树hash
#include <cctype>
#include <chrono>
#include <cstdio>
#include <random>
#include <set>
#include <vector>
typedef unsigned long long ull;
const ull mask = std::chrono::steady_clock::now().time_since_epoch().count();
ull shift(ull x) {
x ^= mask;
x ^= x << 13;
x ^= x >> 7;
x ^= x << 17;
x ^= mask;
return x;
}
const int N = 1e6 + 10;
int n;
ull hash[N];
std::vector<int> edge[N];
std::set<ull> trees;
void getHash(int x, int p) {
hash[x] = 1;
for (int i : edge[x]) {
if (i == p) {
continue;
}
getHash(i, x);
hash[x] += shift(hash[i]);
}
trees.insert(hash[x]);
}
int main() {
scanf("%d", &n);
for (int i = 1; i < n; i++) {
int u, v;
scanf("%d%d", &u, &v);
edge[u].push_back(v);
edge[v].push_back(u);
}
getHash(1, 0);
printf("%lu", trees.size());
}
本质不同子序列数量
#include<iostream>
#include<algorithm>
using namespace std;
const int mod=1e9+7;
int n;
const int maxn=1e6+100;
int dp[maxn];
int a[maxn];
int last[maxn];
int main(){
cin>>n;
for(int i=1;i<=n;i++){
cin>>a[i];
}
for(int i=1;i<=n;i++){
if(!last[a[i]]){
dp[i]=dp[i-1]*2+1;
}
else{
dp[i]=(dp[i-1]*2-dp[last[a[i]]-1]);
}
dp[i]=(dp[i]+mod)%mod;
last[a[i]]=i;
}
cout<<dp[n]<<endl;
}
随机hash
#include <bits/stdc++.h>
using i64 = long long;
bool isprime(int n) {
if (n <= 1) {
return false;
}
for (int i = 2; i * i <= n; i++) {
if (n % i == 0) {
return false;
}
}
return true;
}
int findPrime(int n) {
while (!isprime(n)) {
n++;
}
return n;
}
int main() {
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
std::mt19937 rng(std::chrono::steady_clock::now().time_since_epoch().count());
const int P = findPrime(rng() % 900000000 + 100000000);
return 0;
}
ac自动机
Ac自动机
#include<cstdio>
#include<algorithm>
#include<iostream>
#include<queue>
#include<cstring>
#define fo(i,a,b) for (ll (i)=(a);(i)<=(b);(i)++)
#define fd(i,b,a) for (ll (i)=(b);(i)>=(a);(i)--)
#define eb emplace_back
using namespace std;
typedef long long ll;
const int N=2e6+5;
const ll mo=1e9+7;
int ch[N][26],now,cnt,l,n,c,size[N],id[N],f[N],g[N];
char s[N];
vector<int> e[N];
queue<int> q;
void ins(int x){
now=0;
fo(i,1,l) {
c=s[i]-'a';
if (!ch[now][c]) ch[now][c]=++cnt;
now=ch[now][c];
}
id[x]=now;
}
void build(){
int r,u,v;
fo(i,0,25) if (ch[0][i]) q.push(ch[0][i]);
while (!q.empty()) {
r=q.front(); q.pop();
fo(i,0,25) {
u=ch[r][i];
if (!u) {
ch[r][i]=ch[f[r]][i];
continue;
}
v=f[r];
while (v && !ch[v][i]) v=f[v];
f[u]=ch[v][i];
q.push(u);
}
}
}
void match() {
now=0;
fo(i,1,l) {
c=s[i]-'a';
now=ch[now][c];
g[now]++;
}
}
void dfs(int x){
for (int v:e[x]) {
dfs(v);
g[x]+=g[v];
}
}
int main(){
// freopen("data.in","r",stdin);
scanf("%d",&n);
fo(i,1,n) {
scanf("%s",s+1);
l=strlen(s+1);
ins(i);
}
build();
scanf("%s",s+1);
l=strlen(s+1);
match();
fo(i,1,cnt) e[f[i]].eb(i);
dfs(0);
fo(i,1,n) printf("%d\n", g[id[i]]);
return 0;
}
广义矩阵乘法+ac自动机
#include<bits/stdc++.h>
#define mk(x,y) make_pair((x),(y))
#define ll long long
#define fo(i,a,b) for (ll (i)=(a);(i)<=(b);(i)++)
#define fd(i,b,a) for (ll (i)=(b);(i)>=(a);(i)--)
using namespace std;
