cf1213F. Unstable String Sort

链接

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题解

建图跑$tarjan$然后拓扑排序

代码

#include 
#include 
#include 
#define iinf 0x3f3f3f3f
#define linf (1ll<<60)
#define eps 1e-8
#define maxn 1000010
#define maxe 1000010
#define cl(x) memset(x,0,sizeof(x))
#define rep(_,__) for(_=1;_<=(__);_++)
#define em(x) emplace(x)
#define emb(x) emplace_back(x)
#define emf(x) emplace_front(x)
#define fi first
#define se second
using namespace std;
using namespace __gnu_pbds;
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
ll read(ll x=0)
{
    ll c, f(1);
    for(c=getchar();!isdigit(c);c=getchar())if(c=='-')f=-f;
    for(;isdigit(c);c=getchar())x=x*10+c-0x30;
    return f*x;
}
struct Graph
{
    int etot, head[maxn], to[maxe], next[maxe], w[maxe];
    void clear(int N)
    {
        for(int i=1;i<=N;i++)head[i]=0;
        etot=0;
    }
    void adde(int a, int b, int c=0){to[++etot]=b;w[etot]=c;next[etot]=head[a];head[a]=etot;}
    #define forp(_,__) for(auto p=__.head[_];p;p=__.next[p])
}G, G2;
struct Trajan_SCC
{
    int dfn[maxn], low[maxn], vis[maxn], scc[maxn], tim, scc_cnt;
    stack<int> s;
    void clear(int n)
    {
        for(int i=1;i<=n;i++)vis[i]=0;
        tim=scc_cnt=0;
    }
    void dfs(Graph &G, int pos)
    {
        int p;
        dfn[pos]=low[pos]=++tim;
        s.emplace(pos);
        vis[pos]=1;
        for(p=G.head[pos];p;p=G.next[p])
        {
            if(vis[G.to[p]]==0)dfs(G,G.to[p]);
            if(vis[G.to[p]]==1)low[pos]=min(low[pos],low[G.to[p]]);
        }
        if(dfn[pos]==low[pos])
        {
            int x;
            scc_cnt++;
            do
            {
                x=s.top(), s.pop();
                scc[x]=scc_cnt;
                vis[x]=2;
            }
            while(x!=pos);
        }
    }
    void run(Graph &G, int n)
    {
        for(int i=1;i<=n;i++)if(!vis[i])dfs(G,i);
    }
}tarjan;
struct TopologicalSort
{
    int ord[maxn], indeg[maxn], cnt=0;
    void init(int n){int i;rep(i,n)indeg[i]=0;cnt=0;}
    void run(Graph& G, int n)
    {
        int i;
        queue<int> q;
        rep(i,n)if(indeg[i]==0)q.em(i);
        while(!q.empty())
        {
            auto x=q.front(); q.pop();
            ord[x]=++cnt;
            forp(x,G)
            {
                indeg[G.to[p]]--;
                if(!indeg[G.to[p]])q.em(G.to[p]);
            }
        }
    }
}topo;
ll n, p[maxn], q[maxn], ans[maxn], k;
int main()
{
    ll i, j;
    n=read(), k=read();
    rep(i,n)p[i]=read();
    rep(i,n)q[i]=read();
    rep(i,n-1)G.adde(p[i+1],p[i]);
    rep(i,n-1)G.adde(q[i+1],q[i]);
    tarjan.run(G,n);
    if(tarjan.scc_cnt<k)
    {
        printf("NO");
        return 0;
    }
    printf("YES\n");
    rep(i,n)
    {
        forp(i,G)
        {
            if(tarjan.scc[G.to[p]] != tarjan.scc[i])
                G2.adde(tarjan.scc[i],tarjan.scc[G.to[p]]),
                topo.indeg[tarjan.scc[G.to[p]]]++;
        }
    }
    topo.init(tarjan.scc_cnt);
    topo.run(G2,tarjan.scc_cnt);
    rep(i,n)
    {
        if(topo.ord[tarjan.scc[i]]<=k)
        {
            putchar('a'+topo.ord[tarjan.scc[i]]-1);
        }
        else putchar('z');
    }
    return 0;
}