HEOI2016 题解

HEOI2016 题解

• Q:为什么要在sdoi前做去年的heoi题
• A:我省选药丸

http://cogs.pro/cogs/problem/index.php?key=heoi2016

D1T1 树

树剖直接做

或者操作逆序，并查集维护自己和祖先中第一个打标记的点，注意1号点本身有标记，mark[1]++

代码在最后

D1T2排序

计数排序拿80...

二分答案，(ge)设为1，(<)设为0，排序就可以用线段树模拟了. 鏼鏼鏼！

代码还没写

D1T3序列

md一开始看错题了

写出(O(n^2))的DP，发现裸三维偏序啊，(j<i, max_j < a_i, a_j < min_i)

注意最后调用cdq(mid+1, r)前按id排一下序

cdq真是太棒了！

代码在最后

D2T1游戏

二分图匹配...

硬石头把一行拆成了好几个点...

代码在最后

D2T2求和

以前做了

D2T3字符串

题意：多次询问(S[a,b])的所有子串与(S[c,d])的LCP

40分(O(n^2))暴力 每次重构sam

一开始想的是，反转后建sam，建出Parent Tree，往上找第一个Right集合中有[a,b]的节点。问题在于限制了在[a,b]范围内，不一定是越深的祖先越好因为到b就截断了

考虑二分lcp长度，那么变成了判断Right有没有[a+len-1, b]范围内的点(注意我反转了字符串)

这样就可以倍增了，判断可以对dfs序建主席树权值是后缀

但这样是三个log

其实等价于我们先倍增到val>=len的最浅的点，看看Right集合里有没有，这样就是两个log了

代码

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
using namespace std;
typedef long long ll;
const int N=1e5+5;
inline int read(){
    char c=getchar();int x=0,f=1;
    while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
    while(c>='0'&&c<='9'){x=x*10+c-'0';c=getchar();}
    return x*f;
}
int n, Q, fa[N], u, v, f[N], ans[N], m, mark[N];
int find(int x) {return x==fa[x] ? x : fa[x]=find(fa[x]);}
struct meow{char s[5]; int x, id;} q[N];

struct edge{int v, ne;} e[N];
int cnt=1, h[N];
inline void ins(int u, int v) {e[++cnt]=(edge){v, h[u]}; h[u]=cnt;}
namespace graph {
	int q[N], head, tail;
	void bfs() {
		head=tail=1;
		q[tail++]=1;
		while(head != tail) {
			int u=q[head++];
			if(!fa[u]) fa[u] = find(f[u]);
			for(int i=h[u];i;i=e[i].ne) q[tail++] = e[i].v;
		}
	}
}

int main() {
	//freopen("in","r",stdin);
	freopen("heoi2016_tree.in","r",stdin);
	freopen("heoi2016_tree.out","w",stdout);
	n=read(); Q=read();
	fa[1]=1; mark[1]++;
	for(int i=1; i<n; i++) u=read(), v=read(), f[v]=u, ins(u, v);
	for(int i=1; i<=Q; i++) {
		scanf("%s", q[i].s), q[i].x=read();
		if(q[i].s[0] == 'C') fa[ q[i].x ] = q[i].x, mark[ q[i].x ]++;
		else q[i].id=++m;
	}
	graph::bfs();
	for(int i=Q; i>=1; i--) {
		if(q[i].s[0] == 'C') {
			mark[ q[i].x ]--;
			if(!mark[ q[i].x ]) fa[ q[i].x ] = find(f[q[i].x]);
		}else ans[q[i].id] = find(q[i].x);
	}
	for(int i=1; i<=m; i++) printf("%d
", ans[i]);
}

