「CSP-S 2021」

A. 廊桥分配

签到题，注意数据范围贪心即可.

A_code

#include <bits/stdc++.h>
using namespace std;
namespace BSS
{
#define ll long long
#define lf double
#define ull unsigned ll
#define mp make_pair
#define lb lower_bound
#define ub upper_bound
#define lbt(x) ((x) & (-(x)))
#define Fill(x, y) memset(x, y, sizeof(x))
#define Copy(x, y) memcpy(x, y, sizeof(x))
#define File(x) freopen(#x ".in", "r", stdin), freopen(#x ".out", "w", stdout)
	auto read = []() -> ll
	{
		ll w = 0;
		char ch;
		bool cit = 1;
		while (!isdigit(ch = getchar()))
			if (ch == '-')
				cit = 0;
		while (isdigit(ch))
			w = (w << 3) + (w << 1) + (ch ^ 48), ch = getchar();
		return cit ? w : (-w);
	};
}
using namespace BSS;
const ll N = 2e5 + 21;
ll n, alls;
ll m[3], sum[3];
ll ans[3][N], pre[3][N];
set<pair<ll, ll>> s;
auto Work = [](ll op) -> void
{
	ll a, b, cnt = 0;
	for (ll i = 1; i <= m[op]; i++)
	{
		a = read(), b = read();
		s.insert(mp(a, b));
	}
	while (s.size())
	{
		auto it = s.begin();
		s.erase(it);
		auto it2 = s.lb(mp(it->second, 0));
		ans[op][++cnt] = 1;
		while (it2 != s.end())
		{
			b = it2->second, s.erase(it2);
			it2 = s.lb(mp(b, 0));
			ans[op][cnt]++;
		}
	}
	sum[op] = cnt;
};
signed main()
{
	n = read(), m[0] = read(), m[1] = read();
	Work(0), Work(1);
	for (ll i = 1; i <= n; i++)
		pre[0][i] = pre[0][i - 1] + ans[0][i];
	for (ll i = 1; i <= n; i++)
		pre[1][i] = pre[1][i - 1] + ans[1][i];
	for (ll i = 0; i <= n; i++)
		alls = max(alls, pre[0][i] + pre[1][n - i]);
	printf("%lld\n", alls), exit(0);
}

B. 括号序列

看错题，基本没怎么向正确的方向思考.

B_code

#include<bits/stdc++.h>
using namespace std;
namespace BSS{
	#define ll long long 
	#define lf double
	#define ull unsigned ll 
	#define mp make_pair
	#define lb lower_bound
	#define ub upper_bound
	#define lbt(x) ((x)&(-(x)))
	#define Fill(x,y) memset(x,y,sizeof(x))
	#define Copy(x,y) memcpy(x,y,sizeof(x))
	#define File(x) freopen(#x".in","r",stdin),freopen(#x".out","w",stdout)
	auto read=[]()->ll{
		ll w=0; char ch; bool cit=1;
		while(!isdigit(ch=getchar())) if(ch=='-') cit=0;
		while(isdigit(ch)) w=(w<<3)+(w<<1)+(ch^48),ch=getchar();
		return cit?w:(-w);
	};
}using namespace BSS;

const ll N=1005,mod=1e9+7;

char ch[N];
ll m,n;
ll c[N];
ll f[N][N],g[N][N],s[N][N];
inline void inc(ll &x,ll y){ x=(x+y)%mod; }
signed main(){
	n=read(),m=read(); scanf("%s",ch+1); ll lst;
	for(ll i=1;i<=n;i++){
		if(ch[i]=='(') c[i]=1;
		if(ch[i]=='*') c[i]=2;
		if(ch[i]==')') c[i]=4;
		if(ch[i]=='?') c[i]=7;
		s[i][i]=((c[i]&2)>0),s[i][i-1]=1;
		for(ll j=i-1;j>=1;j--)
			if(!(s[j][i]=(s[j+1][i]&((c[j]&2)>0)))) break;
	}
	for(ll i=1,j=2;j<=n;i++,j++){
		if((c[i]&1) and (c[j]&4)) f[i][j]=1;
	}
	for(ll k=3;k<=n;k++){
		for(ll l=1,r=l+k-1;r<=n;l++,r++){
			if((!(c[l]&1)) or (!(c[r]&4))) continue;
			if(r-l-1<=m) inc(f[l][r],s[l+1][r-1]);
			inc(f[l][r],f[l+1][r-1]+g[l+1][r-1]);
			for(ll i=1;i<=min(m,k);i++){
				if(s[l+1][l+i]) inc(f[l][r],f[l+i+1][r-1]+g[l+i+1][r-1]);
				if(s[r-i][r-1]) inc(f[l][r],f[l+1][r-i-1]+g[l+1][r-i-1]);
			}	
			lst=0;
			for(ll i=l+1,j=i+1;i<r;i++,j=max(i+1,j)){
				while(j<r and j-i-1<=m and s[i+1][j-1]) inc(lst,f[j][r]),j++;
				inc(g[l][r],(f[l][i]+g[l][i])*lst%mod),lst=(lst-f[i+1][r]+mod)%mod;
			}
		}
	}
	printf("%lld\n",(f[1][n]+g[1][n])%mod);
	exit(0);
}

C. 回文

不是很难，像个模拟.

