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Spies

Lo mismo que “Tree Matching” pero sobre un grafo funcional. Podemos usar la misma estrategia voraz de emparejar repetidamente una hoja con un vértice adyacente.

MLE:

#include <bits/stdc++.h> using namespace std; using ll = long long; using ld = long double; using db = double; using str = string; // yay python! using pi = pair<int, int>; using pl = pair<ll, ll>; using pd = pair<db, db>; using vi = vector<int>; using vb = vector<bool>; using vl = vector<ll>; using vd = vector<db>; using vs = vector<str>; using vpi = vector<pi>; using vpl = vector<pl>; using vpd = vector<pd>; #define tcT template <class T #define tcTU tcT, class U // ^ lol this makes everything look weird but I'll try it tcT > using V = vector<T>; tcT, size_t SZ > using AR = array<T, SZ>; tcT > using PR = pair<T, T>; // pairs #define mp make_pair #define f first #define s second // vectors // oops size(x), rbegin(x), rend(x) need C++17 #define sz(x) int((x).size()) #define bg(x) begin(x) #define all(x) bg(x), end(x) #define rall(x) x.rbegin(), x.rend() #define sor(x) sort(all(x)) #define rsz resize #define ins insert #define ft front() #define bk back() #define pb push_back #define eb emplace_back #define pf push_front #define lb lower_bound #define ub upper_bound tcT > int lwb(V<T> &a, const T &b) { return int(lb(all(a), b) - bg(a)); } // loops #define FOR(i, a, b) for (int i = (a); i < (b); ++i) #define F0R(i, a) FOR(i, 0, a) #define ROF(i, a, b) for (int i = (b) - 1; i >= (a); --i) #define R0F(i, a) ROF(i, 0, a) #define trav(a, x) for (auto &a : x) const int MOD = 1e9 + 7; // 998244353; const int MX = 2e5 + 5; const ll INF = 1e18; // not too close to LLONG_MAX const ld PI = acos((ld)-1); const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1}; // for every grid problem!! mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count()); template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>; // bitwise ops // also see https://gcc.gnu.org/onlinedocs/gcc/Other-Builtins.html constexpr int pct(int x) { return __builtin_popcount(x); } // # of bits set constexpr int bits(int x) { // assert(x >= 0); // make C++11 compatible until // USACO updates ... return x == 0 ? 0 : 31 - __builtin_clz(x); } // floor(log2(x)) constexpr int p2(int x) { return 1 << x; } constexpr int msk2(int x) { return p2(x) - 1; } ll cdiv(ll a, ll b) { return a / b + ((a ^ b) > 0 && a % b); } // divide a by b rounded up ll fdiv(ll a, ll b) { return a / b - ((a ^ b) < 0 && a % b); } // divide a by b rounded down tcT > bool ckmin(T &a, const T &b) { return b < a ? a = b, 1 : 0; } // set a = min(a,b) tcT > bool ckmax(T &a, const T &b) { return a < b ? a = b, 1 : 0; } tcTU > T fstTrue(T lo, T hi, U f) { hi++; assert(lo <= hi); // assuming f is increasing while (lo < hi) { // find first index such that f is true T mid = lo + (hi - lo) / 2; f(mid) ? hi = mid : lo = mid + 1; } return lo; } tcTU > T lstTrue(T lo, T hi, U f) { lo--; assert(lo <= hi); // assuming f is decreasing while (lo < hi) { // find first index such that f is true T mid = lo + (hi - lo + 1) / 2; f(mid) ? lo = mid : hi = mid - 1; } return lo; } tcT > void remDup(vector<T> &v) { // sort and remove duplicates sort(all(v)); v.erase(unique(all(v)), end(v)); } tcTU > void