JOISC 2020 补题记录

Day 1 和 Day 4 鸽了，Day 2 和 Day 3 打得像 ** 一样。

Day 2 T3 简单数数题拿到手就化了一堆奇怪的充要条件结果就只能 $\O(n^4)$ dp 了，优化了很久（以为我的充要条件很靠谱），留了 20min rush 没写完，遗憾离场。Day 3 T2 4K- 的 DS 题调了一个小时还没调出来，遗憾离场。赛后 30min 才 AC

感觉这个 2020 年状态一直不太行……经常浮躁而无法静下来去分析一个问题试图突破……希望，能改改吧。感觉在理论状态下应该只有 D1T2 和 D4T2 两个题切不掉的……但实际去考有没有 175 + 200 + 205 + 200 都是个问题……

//先贴代码，题解想起来再补代码也鸽了

D1T1

#include <bits/stdc++.h>
#define rep(i, n) for(int i = 0; i < (int)(n); i ++)
#define rep1(i, n) for(int i = 1; i <= (int)(n); i ++)
#define MP make_pairusing namespace std;
typedef long long LL;
typedef pair<int, int> PII;
const int MOD = 998244353;int n, a[1000005][2];
PII dp[1000005][2];PII unite(const PII& u, const PII& v)
{if(u.first > u.second) return v;if(v.first > v.second) return u;return MP(min(u.first, v.first), max(u.second, v.second));
}char ans[1000005];int main()
{scanf("%d", &n);rep(i, 2) rep(j, 2 * n) scanf("%d", &a[j][i]);dp[0][0] = MP(0, 0);dp[0][1] = MP(1, 1);rep1(i, 2 * n - 1) {dp[i][0] = dp[i][1] = MP(0, -1);rep(j, 2) rep(k, 2) if(a[i - 1][k] <= a[i][j]) dp[i][j] = unite(dp[i][j], dp[i - 1][k]);dp[i][1].first ++;dp[i][1].second ++;}int ct = -1, cs = n;if(dp[2 * n - 1][0].first <= n && dp[2 * n - 1][0].second >= n) ct = 0;else if(dp[2 * n - 1][1].first <= n && dp[2 * n - 1][1].second >= n) ct = 1;if(ct == -1) {printf("-1\n");return 0;}for(int i = 2 * n - 1; i >= 0; i --) {cs -= ct;ans[i] = 'A' + ct;if(i == 0) break;int nt = -1;if(a[i - 1][0] <= a[i][ct] && dp[i - 1][0].first <= cs && dp[i - 1][0].second >= cs) nt = 0;else if(a[i - 1][1] <= a[i][ct] && dp[i - 1][1].first <= cs && dp[i - 1][1].second >= cs) nt = 1;ct = nt;}printf("%s\n", ans);return 0;
}