C_code

#include<bits/stdc++.h>
using namespace std;
namespace BSS{
	#define ll int
	#define lf double
	#define ull unsigned ll
	#define mp make_pair
	#define lb lower_bound
	#define ub upper_bound
	#define lbt(x) ((x)&(-(x)))
	#define Fill(x,y) memset(x,y,sizeof(x))
	#define Copy(x,y) memcpy(x,y,sizeof(x))
	#define File(x) freopen(#x".in","r",stdin),freopen(#x".out","w",stdout)
	auto read=[]()->ll{
		ll w=0; bool cit=1; char ch;
		while(!isdigit(ch=getchar())) if(ch=='-') cit=0;
		while(isdigit(ch)) w=(w<<3)+(w<<1)+(ch^48),ch=getchar();
		return cit?w:(-w);
	};
} using namespace BSS;

const ll N=1e6+21;

char ans[N];

ll m,n,cnt,head,tail;
ll c[N],o[N],val[N],vis[N];
ll pos[2][N];
auto Work=[]()->void{
	n=read(),m=n<<1,cnt=0,c[m+1]=0; ll x,y,flag=1;
	for(ll i=0;i<=n;i++) vis[i]=0;
	for(ll i=1;i<=m;i++) c[i]=read(),pos[vis[c[i]]][c[i]]=i,vis[c[i]]=1,o[i]=c[i];
	val[1]=1,c[1]=0,val[m]=1; head=1,tail=m; 
	for(ll i=2,l=pos[1][o[1]],r=l;i<=n;i++){
		while(!c[head]) head++; while(!c[tail]) tail--;
		x=c[l-1],y=c[r+1];
		// cout<<l<<' '<<r<<' '<<x<<' '<<y<<endl;
		if(x!=c[head] and y!=c[head] and x!=c[tail] and y!=c[tail]){ flag=0; break ; } 
		if(x==c[head] and l-1>head) { c[head]=0,l--,val[i]=1,val[m-i+1]=1; continue; }
		if(y==c[head] and r+1>head) { c[head]=0,r++,val[i]=1,val[m-i+1]=2; continue; }
		if(x==c[tail] and l-1<tail) { c[tail]=0,l--,val[i]=2,val[m-i+1]=1; continue; }
		if(y==c[tail] and r+1<tail) { c[tail]=0,r++,val[i]=2,val[m-i+1]=2; continue; }
		flag=0; break;
	}
	if(flag){
		for(ll i=1;i<=m;i++)
			putchar( (val[i]&1) ? 'L' : 'R' );
		puts(""); return ;
	}
	reverse(o+1,o+1+m); flag=1;
	for(ll i=0;i<=n;i++) vis[i]=0;
	for(ll i=1;i<=m;i++) c[i]=o[i],pos[vis[c[i]]][c[i]]=i,vis[c[i]]=1,val[i]=0;
	val[1]=1,c[1]=0,val[m]=2; head=1,tail=m; 
	for(ll i=2,l=pos[1][o[1]],r=l;i<=n;i++){
		while(!c[head]) head++; while(!c[tail]) tail--;
		x=c[l-1],y=c[r+1];
		// cout<<l<<' '<<r<<' '<<x<<' '<<y<<endl;
		if(x!=c[head] and y!=c[head] and x!=c[tail] and y!=c[tail]){ flag=0; break ; } 
		if(y==c[tail] and r+1<tail) { c[tail]=0,r++,val[i]=2,val[m-i+1]=2; continue; }
		if(x==c[tail] and l-1<tail) { c[tail]=0,l--,val[i]=2,val[m-i+1]=1; continue; }
		if(y==c[head] and r+1>head) { c[head]=0,r++,val[i]=1,val[m-i+1]=2; continue; }
		if(x==c[head] and l-1>head) { c[head]=0,l--,val[i]=1,val[m-i+1]=1; continue; }
		flag=0; break;
	}
	if(flag){
		for(ll i=1;i<=m;i++)
			putchar( (val[i]&1) ? 'R' : 'L' );
		puts(""); return ;
	}
	puts("-1");
};
signed main(){
	for(int Ts=read();Ts;Ts--) Work();
	exit(0);
}

D. 交通规划

不会，先鸽.