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
using namespace std;
typedef long long ll;
const int N=1e5+5;
inline int read(){
    char c=getchar();int x=0,f=1;
    while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
    while(c>='0'&&c<='9'){x=x*10+c-'0';c=getchar();}
    return x*f;
}

int n, Q, x, y, f[N];
struct meow{int a, b, c, id;} a[N]; //max --> b, min --> c;
inline bool cmpb(const meow &a, const meow &b) {return a.b < b.b;}
inline bool cmpa(const meow &a, const meow &b) {return a.a < b.a;}
inline bool cmpid(const meow &a, const meow &b) {return a.id < b.id;}
namespace bit {
	int n, c[N], t[N], T;
	inline void ini() {T++; }
	inline void upd(int p, int v) { //printf("upd %d %d
",p,v);
		for(; p<=n; p+=p&-p) {
			if(t[p] != T) t[p]=T, c[p]=v;
			else if(c[p] < v) c[p]=v;
		}
	}
	inline int max(int p) { //printf("max %d
",p);
		int ans=0;
		for(; p; p-=p&-p) if(t[p] == T && c[p] > ans) ans = c[p];
		return ans;
	}
}
void cdq(int l, int r) { //printf("
-------cdq %d %d
",l,r);
	if(l==r) return;
	int mid=(l+r)>>1;
	cdq(l, mid);

	sort(a+l, a+mid+1, cmpb); sort(a+mid+1, a+r+1, cmpa);
	bit::ini();
	int p1=l, p2=mid+1;
	while(p1 <= mid || p2 <= r) {
		if(p2 > r || (p1 <= mid && a[p1].b <= a[p2].a) ) bit::upd(a[p1].a, f[a[p1].id]), p1++;
		else f[a[p2].id] = max(f[a[p2].id], bit::max(a[p2].c)+1), p2++; //printf("p2  %d  %d %d
", p2, a[p2].id, f[a[p2].id]),p2++;
	}

	sort(a+mid+1, a+r+1, cmpid);
	cdq(mid+1, r);
}
int main() {
	//freopen("in","r",stdin);
	freopen("heoi2016_seq.in","r",stdin);
	freopen("heoi2016_seq.out","w",stdout);
	n=read(); Q=read();
	for(int i=1; i<=n; i++) x=read(), a[i]=(meow){x, x, x, i}, f[i]=1, bit::n = max(bit::n, x);
	for(int i=1; i<=Q; i++) x=read(), y=read(), a[x].b = max(a[x].b, y), a[x].c = min(a[x].c, y), bit::n = max(bit::n, y);
	cdq(1, n);
	int ans=0;
	for(int i=1; i<=n; i++) ans = max(ans, f[i]);// printf("%d ",f[i]); puts(" f");
	printf("%d", ans);
}

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
using namespace std;
typedef long long ll;
const int N=5100, M=1e5+5, INF=1e9+5;
inline int read(){
    char c=getchar();int x=0,f=1;
    while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
    while(c>='0'&&c<='9'){x=x*10+c-'0';c=getchar();}
    return x*f;
}

int n, m, s, t, X, Y, idx[55][55], idy[55][55]; 
char str[55][55];
namespace mf {
	struct edge{int v, ne, c, f;}e[M];
	int cnt=1, h[N];
	inline void ins(int u, int v, int c) {
		e[++cnt]=(edge){v, h[u], c, 0}; h[u]=cnt;
		e[++cnt]=(edge){u, h[v], 0, 0}; h[v]=cnt;
	}
	int q[N], head, tail, d[N], vis[N];
	bool bfs() {
		memset(vis, 0, sizeof(vis));
		head=tail=1;
		q[tail++]=s; d[s]=0; vis[s]=1;
		while(head != tail) {
			int u=q[head++];
			for(int i=h[u];i;i=e[i].ne) 
				if(!vis[e[i].v] && e[i].c>e[i].f) {
					vis[e[i].v]=1; 
					d[e[i].v] = d[u]+1;
					q[tail++]=e[i].v;
					if(e[i].v == t) return true;
				}
		}
		return false;
	}
	int cur[N];
	int dfs(int u, int a) {
		if(u==t || a==0) return a;
		int flow=0, f;
		for(int &i=cur[u];i;i=e[i].ne) 
			if(d[e[i].v] == d[u]+1 && (f = dfs(e[i].v, min(a, e[i].c-e[i].f)) )>0) {
				flow += f;
				e[i].f += f;
				e[i^1].f -= f;
				a -= f;
				if(a==0) break;
			}
		if(a) d[u]=-1;
		return flow;
	}
	int dinic() {
		int flow=0;
		while(bfs()) {
			for(int i=s; i<=t; i++) cur[i]=h[i];
			flow += dfs(s, INF);
		}
		return flow;
	}

	int g[N][N];
	void build() {
		for(int i=1; i<=n; i++) {
			X++; 
			for(int j=1; j<=m; j++) if(str[i][j] == '#') X++;
			else idx[i][j] = X;
		}
		Y=X;
		for(int j=1; j<=m; j++) {
			Y++;
			for(int i=1; i<=n; i++) if(str[i][j] == '#') Y++;
			else idy[i][j] = Y;
		}
		s=0; t=Y+1;