D1T2

这里面的 2-SAT 是假的，然而能通过所有数据（有一说一比这个更假的做法也能过（笑

#include <bits/stdc++.h>
#define rep(i, n) for(int i = 0; i < (int)(n); i ++)
#define rep1(i, n) for(int i = 1; i <= (int)(n); i ++)
#define MP make_pairusing namespace std;
typedef long long LL;
typedef pair<int, int> PII;
const int INF = 0x3f3f3f3f;int n, k;
int del[200005];
int xl[200005], yl[200005], xr[200005], yr[200005];
int permx[200005], permy[200005];
int xa[200005], ya[200005];int sta[200005];
void occupy(int cx, int cy, int ck)
{rep(i, n) {if(del[i]) continue;if(xl[i] <= cx && yl[i] <= cy && xr[i] >= cx && yr[i] >= cy) del[i] = ck;}
}
void disocc(int ck)
{rep(i, n) if(del[i] == ck) del[i] = 0;
}bool s_trivial(int ck, int retx[], int rety[])
{int xlm = -INF, xrm = INF, ylm = -INF, yrm = INF;rep(i, n) {if(del[i]) continue;xlm = max(xlm, xl[i]);xrm = min(xrm, xr[i]);ylm = max(ylm, yl[i]);yrm = min(yrm, yr[i]);}if(xlm == -INF) return true;if(ck == 0) return false;if(xlm <= xrm) {int cnt = 0, cr = INF;for(int i = n - 1; i >= 0; i --) {int cur = permy[i];if(del[cur]) continue;if(cr > yr[cur]) {cr = yl[cur];retx[cnt] = xlm;rety[cnt] = cr;cnt ++;}}return cnt <= ck;} else if(ylm <= yrm) {int cnt = 0, cr = INF;for(int i = n - 1; i >= 0; i --) {int cur = permx[i];if(del[cur]) continue;if(cr > xr[cur]) {cr = xl[cur];retx[cnt] = cr;rety[cnt] = ylm;cnt ++;}}return cnt <= ck;} else if(ck == 1) return false;occupy(xlm, ylm, ck);retx[0] = xlm;rety[0] = ylm;if(s_trivial(ck - 1, retx + 1, rety + 1)) return true;disocc(ck);occupy(xlm, yrm, ck);retx[0] = xlm;rety[0] = yrm;if(s_trivial(ck - 1, retx + 1, rety + 1)) return true;disocc(ck);occupy(xrm, ylm, ck);retx[0] = xrm;rety[0] = ylm;if(s_trivial(ck - 1, retx + 1, rety + 1)) return true;disocc(ck);occupy(xrm, yrm, ck);retx[0] = xrm;rety[0] = yrm;if(s_trivial(ck - 1, retx + 1, rety + 1)) return true;disocc(ck);return false;
}int xs[400005], ys[400005], xtot, ytot, ltot;
int rgl[4][200005], rgr[4][200005];
int ver[4][200005], vcnt;
vector<int> G[4000015];
bool vis[4000015];
int ret[2000015];void add_edge(int x, int y, int vx, int vy)
{G[x << 1 | vx ^ 1].push_back(y << 1 | vy);G[y << 1 | vy ^ 1].push_back(x << 1 | vx);
}void dfs(int v)
{vis[v] = true;rep(i, G[v].size()) if(!vis[G[v][i]]) dfs(G[v][i]);if(ret[v >> 1] == -1) ret[v >> 1] = !(v & 1);
}void s_ntrivial()
{int xlm = -INF, xrm = INF, ylm = -INF, yrm = INF;rep(i, n) {xlm = max(xlm, xl[i]);xrm = min(xrm, xr[i]);ylm = max(ylm, yl[i]);yrm = min(yrm, yr[i]);}rep(i, n) {xs[2 * i] = xl[i];xs[2 * i + 1] = xr[i];}sort(xs, xs + 2 * n);xtot = unique(xs, xs + 2 * n) - xs;rep(i, n) {ys[2 * i] = yl[i];ys[2 * i + 1] = yr[i];}sort(ys, ys + 2 * n);ytot = unique(ys, ys + 2 * n) - ys;rep(i, 4) rep(j, n) rgl[i][j] = rgr[i][j] = -1;rep(i, n) {int lx = xl[i] <= xrm;int rx = xr[i] >= xlm;int ly = yl[i] <= yrm;int ry = yr[i] >= ylm; if(lx + rx + ly + ry >= 3) continue;if(lx) {rgl[0][i] = lower_bound(ys, ys + ytot, max(yl[i], yrm)) - ys;rgr[0][i] = lower_bound(ys, ys + ytot, min(yr[i], ylm)) - ys;}if(rx) {rgl[1][i] = lower_bound(ys, ys + ytot, max(yl[i], yrm)) - ys;rgr[1][i] = lower_bound(ys, ys + ytot, min(yr[i], ylm)) - ys;}if(ly) {rgl[2][i] = lower_bound(xs, xs + xtot, max(xl[i], xrm)) - xs;rgr[2][i] = lower_bound(xs, xs + xtot, min(xr[i], xlm)) - xs;}if(ry) {rgl[3][i] = lower_bound(xs, xs + xtot, max(xl[i], xrm)) - xs;rgr[3][i] = lower_bound(xs, xs + xtot, min(xr[i], xlm)) - xs;}}ltot = max(xtot, ytot) + 1;vcnt = 4 * ltot;rep1(i, ytot) add_edge(i - 1, i, 1, 0);rep1(i, ytot) add_edge(ltot + i - 1, ltot + i, 1, 0);rep1(i, xtot) add_edge(ltot * 2 + i - 1, ltot * 2 + i, 1, 0);rep1(i, xtot) add_edge(ltot * 3 + i - 1, ltot * 3 + i, 1, 0);rep(i, n) {int p0, p1;for(p0 = 0; p0 < 4 && rgl[p0][i] == -1; p0 ++) ;for(p1 = 3; p1 >= 0 && rgl[p1][i] == -1; p1 --) ;if(p1 == -1) continue;ver[p0][i] = vcnt ++;if(p1 > p0) ver[p1][i] = vcnt ++;add_edge(ver[p0][i], p0 * ltot + rgl[p0][i], 1, 1);add_edge(ver[p0][i], p0 * ltot + rgr[p0][i] + 1, 1, 0);if(p0 != -1) {add_edge(ver[p1][i], p1 * ltot + rgl[p1][i], 1, 1);add_edge(ver[p1][i], p1 * ltot + rgr[p1][i] + 1, 1, 0);}add_edge(ver[p0][i], ver[p1][i], 0, 0);}rep(i, vcnt) ret[i] = -1;rep(i, vcnt * 2) if(!vis[i]) dfs(i);rep(i, ytot + 1) if(ret[i] || i == ytot) {xa[0] = xrm;ya[0] = ys[max(i - 1, 0)];break;}rep(i, ytot + 1) if(ret[i + ltot] || i == ytot) {xa[1] = xlm;ya[1] = ys[max(i - 1, 0)];break;}rep(i, xtot + 1) if(ret[i + ltot * 2] || i == xtot) {ya[2] = yrm;xa[2] = xs[max(i - 1, 0)];break;}rep(i, xtot + 1) if(ret[i + ltot * 3] || i == xtot) {ya[3] = ylm;xa[3] = xs[max(i - 1, 0)];break;}
}template<int* arr>
bool cmp(int i, int j)
{return arr[i] < arr[j];
}int main()
{scanf("%d%d", &n, &k);rep(i, n) scanf("%d%d%d%d", &xl[i], &yl[i], &xr[i], &yr[i]);rep(i, n) permx[i] = permy[i] = i;sort(permx, permx + n, cmp<xl>);sort(permy, permy + n, cmp<yl>);rep(i, n) xa[i] = ya[i] = 1;if(!s_trivial(k, xa, ya)) s_ntrivial();rep(i, k) printf("%d %d\n", xa[i], ya[i]);return 0;
}