erase(T &t, const U &u) { // don't erase auto it = t.find(u); assert(it != end(t)); t.erase(it); } // element that doesn't exist from (multi)set // INPUT #define tcTUU tcT, class... U tcT > void re(complex<T> &c); tcTU > void re(pair<T, U> &p); tcT > void re(V<T> &v); tcT, size_t SZ > void re(AR<T, SZ> &a); tcT > void re(T &x) { cin >> x; } void re(db &d) { str t; re(t); d = stod(t); } void re(ld &d) { str t; re(t); d = stold(t); } tcTUU > void re(T &t, U &...u) { re(t); re(u...); } tcT > void re(complex<T> &c) { T a, b; re(a, b); c = {a, b}; } tcTU > void re(pair<T, U> &p) { re(p.f, p.s); } tcT > void re(V<T> &x) { trav(a, x) re(a); } tcT, size_t SZ > void re(AR<T, SZ> &x) { trav(a, x) re(a); } tcT > void rv(int n, V<T> &x) { x.rsz(n); re(x); } // TO_STRING #define ts to_string str ts(char c) { return str(1, c); } str ts(const char *s) { return (str)s; } str ts(str s) { return s; } str ts(bool b) { #ifdef LOCAL return b ? "true" : "false"; #else return ts((int)b); #endif } tcT > str ts(complex<T> c) { stringstream ss; ss << c; return ss.str(); } str ts(V<bool> v) { str res = "{"; F0R(i, sz(v)) res += char('0' + v[i]); res += "}"; return res; } template <size_t SZ> str ts(bitset<SZ> b) { str res = ""; F0R(i, SZ) res += char('0' + b[i]); return res; } tcTU > str ts(pair<T, U> p); tcT > str ts(T v) { // containers with begin(), end() #ifdef LOCAL bool fst = 1; str res = "{"; for (const auto &x : v) { if (!fst) res += ", "; fst = 0; res += ts(x); } res += "}"; return res; #else bool fst = 1; str res = ""; for (const auto &x : v) { if (!fst) res += " "; fst = 0; res += ts(x); } return res; #endif } tcTU > str ts(pair<T, U> p) { #ifdef LOCAL return "(" + ts(p.f) + ", " + ts(p.s) + ")"; #else return ts(p.f) + " " + ts(p.s); #endif } // OUTPUT tcT > void pr(T x) { cout << ts(x); } tcTUU > void pr(const T &t, const U &...u) { pr(t); pr(u...); } void ps() { pr("\n"); } // print w/ spaces tcTUU > void ps(const T &t, const U &...u) { pr(t); if (sizeof...(u)) pr(" "); ps(u...); } // DEBUG void DBG() { cerr << "]" << endl; } tcTUU > void DBG(const T &t, const U &...u) { cerr << ts(t); if (sizeof...(u)) cerr << ", "; DBG(u...); } #ifdef LOCAL // compile with -DLOCAL, chk -> fake assert #define dbg(...) \ cerr << "Line(" << __LINE__ << ") -> [" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__) #define chk(...) \ if (!(__VA_ARGS__)) \ cerr << "Line(" << __LINE__ << ") -> function(" << __FUNCTION__ \ << ") -> CHK FAILED: (" << #__VA_ARGS__ << ")" << "\n", \ exit(0); #else #define dbg(...) 0 #define chk(...) 0 #endif void setPrec() { cout << fixed << setprecision(15); } void unsyncIO() { cin.tie(0)->sync_with_stdio(0); } // FILE I/O void setIn(str s) { freopen(s.c_str(), "r", stdin); } void setOut(str s) { freopen(s.c_str(), "w", stdout); } void setIO(str s = "") { unsyncIO(); setPrec(); // cin.exceptions(cin.failbit); // throws exception when do smth illegal // ex. try to read letter into int if (sz(s)) setIn(s + ".in"), setOut(s + ".out"); // for USACO } int n, spy[MX]; bool vis[MX], used[MX]; vi adj[MX]; int sum; void dfs(int x) { vis[x] = 1; trav(t, adj[x]) if (!vis[t]) { dfs(t); if (!used[t]) used[x] = 1; } sum += used[x]; } int main() { setIO(); re(n); FOR(i, 1, n + 1) { re(spy[i]); assert(spy[i] != i); adj[spy[i]].pb(i); } FOR(i, 1, n + 1) if (!vis[i]) { int x = i, y = spy[i]; while (x != y) x = spy[x], y = spy[spy[y]]; vi cyc = {x}; while (spy[cyc.bk] != x) cyc.pb(spy[cyc.bk]); trav(t, cyc) vis[t] = 1; vector<bool> v; trav(t, cyc) { dfs(t); v.pb(used[t]); } F0R(j, sz(v)) if (v[j] == 1) { rotate(begin(v), begin(v) + j, end(v)); break; } int cur = 0; F0R(j, sz(v)) { if (v[j] == 0) cur++; else sum += cur / 2, cur = 0; } sum += cur / 2; } ps(sum); }