		//for(int i=1; i<=n; i++) for(int j=1; j<=m; j++) printf("idx %d %d   %d
",i,j,idx[i][j]);
		//for(int j=1; j<=m; j++) for(int i=1; i<=n; i++) printf("idy %d %d   %d
",i,j,idy[i][j]);
		int has[N];
		for(int i=1; i<=n; i++) 
			for(int j=1; j<=m; j++) if(str[i][j] == '*') 
				ins(idx[i][j], idy[i][j], 1), has[idx[i][j]]=1, has[idy[i][j]]=1;
		for(int i=1; i<=X; i++) if(has[i]) ins(s, i, 1);
		for(int i=X+1; i<=Y; i++) if(has[i]) ins(i, t, 1);
	}
}

int main() {
	//freopen("in","r",stdin);
	//freopen("heoi2016_game.in","r",stdin);
	//freopen("heoi2016_game.out","w",stdout);
	n=read(); m=read(); 
	for(int i=1; i<=n; i++) scanf("%s",str[i]+1);
	mf::build();
	int ans = mf::dinic();
	printf("%d", ans);
}

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
using namespace std;
typedef long long ll;
#define lc(x) t[x].l
#define rc(x) t[x].r
const int N=2e5+5;
inline int read(){
    char c=getchar();int x=0,f=1;
    while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
    while(c>='0'&&c<='9'){x=x*10+c-'0';c=getchar();}
    return x*f;
}

int n, Q, pos[N], a, b, c, d; 
char s[N];
namespace sam {
	struct meow{int ch[26], par, val;}t[N];
	int sz=1, last=1, root=1;
	int ri[N], suf[N];
	inline void extend(int c, int id) {
		int p=last, np=++sz; t[np].val = t[p].val+1; 
		pos[id] = np; suf[np] = id; //printf("id %d %d
",id,np);
		for(; p && !t[p].ch[c]; p=t[p].par) t[p].ch[c]=np;
		if(!p) t[np].par = root;
		else {
			int q = t[p].ch[c];
			if(t[q].val == t[p].val+1) t[np].par = q;
			else {
				int nq=++sz; t[nq]=t[q]; t[nq].val = t[p].val+1;
				t[q].par = t[np].par = nq;
				for(; p && t[p].ch[c]==q; p=t[p].par) t[p].ch[c]=nq;
			}
		}
		last=np;
	}
} using sam::suf; using sam::extend;

namespace tr {
	struct edge{int v, ne;} e[N];
	int cnt=1, h[N];
	inline void ins(int u, int v) { //printf("ins %d %d
",u,v);
		e[++cnt]=(edge){v, h[u]}; h[u]=cnt;}

	struct meow{int l, r, size;} t[N*20];
	int sz=0, root[N];
	inline void insert(int &x, int l, int r, int p) {
		t[++sz]=t[x]; x=sz;
		t[x].size++;
		if(l==r) return;
		int mid=(l+r)>>1;
		if(p<=mid) insert(lc(x), l, mid, p);
		else insert(rc(x), mid+1, r, p);
	}
	inline bool exist(int x, int y, int l, int r, int ql, int qr) {
		if(ql<=l && r<=qr) return t[y].size - t[x].size > 0;
		if(t[y].size - t[x].size == 0) return 0;
		int mid = (l+r)>>1, ans=0;
		if(ql<=mid) ans |= exist(lc(x), lc(y), l, mid, ql, qr);
		if(mid<qr ) ans |= exist(rc(x), rc(y), mid+1, r, ql, qr);
		return ans;
	}