ll n, m, v, now, cnt;
const ll inf = 1ll << 60;
const int N=1000;
string s;
int ch[N][26];
ll val[N],f[N];
queue<int> q;
void cmax(ll & x, ll y) {
x = max(x, y);
}
struct mat {
ll a[205][205];
void init() {
fo(i, 0, cnt) fo(j, 0, cnt) a[i][j] = 0;
}
void initMin() {
fo(i, 0, cnt) fo(j, 0, cnt) a[i][j] = -inf;
}
void print() {
fo(i,0,cnt) {
fo(j,0,cnt) {
cout<<a[i][j]<<" ";
}
cout<<"\n";
}
}
};
mat A,t;
mat operator * (mat& a, mat& b) {
mat c;
c.initMin();
fo(i, 0, cnt) fo(j, 0, cnt) fo(k, 0, cnt) {
cmax(c.a[i][j], a.a[i][k] + b.a[k][j]);
}
return c;
}
void ins() {
now = 0;
int c;
for (int i=0;i<(int)s.length();i++) {
c = s[i] - 'a';
if (!ch[now][c]) ch[now][c] = ++cnt;
now = ch[now][c];
}
val[now] += v;
}
void build() {
fo(i, 0, 25) if (ch[0][i]) q.push(ch[0][i]);
while (!q.empty()) {
int r = q.front(); q.pop();
fo(i, 0, 25) {
int u = ch[r][i];
if (!u) {
ch[r][i] = ch[f[r]][i]; continue;
}
v = f[r];
while (v && !ch[v][i]) v = f[v];
f[u] = ch[v][i];
val[u] += val[f[u]];
q.push(u);
}
}
}
void power(ll b) {
while (b) {
if (b & 1) t = t * A;
A = A * A;
b /= 2;
}
}
signed main() {
// freopen("data.in","r",stdin);
ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
cin >> n >> m;
fo(i, 1, m) {
cin >> s >> v;
ins();
}
build();
A.initMin();
fo(i, 0, cnt) {
fo(j, 0, 25) {
A.a[ch[i][j]][i] = val[ch[i][j]];
}
}
t.init();
fo(i, 1, cnt) t.a[i][0] = -inf;
power(n);
ll ans = -inf;
fo(i, 0, cnt) ans = max(ans, t.a[i][0]);
cout << ans;
return 0;
}
P5787 二分图 /【模板】线段树分治
#include<bits/stdc++.h>
#define fo(i,a,b) for (int (i)=(a);(i)<=(b);(i)++)
#define fd(i,b,a) for (int (i)=(b);(i)>=(a);(i)--)
#define eb emplace_back
#define lc (o<<1)
#define rc ((o<<1)|1)
#define A puts("Yes")
#define B puts("No")
using namespace std;
typedef long long ll;
typedef double db;
const int N=5e5+5;
int f[N],s[N],n,x,y,top,m,k,f1,f2,ans[N];
struct node{
int x,y;
};
node st[N];
vector<node> e[N*4];
int find(int x){
if (x==f[x]) return x;
return find(f[x]);
}
void merge(int x,int y){
f1=find(x); f2=find(y);
if (s[f1]<s[f2]) swap(f1,f2);
f[f2]=f1;
s[f1]+=s[f2];
st[++top]=(node){f1,f2};
}
void del(int now){
while (top>now) {
f1=st[top].x; f2=st[top].y; top--;
s[f1]-=s[f2];
f[f2]=f2;
}
}
void upd(int o,int l,int r,int x,int y,int u,int v){
if (x>y) return;
if (x<=l && r<=y) {
e[o].eb((node){u,v});
return;
}
int m=(l+r)>>1;
if (x<=m) upd(lc,l,m,x,y,u,v);
if (m<y) upd(rc,m+1,r,x,y,u,v);
}
void ask(int o,int l,int r){
int now=top;
bool flag=1;
for (int i=0;i<(int)e[o].size();i++) {
f1=find(e[o][i].x); f2=find(e[o][i].y);
if (f1==f2) {
flag=0;
break;
}
merge(e[o][i].x, e[o][i].y+n);
merge(e[o][i].x+n, e[o][i].y);
}
if (flag) {
if (l==r) {
ans[l]=1;
}
else {
int m=(l+r)>>1;
ask(lc,l,m);
ask(rc,m+1,r);
}
}
del(now);
}
int main(){
// freopen("data.in","r",stdin);
int l,r;
scanf("%d %d %d",&n,&m,&k);
fo(i,1,n*2) {
f[i]=i; s[i]=1;
}
fo(i,1,m) {
scanf("%d %d %d %d",&x,&y,&l,&r);
upd(1,1,k,l+1,r,x,y);
}
ask(1,1,k);
fo(i,1,k) if (ans[i]) A; else B;
return 0;
}