D1T3

#include <bits/stdc++.h>
#define rep(i, n) for(int i = 0; i < (int)(n); i ++)
#define rep1(i, n) for(int i = 1; i <= (int)(n); i ++)
#define MP make_pairusing namespace std;
typedef long long LL;
typedef pair<int, int> PII;
const int MOD = 998244353;namespace s64
{int n, m, q;int x[500005], y[500005];int qt[1000005], qv[1000005];int px[500005], perm[500005], pos[500005];int ax[1000005], ay[1000005];bool cmpx(int i, int j){return x[i] < x[j] || x[i] == x[j] && y[i] < y[j];}bool cmpy(int i, int j){return i == -1 ? false : (j == -1 ? true : y[i] < y[j]);}struct segt{int dat[1048576];segt(){memset(dat, -1, sizeof(dat));}void build(){rep(i, m) dat[i + 524288] = perm[i];int l = 524288, r = m + 524287;l >>= 1; r >>= 1;while(l > 0) {for(int i = l; i <= r; i ++) dat[i] = cmpy(dat[i << 1], dat[i << 1 | 1]) ? dat[i << 1] : dat[i << 1 | 1];l >>= 1;r >>= 1;}}void erase(int cur){cur = pos[cur] + 524288;dat[cur] = -1;for(cur >>= 1; cur > 0; cur >>= 1) dat[cur] = cmpy(dat[cur << 1], dat[cur << 1 | 1]) ? dat[cur << 1] : dat[cur << 1 | 1];}int query(int cx){int l = 524288, r = upper_bound(px, px + m, cx) - px + 524287;int ret = -1;while(l < r) {if(l & 1) ret = cmpy(ret, dat[l]) ? ret : dat[l];if(!(r & 1)) ret = cmpy(ret, dat[r]) ? ret : dat[r];l = l + 1 >> 1;r = r - 1 >> 1;}if(l == r) ret = cmpy(ret, dat[l]) ? ret : dat[l];return ret;}}tre;struct dsu{int pre[500005];void init(){rep(i, m) pre[i] = i;}int root(int x){return pre[x] == x ? x : pre[x] = root(pre[x]);}}con;bool del[500005];int tp[500005];set<int> hv, hvu, hvr;map<int, int> ver, hor;void insert_d(map<int, int>& cur, int cv, int cdat){if(cur.find(cdat) == cur.end()) cur.insert(MP(cdat, cv));else con.pre[cv] = cur[cdat];}void solve(){rep(i, m) perm[i] = i;sort(perm, perm + m, cmpx);rep(i, m) pos[perm[i]] = i;rep(i, m) px[i] = x[perm[i]];tre.build();con.init();rep(i, m) del[i] = false;rep(i, m) tp[i] = -1;hv.clear();hvu.clear();hvr.clear();ver.clear();hor.clear();hv.insert(-1);hv.insert(n + 1);rep(i, q) {int pre, nxt;if(qt[i] == 2) {set<int>::iterator it = hv.lower_bound(qv[i]);nxt = *it;pre = *prev(it);while(true) {int cv = tre.query(qv[i]);if(cv == -1 || y[cv] > n - qv[i]) break;tre.erase(cv);tp[cv] = 0;insert_d(ver, cv, y[cv]);}if(ver.find(n - qv[i]) != ver.end()) {int cv = ver[n - qv[i]];del[cv] = true;ver.erase(n - qv[i]);}while(true) {map<int, int>::iterator it = hor.lower_bound(pre);if(it == hor.end() || it->first >= qv[i]) break;x[it->second] = qv[i];insert_d(hor, it->second, qv[i]);hor.erase(it);}map<int, int>::iterator it2 = hor.find(qv[i]);if(it2 != hor.end() && hvu.find(qv[i]) != hvu.end()) {del[it2->second] = true;hor.erase(it2);}hv.insert(qv[i]);hvr.insert(qv[i]);} else if(qt[i] == 3) {set<int>::iterator it = hv.upper_bound(qv[i]);nxt = *it;pre = *prev(it);while(true) {int cv = tre.query(qv[i]);if(cv == -1 || y[cv] > n - qv[i]) break;tre.erase(cv);tp[cv] = 1;insert_d(hor, cv, x[cv]);}if(hor.find(qv[i]) != hor.end()) {int cur = hor[qv[i]];del[cur] = true;hor.erase(qv[i]);}while(true) {map<int, int>::iterator it = ver.lower_bound(n - nxt);if(it == ver.end() || it->first >= n - qv[i]) break;y[it->second] = n - qv[i];insert_d(ver, it->second, n - qv[i]);ver.erase(it);}map<int, int>::iterator it2 = ver.find(n - qv[i]);if(it2 != ver.end() && hvr.find(qv[i]) != hvr.end()) {del[it2->second] = true;ver.erase(it2);}hv.insert(qv[i]);hvu.insert(qv[i]);} else {int cqv = con.root(qv[i]);if(tp[cqv] == -1) {ax[i] = x[cqv];ay[i] = y[cqv];} else if(tp[cqv]) {ax[i] = x[cqv];ay[i] = del[cqv] ? n - x[cqv] : n - *hv.upper_bound(x[cqv]);} else {ax[i] = del[cqv] ? n - y[cqv] : *prev(hv.lower_bound(n - y[cqv]));ay[i] = y[cqv];}}}rep(i, m) if(tp[i] == -1) tre.erase(i);rep(i, m) {if(tp[i] == -1) continue;int cqv = con.root(i);if(tp[cqv]) {x[i] = x[cqv];y[i] = del[cqv] ? n - x[cqv] : n - *hv.upper_bound(x[cqv]);} else {x[i] = del[cqv] ? n - y[cqv] : *prev(hv.lower_bound(n - y[cqv]));y[i] = y[cqv];}}}
}int n, m, q;
int x[500005], y[500005];
int qt[1000005], qv[1000005], qw[1000005];
int ax[1000005], ay[1000005];
int vid[1000005], qid[1000005], vcnt;void deposit(int l, int r)
{if(l == r) return;int mid = l + r >> 1;deposit(l, mid);deposit(mid + 1, r);int mv = -1;s64::m = 0;for(int i = l; i <= mid; i ++) {if(qt[i] != 4) continue;if(mv == -1) mv = vid[i];s64::x[s64::m] = qv[i];s64::y[s64::m] = qw[i];s64::m ++;}if(mv == -1) return;s64::q = 0;for(int i = mid + 1; i <= r; i ++) {if(qt[i] == 4 || qt[i] == 1 && (qv[i] < mv || qv[i] >= mv + s64::m)) continue;s64::qt[s64::q] = qt[i];s64::qv[s64::q] = qt[i] == 1 ? qv[i] - mv : qv[i];qid[i] = s64::q;s64::q ++;}s64::solve();for(int i = mid + 1; i <= r; i ++) if(qt[i] == 1 && qv[i] >= mv && qv[i] < mv + s64::m) {ax[i] = s64::ax[qid[i]];ay[i] = s64::ay[qid[i]];}s64::m = 0;for(int i = l; i <= mid; i ++) {if(qt[i] != 4) continue;qv[i] = s64::x[s64::m];qw[i] = s64::y[s64::m];s64::m ++;}
}int main()
{scanf("%d%d%d", &n, &m, &q);rep(i, m) scanf("%d%d", &x[i], &y[i]);vcnt = m;rep(i, q) {scanf("%d%d", &qt[i], &qv[i]);if(qt[i] == 4) {scanf("%d", &qw[i]);vid[i] = vcnt ++;}}rep(i, q) if(qt[i] == 1) qv[i] --;else if(qt[i] == 2) qv[i] = n - qv[i];s64::n = n;s64::m = m;s64::q = 0;rep(i, m) {s64::x[i] = x[i];s64::y[i] = y[i];}rep(i, q) {if(qt[i] == 4 || qt[i] == 1 && qv[i] >= m) continue;s64::qt[s64::q] = qt[i];s64::qv[s64::q] = qv[i];qid[i] = s64::q;s64::q ++;}s64::solve();rep(i, q) if(qt[i] == 1 && qv[i] < m) {ax[i] = s64::ax[qid[i]];ay[i] = s64::ay[qid[i]];}deposit(0, q - 1);rep(i, q) if(qt[i] == 1) printf("%d %d\n", ax[i], ay[i]);return 0;
}

