2019 牛客多校第一场 A Equivalent Prefixes

题目链接：https://ac.nowcoder.com/acm/contest/881/A

题目大意

　　定义 RMQ(u, L, R) 为 u 数组在区间 [L, R] 上最小值的下标。

　　如果有 2 个数组 u，v，长度都为 m，且元素值互不相同，对于 [1, m] 的任意一个子区间 [L, R]，都有 RMQ(u, L, R) = RMQ(v, L, R)，那我们就说这两个数组是同构的。

　　现给定 2 个数组 a, b，求最大的 p，使得 a，b 在 [1, p] 上同构。

分析

　　假设 p 现在取到 i，这个时候遍历到 i + 1 项，如果 a[i + 1] 和 b[i + 1] 都是前 i + 1 项的第 k 小，那么 p 就可以加一，因为这时数组在以 i + 1 为右区间的所有区间上都满足条件（如果 [L, i + 1] 最小值的下标不是 i + 1，那么成立，因为前 i 项也是这么过来的，都满足条件；如果 [L, i + 1] 最小值的下标是 i + 1，根据前提，两数组最小值的下标就是 i + 1，也成立）。

　　一旦 i + 1 项不满足，那么 p 的最大就是 i，这个就不赘述了，找个例子或者自行理解。

代码如下

 #include <bits/stdc++.h>
 using namespace std;

 #define INIT() ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
 #define Rep(i,n) for (int i = 0; i < (n); ++i)
 #define For(i,s,t) for (int i = (s); i <= (t); ++i)
 #define rFor(i,t,s) for (int i = (t); i >= (s); --i)
 #define ForLL(i, s, t) for (LL i = LL(s); i <= LL(t); ++i)
 #define rForLL(i, t, s) for (LL i = LL(t); i >= LL(s); --i)
 #define foreach(i,c) for (__typeof(c.begin()) i = c.begin(); i != c.end(); ++i)
 #define rforeach(i,c) for (__typeof(c.rbegin()) i = c.rbegin(); i != c.rend(); ++i)

 #define pr(x) cout << #x << " = " << x << "  "
 #define prln(x) cout << #x << " = " << x << endl

 #define LOWBIT(x) ((x)&(-x))

 #define ALL(x) x.begin(),x.end()
 #define INS(x) inserter(x,x.begin())
 #define UNIQUE(x) x.erase(unique(x.begin(), x.end()), x.end())
 #define REMOVE(x, c) x.erase(remove(x.begin(), x.end(), c), x.end()); // 删去 x 中所有 c
 #define TOLOWER(x) transform(x.begin(), x.end(), x.begin(),::tolower);
 #define TOUPPER(x) transform(x.begin(), x.end(), x.begin(),::toupper);

 #define ms0(a) memset(a,0,sizeof(a))
 #define msI(a) memset(a,inf,sizeof(a))
 #define msM(a) memset(a,-1,sizeof(a))

 #define MP make_pair
 #define PB push_back
 #define ft first
 #define sd second

 template<typename T1, typename T2>
 istream &operator>>(istream &in, pair<T1, T2> &p) {
     in >> p.first >> p.second;
     return in;
 }

 template<typename T>
 istream &operator>>(istream &in, vector<T> &v) {
     for (auto &x: v)
         in >> x;
     return in;
 }

 template<typename T>
 ostream &operator<<(ostream &out, vector<T> &v) {
     Rep(i, v.size()) out << v[i] << " \n"[i == v.size()];
     return out;
 }

 template<typename T1, typename T2>
 ostream &operator<<(ostream &out, const std::pair<T1, T2> &p) {
     out << "[" << p.first << ", " << p.second << "]" << "\n";
     return out;
 }

 inline int gc(){
     static const int BUF = 1e7;
     static char buf[BUF], *bg = buf + BUF, *ed = bg;

     if(bg == ed) fread(bg = buf, , BUF, stdin);
     return *bg++;
 } 

 inline int ri(){
     int x = , f = , c = gc();
     for(; c<||c>; f = c=='-'?-:f, c=gc());
     for(; c>&&c<; x = x* + c - , c=gc());
     return x*f;
 }

 template<class T>
 inline string toString(T x) {
     ostringstream sout;
     sout << x;
     return sout.str();
 }

 inline int toInt(string s) {
     int v;
     istringstream sin(s);
     sin >> v;
     return v;
 }

 //min <= aim <= max
 template<typename T>
 inline bool BETWEEN(const T aim, const T min, const T max) {
     return min <= aim && aim <= max;
 }

 typedef long long LL;
 typedef unsigned long long uLL;
 typedef pair< double, double > PDD;
 typedef pair< int, int > PII;
 typedef pair< int, PII > PIPII;
 typedef pair< string, int > PSI;
 typedef pair< int, PSI > PIPSI;
 typedef set< int > SI;
 typedef set< PII > SPII;
 typedef vector< int > VI;
 typedef vector< double > VD;
 typedef vector< VI > VVI;
 typedef vector< SI > VSI;
 typedef vector< PII > VPII;
 typedef map< int, int > MII;
 typedef map< int, string > MIS;
 typedef map< int, PII > MIPII;
 typedef map< PII, int > MPIII;
 typedef map< string, int > MSI;
 typedef map< string, string > MSS;
 typedef map< PII, string > MPIIS;
 typedef map< PII, PII > MPIIPII;
 typedef multimap< int, int > MMII;
 typedef multimap< string, int > MMSI;
 //typedef unordered_map< int, int > uMII;
 typedef pair< LL, LL > PLL;
 typedef vector< LL > VL;
 typedef vector< VL > VVL;
 typedef priority_queue< int > PQIMax;
 typedef priority_queue< int, VI, greater< int > > PQIMin;
 const double EPS = 1e-;
 const LL inf = 0x7fffffff;
 const LL infLL = 0x7fffffffffffffffLL;
 const LL mod = 1e9 + ;
 const int maxN = 1e5 + ;
 const LL ONE = ;
 const LL evenBits = 0xaaaaaaaaaaaaaaaa;
 const LL oddBits = 0x5555555555555555;

 int n, a[maxN], b[maxN], ans; 

 void solve(VPII &x, PII &y) {
     while(!x.empty() && y.ft < x.back().ft) x.pop_back();
     x.PB(y);
 }

 int main(){
     //freopen("MyOutput.txt","w",stdout);
     //freopen("input.txt","r",stdin);
     //INIT();
     while(~scanf("%d", &n)) {
         For(i, , n) scanf("%d", &a[i]);
         For(i, , n) scanf("%d", &b[i]);

         VPII sta, stb;
         ans = n;

         For(i, , n) {
             PII x(a[i], i);
             solve(sta, x);

             x = PII(b[i], i);
             solve(stb, x);

             if(sta.size() != stb.size() || sta.back().sd != stb.back().sd) {
                 ans = i - ;
                 break;
             }
         }

         printf("%d\n", ans);
     }
     return ;
 }