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\n", 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\n",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\n",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("\n-------cdq %d %d\n",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\n", 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\n",i,j,idx[i][j]);
//for(int j=1; j<=m; j++) for(int i=1; i<=n; i++) printf("idy %d %d %d\n",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\n",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\n",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 \n",i,L[i],R[i]);
//for(int i=2; i<=dfc; i++) printf("val %d %d\n",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\n", i, u, suf[u]);
}
}
bool check(int len, int l, int r, int x) { //printf("check %d [%d, %d] %d\n", 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\n",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("\nsolve %d %d %d %d\n",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\n", 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\n",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()]);
}
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