D2T1

#include "chameleon.h"
#include <bits/stdc++.h>
#define rep(i, n) for(int i = 0; i < (int)(n); i ++)
#define rep1(i, n) for(int i = 1; i <= (int)(n); i ++)
#define MP make_pairusing namespace std;
typedef long long LL;
typedef pair<int, int> PII;
const int MOD = 998244353;int n;
vector<int> G[1005];
int rt[1005], xval[1005];
bool ban[1005][1005];void add_edge(int u, int v)
{G[u].push_back(v);G[v].push_back(u);int nxv = xval[u] ^ xval[v] ^ 1;int cu = rt[u], cv = rt[v];rep1(i, 2 * n) if(rt[i] == cu) {rt[i] = cv;xval[i] ^= nxv;}
}bool check(int x, int l, int r, int tp)
{vector<int> cq;cq.push_back(x);for(int i = l; i <= r; i ++)if(xval[i] == tp) cq.push_back(i);return Query(cq) + 1 <= cq.size();
}bool check3(int a, int b, int c)
{vector<int> cq;cq.push_back(a);cq.push_back(b);cq.push_back(c);return Query(cq) == 1;
}int query_pr(int x, int l, int r, int tp)
{if(l > r || !check(x, l, r, tp)) return -1;while(l < r) {int mid = l + r >> 1;if(check(x, mid + 1, r, tp)) l = mid + 1;else r = mid;}return r;
}void Solve(int N)
{n = N;rep1(i, 2 * n) rep1(j, 2 * n) ban[i][j] = false;rep1(i, 2 * n) {rt[i] = i;xval[i] = 0;}rep1(i, 2 * n) {int cr = i - 1;vector<int> hv;while(true) {cr = query_pr(i, 1, cr, 0);if(cr == -1) break;hv.push_back(cr);cr --;}cr = i - 1;while(true) {cr = query_pr(i, 1, cr, 1);if(cr == -1) break;hv.push_back(cr);cr --;}rep(j, hv.size()) add_edge(i, hv[j]);}rep1(i, 2 * n) if(G[i].size() == 3) {if(check3(i, G[i][0], G[i][1])) ban[i][G[i][2]] = ban[G[i][2]][i] = true;else if(check3(i, G[i][0], G[i][2])) ban[i][G[i][1]] = ban[G[i][1]][i] = true;else ban[i][G[i][0]] = ban[G[i][0]][i] = true;}rep1(i, 2 * n) if(!xval[i])rep(j, G[i].size()) if(!ban[i][G[i][j]]) Answer(i, G[i][j]);
}

D2T2

#include <bits/stdc++.h>
#define rep(i, n) for(int i = 0; i < (int)(n); i ++)
#define rep1(i, n) for(int i = 1; i <= (int)(n); i ++)
#define MP make_pairusing namespace std;
typedef long long LL;
typedef pair<int, int> PII;
const int MOD = 998244353;int pre[100005], siz[100005];
int deg[100005], rdeg[100005];
set<int> G[100005], RG[100005], S[100005];
LL tot;int root(int x)
{return pre[x] == x ? x : pre[x] = root(pre[x]);
}void add_edge(int, int);
void merge(int u, int v)
{if(siz[u] < siz[v]) swap(u, v);pre[v] = u;vector<int> hv, rhv;for(set<int>::iterator it = G[v].begin(); it != G[v].end(); it ++) hv.push_back(*it);for(set<int>::iterator it = RG[v].begin(); it != RG[v].end(); it ++) rhv.push_back(*it);tot += 1LL * S[u].size() * siz[v];tot += 1LL * S[v].size() * siz[u];for(set<int>::iterator it = S[v].begin(); it != S[v].end(); it ++) {if(S[u].find(*it) != S[u].end()) tot -= siz[u] + siz[v];else S[u].insert(*it);}S[v].clear();siz[u] += siz[v];rep(i, hv.size()) {G[v].erase(hv[i]);RG[hv[i]].erase(v);}rep(i, rhv.size()) {RG[v].erase(rhv[i]);G[rhv[i]].erase(v);}rep(i, hv.size()) add_edge(u, hv[i]);rep(i, rhv.size()) add_edge(rhv[i], u);
}void add_edge(int u, int v)
{u = root(u);v = root(v);if(u == v) return;if(G[u].find(v) != G[u].end()) return;if(G[v].find(u) != G[v].end()) {merge(u, v);return;}G[u].insert(v);RG[v].insert(u);deg[u] += siz[v];rdeg[v] += siz[u];
}int main()
{int n, m;scanf("%d%d", &n, &m);rep1(i, n) {pre[i] = i;siz[i] = 1;}rep1(i, n) S[i].insert(i);rep(i, m) {int u, v;scanf("%d%d", &u, &v);v = root(v);if(S[v].find(u) == S[v].end()) {S[v].insert(u);tot += siz[v];}add_edge(u, v);printf("%lld\n", tot);}return 0;
}