	int fa[N][20], deep[N], L[N], R[N], dfc, ver[N]; // dfc = sam::sz
	int tot;
	void dfs(int u) {
		L[u]=++dfc; ver[dfc]=u;
		for(int i=1; (1<<i)<=deep[u]; i++)
			fa[u][i] = fa[ fa[u][i-1] ][i-1];
		for(int i=h[u];i;i=e[i].ne)
			if(e[i].v != fa[u][0]) {
				fa[e[i].v][0] = u;
				deep[e[i].v] = deep[u]+1;
				dfs(e[i].v);
			}
		R[u]=dfc;
	}

	void build() {
		//for(int i=1; i<=dfc; i++) printf("%d ",ver[i]); puts("");
		//for(int i=1; i<=dfc; i++) printf("lr %d %d %d 
",i,L[i],R[i]);
		//for(int i=2; i<=dfc; i++) printf("val %d %d
",i,sam::t[i].val);
		for(int i=1; i<=dfc; i++) {
			root[i] = root[i-1];
			int u=ver[i];
			if(suf[u]) insert(root[i], 1, n, suf[u]);// printf("suf %d --> %d --> %d
", i, u, suf[u]);
		}
	}
	bool check(int len, int l, int r, int x) { //printf("check %d  [%d, %d]  %d
", len, l, r, x);
		using sam::t;
		for(int i=17; i>=0; i--) 
			if(fa[x][i] && t[ fa[x][i] ].val >= len) x=fa[x][i];
		//printf("x %d  %d  L %d R %d
",x, t[x].val, L[x], R[x]);
		return exist(root[L[x]], root[R[x]], 1, n, l, r);
	}
	void solve(int a, int b, int c, int d) { //printf("
solve %d %d  %d %d
",a,b,c,d);
		int l=0, r=min(d-c+1, b-a+1), ans=-1;
		while(l<=r) {
			int mid=(l+r)>>1;
			if(check(mid, a+mid-1, b, pos[d])) ans=mid, l=mid+1;
			else r=mid-1;
		}
		printf("%d
", ans);
	}
}

int main() {
	//freopen("in","r",stdin);
	//freopen("heoi2016_str.in","r",stdin);
	//freopen("heoi2016_str.out","w",stdout);
	n=read(); Q=read(); scanf("%s", s+1);
	reverse(s+1, s+1+n);
	for(int i=1; i<=n; i++) extend(s[i]-'a', i);
	for(int i=2; i<= sam::sz; i++) tr::ins(sam::t[i].par, i);
	tr::dfs(1); tr::build();
	
	for(int i=1; i<=Q; i++) {
		a=n-read()+1; b=n-read()+1; c=n-read()+1; d=n-read()+1;
		swap(a, b); swap(c, d);
		tr::solve(a, b, c, d);
	}
}

sort的80分暴力

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
using namespace std;
typedef long long ll;
const int N=2e5+5;
inline int read(){
    char c=getchar();int x=0,f=1;
    while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
    while(c>='0'&&c<='9'){x=x*10+c-'0';c=getchar();}
    return x*f;
}

int n, Q, x, op, l, r, t1[N], t2[N];
int *a = t1, *b = t2;
int c[N], SIZE;
void csort(int *a, int m) { 
	memset(c, 0, SIZE);
	for(register int i=1; i<=m; i++) c[a[i]]++;// printf("%d ",a[i]); puts(" sort");
	for(register int i=1; i<=n; i++) c[i] += c[i-1];
	for(register int i=1; i<=m; i++) b[c[a[i]]--] = a[i];
	for(register int i=1; i<=m; i++) a[i]=b[i];// printf("b %d %d
",i,b[i]);
}
void rever(int l, int r) { while(l<r) swap(a[l++], a[r--]); }
int main() {
	//freopen("in","r",stdin);
	freopen("heoi2016_sort.in","r",stdin);
	freopen("heoi2016_sort.out","w",stdout);
	n=read(); Q=read(); SIZE = sizeof(int)*(n+1);
	for(int i=1; i<=n; i++) a[i]=read();
	for(int i=1; i<=Q; i++) {
		op=read(); l=read(); r=read();
		csort(a+l-1, r-l+1);
		if(op==1) rever(l, r);
		//for(int i=1; i<=n; i++) printf("%d ", a[i]); puts("");
	}
	printf("%d", a[read()]);
}