::max(tr[u].tag_his_add, tr[u].tag_add); + + tr[u].tag_add_max += k; + tr[u].tag_his_add_max = std::max(tr[u].tag_his_add_max, tr[u].tag_add_max); + + return; + } + + int mid = (tr[u].l + tr[u].r) >> 1; + + pushdown(u); + + if (l <= mid) modify_add(u << 1, l, r, k); + if (r > mid) modify_add(u << 1 | 1, l, r, k); + + pushup(u); +} + +/** + * 对于所有的 i ∈ [l, r]，将 a[i] 变为 min(a[i], v) + */ +void modify_min(int u, int l, int r, int v) { + if (tr[u].max <= v) return; + + if (l <= tr[u].l && tr[u].r <= r && tr[u].max_2nd < v) { + int t = v - tr[u].max; + + tr[u].sum += static_cast(t) * tr[u].max_cnt; + + tr[u].max += t; + tr[u].his_max = std::max(tr[u].his_max, tr[u].max); + + tr[u].tag_add_max += t; + tr[u].tag_his_add_max = std::max(tr[u].tag_his_add_max, tr[u].tag_add_max); + + return; + } + + int mid = (tr[u].l + tr[u].r) >> 1; + + pushdown(u); + + if (l <= mid) modify_min(u << 1, l, r, v); + if (r > mid) modify_min(u << 1 | 1, l, r, v); + + pushup(u); +} + +/** + * 求满足 i ∈ [l, r] 的所有 a[i] 的和 + */ +long long query_sum(int u, int l, int r) { + if (l <= tr[u].l && tr[u].r <= r) return tr[u].sum; + + int mid = (tr[u].l + tr[u].r) >> 1; + long long res = 0; + + pushdown(u); + + if (l <= mid) res += query_sum(u << 1, l, r); + if (r > mid) res += query_sum(u << 1 | 1, l, r); + + return res; +} + +/** + * 求满足 i ∈ [l, r] 的所有 a[i] 的最大值 + */ +int query_max(int u, int l, int r) { + if (l <= tr[u].l && tr[u].r <= r) return tr[u].max; + + int mid = (tr[u].l + tr[u].r) >> 1; + int res = -INF; + + pushdown(u); + + if (l <= mid) res = std::max(res, query_max(u << 1, l, r)); + if (r > mid) res = std::max(res, query_max(u << 1 | 1, l, r)); + + return res; +} + +/** + * 求满足 i ∈ [l, r] 的所有 a[i] 的历史最大值 + */ +int query_his_max(int u, int l, int r) { + if (l <= tr[u].l && tr[u].r <= r) return tr[u].his_max; + + int mid = (tr[u].l + tr[u].r) >> 1; + int res = -INF; + + pushdown(u); + + if (l <= mid) res = std::max(res, query_his_max(u << 1, l, r)); + if (r > mid) res = std::max(res, query_his_max(u << 1 | 1, l, r)); + + return res; +} + +int main() { + std::ios::sync_with_stdio(false); + cin.tie(nullptr); + + cin >> n >> m; + + for (int i = 1; i <= n; i++) { + cin >> a[i]; + } + + build(1, 1, n); + + while (m--) { + int op; + + cin >> op; + + if (op == 1) { + int l, r, k; + + cin >> l >> r >> k; + + modify_add(1, l, r, k); + } else if (op == 2) { + int l, r, v; + + cin >> l >> r >> v; + + modify_min(1, l, r, v); + } else if (op == 3) { + int l, r; + + cin >> l >> r; + + cout << query_sum(1, l, r) << endl; + } else if (op == 4) { + int l, r; + + cin >> l >> r; + + cout << query_max(1, l, r) << endl; + } else { // op == 5 + int l, r; + + cin >> l >> r; + + cout << query_his_max(1, l, r) << endl; + } + } + + return 0; +} diff --git a/Luogu/P6242/data/P6242_1.in b/Luogu/P6242/data/P6242_1.in new file mode 100644 index 00000000..32b6669c --- /dev/null +++ b/Luogu/P6242/data/P6242_1.in @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:aba002b19055e2e8125362b77860787acc4b8f9b728ce33628d0529f2e397a22 +size 541 diff --git a/Luogu/P6242/data/P6242_1.out b/Luogu/P6242/data/P6242_1.out new file mode 100644 index 00000000..36b14350 --- /dev/null +++ b/Luogu/P6242/data/P6242_1.out @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:5fc80cd85ebe69204636a73dadfc620257fc4a97f3e589707c06d107dc21f266 +size 143 diff --git a/Luogu/P6242/data/P6242_2.in b/Luogu/P6242/data/P6242_2.in new file mode 100644 index 00000000..d01a5253 --- /dev/null +++ b/Luogu/P6242/data/P6242_2.in @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:139063d2c43057e2b91174e8a0a6a632499fa78f7b684b091d38f9129b7b487f +size 123890 diff --git a/Luogu/P6242/data/P6242_2.out b/Luogu/P6242/data/P6242_2.out new file mode 100644 index 00000000..3c08f219 --- /dev/null +++ b/Luogu/P6242/data/P6242_2.out @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:0aa88eda398a4ebe8ad828341a00397085f8fca81b88b9bdb4c17330fa1e7a62 +size 36796