D2T3

#include <bits/stdc++.h>
#define rep(i, n) for(int i = 0; i < (int)(n); i ++)
#define rep1(i, n) for(int i = 1; i <= (int)(n); i ++)
#define MP make_pairusing namespace std;
typedef long long LL;
typedef pair<int, int> PII;
const int MOD = 1e9 + 7;int n, a[605];
bool inq[1205];
int dp[1205][605];
int comb[1205][605], cdp[605][605], gtot[605];int main()
{comb[0][0] = 1;rep(i, 1200) rep(j, 600) {comb[i + 1][j] = (comb[i + 1][j] + comb[i][j]) % MOD;comb[i + 1][j + 1] = (comb[i + 1][j + 1] + comb[i][j]) % MOD;}cdp[0][0] = 1;rep(i, 600) rep(j, 600) {cdp[i + 1][j + 1] = (cdp[i + 1][j + 1] + cdp[i][j]) % MOD;cdp[i + 1][j] = (cdp[i + 1][j] + 2LL * cdp[i][j]) % MOD;if(j > 0) cdp[i + 1][j - 1] = (cdp[i + 1][j - 1] + cdp[i][j]) % MOD;}gtot[0] = 1;rep1(i, 600) gtot[i] = 1LL * gtot[i - 1] * i % MOD;rep(i, 601) gtot[i] = 1LL * gtot[i] * cdp[i][0] % MOD; for(int i = 600; i >= 1; i --) gtot[i] = 1LL * gtot[i - 1]  * (i + 1) % MOD;scanf("%d", &n);rep(i, n) scanf("%d", &a[i]);rep(i, n) inq[a[i]] = true;dp[2 * n][0] = 1;int ccnt = 0;for(int i = 2 * n; i >= 1; i --)if(!inq[i]) {rep(j, n + 1) {if(dp[i][j] == 0) continue;dp[i - 1][j] = (dp[i - 1][j] + 1LL * dp[i][j] * (j - ccnt)) % MOD;}ccnt ++;} else {rep(j, n + 1) {if(dp[i][j] == 0) continue;dp[i - 1][j] = (dp[i - 1][j] + dp[i][j]) % MOD;for(int k = j + 1; k <= n; k ++) dp[i - 1][k] = (dp[i - 1][k] +1LL * dp[i][j] * comb[2 * n - i - j - ccnt][k - j - 1] % MOD * gtot[k - j]) % MOD;}}int ans = dp[0][n];rep(i, n) ans = 1LL * ans * (MOD + 1) / 2 % MOD;printf("%d\n", ans);return 0;
}

D3T1

#include <bits/stdc++.h>
#define rep(i, n) for(int i = 0; i < (int)(n); i ++)
#define rep1(i, n) for(int i = 1; i <= (int)(n); i ++)
#define MP make_pairusing namespace std;
typedef long long LL;
typedef pair<int, int> PII;
const int INF = 0x3f3f3f3f;struct segt
{LL dat[524288];void add(int l, int r, LL d){l += 262144; r += 262144;while(l < r) {if(l & 1) dat[l] += d;if(!(r & 1)) dat[r] += d;l = l + 1 >> 1;r = r - 1 >> 1;}if(l == r) dat[l] += d;}LL query(int x){LL ret = 0;for(x += 262144; x > 0; x >>= 1) ret += dat[x];return ret;}
}tre;int n, a[200005];
int m, x[200005], y[200005], c[200005];
int par[200005];
int pre[200005][18];
vector<int> T[200005];
int dfn[200005], dfo[200005], tot;
vector<PII> qs[200005];
LL dp[200005];int sta[100005], ssiz;
void gen_tre()
{ssiz = 1;sta[1] = -1;rep1(i, n) {while(a[sta[ssiz - 1]] < a[i]) ssiz --;if(sta[ssiz] != -1) par[sta[ssiz]] = i;par[i] = sta[ssiz - 1];sta[ssiz ++] = i;sta[ssiz] = -1;}rep1(i, n) pre[i][0] = par[i];rep1(i, 17) rep1(j, n) pre[j][i] = pre[pre[j][i - 1]][i - 1];rep1(i, n) T[par[i]].push_back(i);
}int find_pre(int x, int y)
{for(int i = 17; i >= 0; i --) if(a[pre[x][i]] < y) x = pre[x][i];return x;
}void dfs(int v)
{dfn[v] = tot ++;rep(i, T[v].size()) dfs(T[v][i]);dfo[v] = tot - 1;
}void gen_dp(int v)
{rep(i, T[v].size()) {gen_dp(T[v][i]);dp[v] += dp[T[v][i]];}tre.add(dfn[v], dfn[v], dp[v]);rep(i, T[v].size()) {tre.add(dfn[v] + 1, dfn[T[v][i]] - 1, dp[T[v][i]]);tre.add(dfo[T[v][i]] + 1, dfo[v], dp[T[v][i]]);}rep(i, qs[v].size()) dp[v] = max(dp[v], tre.query(dfn[qs[v][i].first]) + qs[v][i].second);
}int main()
{scanf("%d", &n);rep1(i, n) scanf("%d", &a[i]);a[0] = INF;gen_tre();scanf("%d", &m);LL ans = 0;rep(i, m) {scanf("%d%d%d", &x[i], &y[i], &c[i]);qs[find_pre(x[i], y[i])].push_back(MP(x[i], c[i]));ans += c[i];}dfs(0);gen_dp(0);ans -= dp[0];printf("%lld\n", ans);return 0;
}

D3T2

#include <bits/stdc++.h>
#define rep(i, n) for(int i = 0; i < (int)(n); i ++)
#define rep1(i, n) for(int i = 1; i <= (int)(n); i ++)
#define MP make_pairusing namespace std;
typedef long long LL;
typedef pair<int, int> PII;
const int MOD = 998244353;int n, m, l, c, q;
int a[200005], b[200005];
int pre[400005];
LL pdis[400005];int ccnt;
bool inc[400005];
int cid[400005];
vector<int> hv[200005];
vector<int> T[400005];
int dfn[400005], dfo[400005], tot;
LL clen[200005];
LL dep[400005];void dfs(int v, LL cd)
{cid[v] = ccnt;dep[v] = cd;dfn[v] = tot ++;rep(i, T[v].size()) {int u = T[v][i];dfs(u, cd + pdis[u]);}dfo[v] = tot - 1;
}int deg[400005];
void gen_cyc()
{rep(i, n + m) deg[pre[i]] ++;queue<int> que;rep(i, n + m) if(deg[i] == 0) que.push(i);while(!que.empty()) {int v = que.front();que.pop();T[pre[v]].push_back(v);deg[pre[v]] --;if(deg[pre[v]] == 0) que.push(pre[v]);}rep(i, n + m) if(deg[i] != 0) {for(int j = i; deg[j] != 0; j = pre[j]) {inc[j] = true;hv[ccnt].push_back(j);deg[j] = 0;}for(int j = hv[ccnt].size() - 1; j >= 0; j --) {if(j != hv[ccnt].size() - 1) clen[ccnt] += pdis[hv[ccnt][j]];dfs(hv[ccnt][j], clen[ccnt]);}clen[ccnt] += pdis[hv[ccnt].back()];ccnt ++;}
}int qv[200005];
LL qt[200005];
LL ans[200005]; vector<int> cs[200005];
vector<int> qs[200005];bool cmpc(int c0, int c1)
{return dep[c0] < dep[c1] || dep[c0] == dep[c1] && c0 < c1;
}
bool cmpq(int q0, int q1)
{return dep[qv[q0]] + qt[q0] < dep[qv[q1]] + qt[q1] || dep[qv[q0]] + qt[q0] == dep[qv[q1]] + qt[q1] && q0 < q1;
}int cc;
int tot1;
LL tot2;
struct fwt
{LL dat[524295];void add(int x, LL d){for(; x <= 524288; x += x & -x) dat[x] += d;}LL query(int x){LL ret = 0;for(; x > 0; x -= x & -x) ret += dat[x];return ret;}
} t3, t4;
vector<LL> rem;void add_c(int x, int coef)
{tot1 += coef;tot2 += coef * (dep[x] / clen[cc]);t3.add(lower_bound(rem.begin(), rem.end(), dep[x] % clen[cc]) - rem.begin() + 1, coef);t4.add(dfn[x] + 1, coef);
}LL query_q(int x, LL ct)
{if(!inc[x]) return t4.query(dfo[x] + 1) - t4.query(dfn[x]);LL ret = 0;ret += tot1 * (ct / clen[cc] + 1);ret -= tot2;ret -= tot1 - t3.query(upper_bound(rem.begin(), rem.end(), ct % clen[cc]) - rem.begin());ret -= t4.query(dfn[x]);return ret;
}void solve_q(int id)
{cc = id;sort(cs[id].begin(), cs[id].end(), cmpc);sort(qs[id].begin(), qs[id].end(), cmpq);rem.clear();rep(i, cs[id].size()) rem.push_back(dep[cs[id][i]] % clen[cc]);sort(rem.begin(), rem.end());rem.resize(unique(rem.begin(), rem.end()) - rem.begin());int j = 0;rep(i, qs[id].size()) {while(j < cs[id].size() && dep[cs[id][j]] <= dep[qv[qs[id][i]]] + qt[qs[id][i]]) add_c(cs[id][j ++], 1);ans[qs[id][i]] = query_q(qv[qs[id][i]], dep[qv[qs[id][i]]] + qt[qs[id][i]]);}while(j > 0) add_c(cs[id][-- j], -1);
}int main()
{scanf("%d%d%d%d", &n, &m, &l, &c);rep(i, n) scanf("%d", &a[i]);rep(i, m) scanf("%d", &b[i]);rep(i, n) {int pos = upper_bound(a, a + n, a[i] - c % l) - a;pdis[i] = c - c % l;if(pos == 0) {pdis[i] += l;pos = upper_bound(a, a + n, a[i] + l - c % l) - a;}pre[i] = pos - 1;pdis[i] += a[i] - a[pos - 1];}rep(i, m) {int pos = upper_bound(a, a + n, b[i]) - a;pdis[i + n] = 0;if(pos == 0) {pdis[i + n] += l;pos = upper_bound(a, a + n, b[i] + l) - a;}pre[i + n] = pos - 1;pdis[i + n] += b[i] - a[pos - 1];}gen_cyc();scanf("%d", &q);rep(i, q) {scanf("%d%lld", &qv[i], &qt[i]);qv[i] --;}rep(i, q) qs[cid[qv[i]]].push_back(i);for(int i = n; i < n + m; i ++) cs[cid[i]].push_back(i);rep(i, ccnt) solve_q(i);rep(i, q) printf("%lld\n", ans[i]);return 0;
}

D3T3

Subtask 1 Anthony

#include "Anthony.h"
#include <bits/stdc++.h>
#define rep(i, n) for(int i = 0; i < (int)(n); i ++)
#define rep1(i, n) for(int i = 1; i <= (int)(n); i ++)
#define MP make_pairusing namespace std;
typedef long long LL;
typedef pair<int, int> PII;
const int MOD = 998244353;vector<int> G[20005];
int dis[20005];
vector<int> Mark(int n, int m, int a, int b, vector<int> u, vector<int> v)
{rep(i, m) {G[u[i]].push_back(v[i]);G[v[i]].push_back(u[i]);}rep(i, n) dis[i] = -1;queue<int> que;que.push(0);dis[0] = 0;while(!que.empty()) {int v = que.front();que.pop();rep(i, G[v].size()) {int u = G[v][i];if(dis[u] != -1) continue;que.push(u);dis[u] = dis[v] + 1;}}vector<int> ret;rep(i, m) ret.push_back(min(dis[u[i]], dis[v[i]]) % 3);return ret;
}

Subtask 1 Catherine

#include "Catherine.h"
#include <bits/stdc++.h>
#define rep(i, n) for(int i = 0; i < (int)(n); i ++)
#define rep1(i, n) for(int i = 1; i <= (int)(n); i ++)
#define MP make_pairusing namespace std;
typedef long long LL;
typedef pair<int, int> PII;
const int MOD = 998244353;void Init(int a, int b)
{
}int Move(vector<int> y)
{vector<int> hv;rep(i, 3) if(y[i] != 0) hv.push_back(i);if(hv.size() == 1) return hv[0];else return hv[1] - hv[0] == 2 ? 2 : hv[0];
}

Subtask 2 Anthony

#include "Anthony.h"
#include <bits/stdc++.h>
#define rep(i, n) for(int i = 0; i < (int)(n); i ++)
#define rep1(i, n) for(int i = 1; i <= (int)(n); i ++)
#define MP make_pairusing namespace std;
typedef long long LL;
typedef pair<int, int> PII;
const int MOD = 998244353;int dat[6] = {0, 0, 1, 1, 0, 1};vector<PII> G[20005];
int ans[20005];void dfs(int v, int par, int cd)
{rep(i, G[v].size())  {int u = G[v][i].first;if(u == par) continue;int nc = G[v].size() == 2 ? (cd + 1) % 6 : (dat[cd] ? 0 : 2);ans[G[v][i].second] = dat[nc];dfs(u, v, nc);}
}vector<int> Mark(int n, int m, int a, int b, vector<int> u, vector<int> v)
{rep(i, m) {G[u[i]].push_back(MP(v[i], i));G[v[i]].push_back(MP(u[i], i));}dfs(0, -1, 0);vector<int> ret;rep(i, m) ret.push_back(ans[i]);return ret;
}

Subtask 2 Catherine

#include "Catherine.h"
#include <bits/stdc++.h>
#define rep(i, n) for(int i = 0; i < (int)(n); i ++)
#define rep1(i, n) for(int i = 1; i <= (int)(n); i ++)
#define MP make_pairusing namespace std;
typedef long long LL;
typedef pair<int, int> PII;
const int MOD = 998244353;const int dat[6] = {0, 0, 1, 1, 0, 1};
bool insm;
int pre;
int sc[5], scnt; void Init(int a, int b)
{insm = true;pre = -1;scnt = 0;
}int getone(vector<int> cc)
{return cc[0] ? 0 : 1;
}int countt(vector<int> cc)
{return cc[0] + cc[1];
}bool isdown()
{rep(i, 6) {bool ok = true;rep(j, 5) if(dat[(i + j) % 6] != sc[j]) ok = false;if(ok) return true;}return false;
}int move_up(vector<int> cc)
{if(countt(cc) + (pre != -1) != 2) {if(cc[0] + (pre == 0) == 1) return pre == 0 ? -1 : (pre = 0);else return pre == 1 ? -1 : (pre = 1);} else return cc[1] ? (pre = 1) : (pre = 0);
}int Move(vector<int> cur)
{if(countt(cur) + (pre != -1) != 2) insm = false;if(!insm) return move_up(cur);if(pre == -1) {sc[scnt ++] = getone(cur);cur[sc[0]] --;}sc[scnt ++] = getone(cur);if(scnt == 5) {insm = false;if(isdown()) return -1;else return move_up(cur);} else return pre = sc[scnt - 1];
}

D4T1

#include <bits/stdc++.h>
#define rep(i, n) for(int i = 0; i < (int)(n); i ++)
#define rep1(i, n) for(int i = 1; i <= (int)(n); i ++)
#define MP make_pairusing namespace std;
typedef long long LL;
typedef pair<int, int> PII;
const int INF = 0x3f3f3f3f;int n, k, c[200005];
int occ[200005];
vector<int> G[200005];
vector<int> G0[200005];
bool del[200005];int siz[200005];
void dfs0(int v, int par)
{siz[v] = 1;rep(i, G[v].size()) {int u = G[v][i];if(del[u] || u == par) continue;dfs0(u, v);siz[v] += siz[u];}
}int cent(int v, int par, int csiz)
{rep(i, G[v].size()) {int u = G[v][i];if(del[u] || u == par) continue;if(siz[u] > csiz / 2) return cent(u, v, csiz);}return v;
}int pre[200005], vis[200005];
bool inq[200005], ing[200005];
void dfs1(int v, int par, int cid)
{pre[v] = par;vis[v] = cid;inq[v] = false;ing[c[v]] = false;rep(i, G[v].size()) {int u = G[v][i];if(del[u] || u == par) continue;dfs1(u, v, cid);}
}int tsolve(int v)
{dfs1(v, -1, v);int ret = 0;queue<int> que;inq[v] = true;que.push(v);while(!que.empty()) {int u = que.front();if(!ing[c[u]]) {ing[c[u]] = true;ret ++;}que.pop();rep(i, G0[u].size()) {int nu = G0[u][i];if(vis[nu] != v) return INF;while(!inq[nu]) {inq[nu] = true;que.push(nu);nu = pre[nu];}}}return ret;
}int solve(int v)
{dfs0(v, -1);v = cent(v, -1, siz[v]);int ret = tsolve(v);del[v] = true;rep(i, G[v].size()) {int u = G[v][i];if(del[u]) continue;ret = min(ret, solve(u));}return ret;
}int main()
{scanf("%d%d", &n, &k);rep(i, n - 1) {int u, v;scanf("%d%d", &u, &v);G[u].push_back(v);G[v].push_back(u);}rep1(i, n) {scanf("%d", &c[i]);if(occ[c[i]] != 0) {G0[occ[c[i]]].push_back(i);G0[i].push_back(occ[c[i]]);}occ[c[i]] = i;}printf("%d\n", solve(1) - 1);return 0;
}

D4T2

提答是不会碰的，这辈子都不会碰的

test 5 跑了 40min，属实垃圾

#include <bits/stdc++.h>
#define rep(i, n) for(int i = 0; i < (int)(n); i ++)
#define rep1(i, n) for(int i = 1; i <= (int)(n); i ++)
#define MP make_pairusing namespace std;
typedef long long LL;
typedef pair<int, int> PII;
const int MOD = 998244353;mt19937 rng(time(0));
int r, c;
char s[505][505];
int perm[1000005];
char cha[5] = "-|\\/";
int dx[4] = {0, -1, -1, -1}, dy[4] = {-1, 0, -1, 1};
int ret[505][505];
int occx[505][505], occy[505][505];bool check(int i, int j, int k)
{return s[i][j] == 'W' && s[i - dx[k]][j - dy[k]] != 'W' && s[i + dx[k]][j + dy[k]] != 'W'&& s[i - dx[k]][j - dy[k]] != s[i + dx[k]][j + dy[k]];
}void undo(int i, int j)
{if(occx[i][j] == -1) return;int ni = occx[i][j], nj = occy[i][j];occx[ni][nj] = occy[ni][nj] = -1;occx[ni - dx[ret[ni][nj]]][nj - dy[ret[ni][nj]]] = occy[ni - dx[ret[ni][nj]]][nj - dy[ret[ni][nj]]] = -1;occx[ni + dx[ret[ni][nj]]][nj + dy[ret[ni][nj]]] = occy[ni + dx[ret[ni][nj]]][nj + dy[ret[ni][nj]]] = -1;ret[ni][nj] = -1;
}void endo(int i, int j, int k)
{occx[i][j] = occx[i - dx[k]][j - dy[k]] = occx[i + dx[k]][j + dy[k]] = i;occy[i][j] = occy[i - dx[k]][j - dy[k]] = occy[i + dx[k]][j + dy[k]] = j;ret[i][j] = k;
}int cans = -1;
char ans[505][505];int main()
{freopen("input_05.txt", "r", stdin);scanf("%d%d", &r, &c);rep(i, r) scanf("%s", s[i]);rep(i, 4 * r * c) perm[i] = i;rep(i, r) rep(j, c) {ret[i][j] = -1;occx[i][j] = occy[i][j] = -1;}rep(T, 100000) {shuffle(perm, perm + 4 * r * c, rng);rep(t, 4 * r * c) {int i = (t >> 2) / c, j = (t >> 2) % c, k = t & 3;if(i + dx[k] < 0 || i - dx[k] >= r) continue;if(j - dy[k] < 0 || j + dy[k] >= c || j + dy[k] < 0 || j - dy[k] >= c) continue;if(!check(i, j, k)) continue;int ccnt = (occx[i][j] != -1) + (occx[i + dx[k]][j + dy[k]] != -1) + (occx[i - dx[k]][j - dy[k]] != -1)
//          - (occx[i][j] == occx[i + dx[k]][j + dy[k]] && occy[i][j] == occy[i + dx[k]][j + dy[k]])
//          - (occx[i][j] == occx[i - dx[k]][j - dy[k]] && occy[i][j] == occy[i - dx[k]][j - dy[k]]);
;if(ccnt >= 2 && (rng() & 262143)) continue;if(ccnt == 1 && (rng() & 1)) continue;undo(i, j);undo(i + dx[k], j + dy[k]);undo(i - dx[k], j - dy[k]);endo(i, j, k);}int tot = 0;rep(i, r) rep(j, c) if(ret[i][j] != -1) tot ++;if(tot > cans) {fprintf(stderr, "new answer: %d\n", tot);cans = tot;rep(i, r) rep(j, c) ans[i][j] = ret[i][j] == -1 ? s[i][j] : cha[ret[i][j]];freopen("current2.txt", "w", stdout);rep(i, r) printf("%s\n", ans[i]);fclose(stdout);if(tot >= 48620) break;}}return 0;
}

D4T3

#include <bits/stdc++.h>
#define rep(i, n) for(int i = 0; i < (int)(n); i ++)
#define rep1(i, n) for(int i = 1; i <= (int)(n); i ++)
#define MP make_pairusing namespace std;
typedef long long LL;
typedef pair<int, int> PII;
const LL INF = 0x3f3f3f3f3f3f3f3f;int n, m;
int t[100005], l[100005], r[100005], c[100005];
int cx[100005], cy[100005], qx[100005], qy[100005];
PII xval[100005];
LL dp[100005];
int del[100005];int cmin(int i, int j)
{return (j == -1 || i != -1 && cy[i] < cy[j]) ? i : j;
}struct segt
{int dat[262144];void build(){memset(dat, -1, sizeof(dat));rep(i, m) dat[131072 | cx[i]] = i;for(int i = 131071; i >= 0; i --) dat[i] = cmin(dat[i << 1], dat[i << 1 | 1]);}void erase(int x){int id = 131072 | cx[x];dat[id] = -1;for(id >>= 1; id > 0; id >>= 1) dat[id] = cmin(dat[id << 1], dat[id << 1 | 1]);}int query(int x){int l = 131072, r = 131072 | x;int ret = -1;while(l < r) {if(l & 1) ret = cmin(ret, dat[l]);if(!(r & 1)) ret = cmin(ret, dat[r]);l = l + 1 >> 1;r = r - 1 >> 1;}if(l == r) ret = cmin(ret, dat[l]);return ret;}
}tre;int main()
{scanf("%d%d", &n, &m);rep(i, m) scanf("%d%d%d%d", &t[i], &l[i], &r[i], &c[i]);rep(i, m) {cx[i] = l[i] - t[i];cy[i] = l[i] + t[i];qx[i] = r[i] - t[i] + 1;qy[i] = r[i] + t[i] + 1;}rep(i, m) xval[i] = MP(cx[i], i);sort(xval, xval + m);rep(i, m) {cx[i] = lower_bound(xval, xval + m, MP(cx[i], i)) - xval;qx[i] = lower_bound(xval, xval + m, MP(qx[i], m)) - xval - 1;}rep(i, m) dp[i] = INF;LL ans = INF;tre.build();priority_queue<pair<LL, int> > que;rep(i, m) if(l[i] == 1) {dp[i] = c[i];que.push(MP(-dp[i], i));tre.erase(i);}while(!que.empty()) {int v = que.top().second;que.pop();if(r[v] == n) {printf("%lld\n", dp[v]);return 0;}while(true) {int i = tre.query(qx[v]);if(i == -1 || cy[i] > qy[v]) break;tre.erase(i);dp[i] = dp[v] + c[i];que.push(MP(-dp[i], i));}}printf("-1\n");return 0;
}

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