OK:

#include <bits/stdc++.h> using namespace std; using ll = long long; using ld = long double; using db = double; using str = string; // yay python! using pi = pair<int, int>; using pl = pair<ll, ll>; using pd = pair<db, db>; using vi = vector<int>; using vb = vector<bool>; using vl = vector<ll>; using vd = vector<db>; using vs = vector<str>; using vpi = vector<pi>; using vpl = vector<pl>; using vpd = vector<pd>; #define tcT template <class T #define tcTU tcT, class U // ^ lol this makes everything look weird but I'll try it tcT > using V = vector<T>; tcT, size_t SZ > using AR = array<T, SZ>; tcT > using PR = pair<T, T>; // pairs #define mp make_pair #define f first #define s second // vectors // oops size(x), rbegin(x), rend(x) need C++17 #define sz(x) int((x).size()) #define bg(x) begin(x) #define all(x) bg(x), end(x) #define rall(x) x.rbegin(), x.rend() #define sor(x) sort(all(x)) #define rsz resize #define ins insert #define ft front() #define bk back() #define pb push_back #define eb emplace_back #define pf push_front #define lb lower_bound #define ub upper_bound tcT > int lwb(V<T> &a, const T &b) { return int(lb(all(a), b) - bg(a)); } // loops #define FOR(i, a, b) for (int i = (a); i < (b); ++i) #define F0R(i, a) FOR(i, 0, a) #define ROF(i, a, b) for (int i = (b) - 1; i >= (a); --i) #define R0F(i, a) ROF(i, 0, a) #define trav(a, x) for (auto &a : x) const int MOD = 1e9 + 7; // 998244353; const int MX = 2e5 + 5; const ll INF = 1e18; // not too close to LLONG_MAX const ld PI = acos((ld)-1); const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1}; // for every grid problem!! mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count()); template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>; // bitwise ops // also see https://gcc.gnu.org/onlinedocs/gcc/Other-Builtins.html constexpr int pct(int x) { return __builtin_popcount(x); } // # of bits set constexpr int bits(int x) { // assert(x >= 0); // make C++11 compatible until // USACO updates ... return x == 0 ? 0 : 31 - __builtin_clz(x); } // floor(log2(x)) constexpr int p2(int x) { return 1 << x; } constexpr int msk2(int x) { return p2(x) - 1; } ll cdiv(ll a, ll b) { return a / b + ((a ^ b) > 0 && a % b); } // divide a by b rounded up ll fdiv(ll a, ll b) { return a / b - ((a ^ b) < 0 && a % b); } // divide a by b rounded down tcT > bool ckmin(T &a, const T &b) { return b < a ? a = b, 1 : 0; } // set a = min(a,b) tcT > bool ckmax(T &a, const T &b) { return a < b ? a = b, 1 : 0; } tcTU > T fstTrue(T lo, T hi, U f) { hi++; assert(lo <= hi); // assuming f is increasing while (lo < hi) { // find first index such that f is true T mid = lo + (hi - lo) / 2; f(mid) ? hi = mid : lo = mid + 1; } return lo; } tcTU > T lstTrue(T lo, T hi, U f) { lo--; assert(lo <= hi); // assuming f is decreasing while (lo < hi) { // find first index such that f is true T mid = lo + (hi - lo + 1) / 2; f(mid) ? lo = mid : hi = mid - 1; } return lo; } tcT > void remDup(vector<T> &v) { // sort and remove duplicates sort(all(v)); v.erase(unique(all(v)), end(v)); } tcTU > void erase(T &t, const U &u) { // don't erase auto it = t.find(u); assert(it != end(t)); t.erase(it); } // element that doesn't exist from (multi)set // INPUT #define tcTUU tcT, class... U tcT > void re(complex<T> &c); tcTU > void re(pair<T, U> &p); tcT > void re(V<T> &v); tcT, size_t SZ > void re(AR<T, SZ> &a); tcT > void re(T &x) { cin >> x; } void re(db &d) { str t; re(t); d = stod(t); } void re(ld &d) { str t; re(t); d = stold(t); } tcTUU > void re(T &t, U &...u) { re(t); re(u...); } tcT > void re(complex<T> &c) { T a, b; re(a, b); c = {a, b}; } tcTU > void re(pair<T, U> &p) { re(p.f, p.s); } tcT > void re(V<T> &x) { trav(a, x) re(a); } tcT, size_t SZ > void re(AR<T, SZ> &x) { trav(a, x) re(a); } tcT > void rv(int n, V<T> &x) { x.rsz(n); re(x); } // TO_STRING #define ts to_string str ts(char c) { return str(1, c); } str ts(const char *s) { return (str)s; } str ts(str s) { return s; } str ts(bool b) { #ifdef LOCAL return b ? "true" : "false"; #else return ts((int)b); #endif } tcT > str ts(complex<T> c) { stringstream ss; ss << c; return ss.str(); } str ts(V<bool> v) { str res = "{"; F0R(i, sz(v)) res += char('0' + v[i]); res += "}"; return res; } template <size_t SZ> str ts(bitset<SZ> b) { str res = ""; F0R(i, SZ) res += char('0' + b[i]); return res; } tcTU > str ts(pair<T, U> p); tcT > str ts(T v) { // containers with begin(), end() #ifdef LOCAL bool fst = 1; str res = "{"; for (const auto &x : v) { if (!fst) res += ", "; fst = 0; res += ts(x); } res += "}"; return res; #else bool fst = 1; str res = ""; for (const auto &x : v) { if (!fst) res += " "; fst = 0; res += ts(x); } return res; #endif } tcTU > str ts(pair<T, U> p) { #ifdef LOCAL return "(" + ts(p.f) + ", " + ts(p.s) + ")"; #else return ts(p.f) + " " + ts(p.s); #endif } // OUTPUT tcT > void pr(T x) { cout << ts(x); } tcTUU > void pr(const T &t, const U &...u) { pr(t); pr(u...); } void ps() { pr("\n"); } // print w/ spaces tcTUU > void ps(const T &t, const U &...u) { pr(t); if (sizeof...(u)) pr(" "); ps(u...); } // DEBUG void DBG() { cerr << "]" << endl; } tcTUU > void DBG(const T &t, const U &...u) { cerr << ts(t); if (sizeof...(u)) cerr << ", "; DBG(u...); } #ifdef LOCAL // compile with -DLOCAL, chk -> fake assert #define dbg(...) \ cerr << "Line(" << __LINE__ << ") -> [" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__) #define chk(...) \ if (!(__VA_ARGS__)) \ cerr << "Line(" << __LINE__ << ") -> function(" << __FUNCTION__ \ << ") -> CHK FAILED: (" << #__VA_ARGS__ << ")" << "\n", \ exit(0); #else #define dbg(...) 0 #define chk(...) 0 #endif void setPrec() { cout << fixed << setprecision(15); } void unsyncIO() { cin.tie(0)->sync_with_stdio(0); } // FILE I/O void setIn(str s) { freopen(s.c_str(), "r", stdin); } void setOut(str s) { freopen(s.c_str(), "w", stdout); } void setIO(str s = "") { unsyncIO(); setPrec(); // cin.exceptions(cin.failbit); // throws exception when do smth illegal // ex. try to read letter into int if (sz(s)) setIn(s + ".in"), setOut(s + ".out"); // for USACO } int n, spy[MX], ST[MX], EN[MX], adj[MX]; bitset<MX> vis, used; int sum; void dfs(int _) { vi st{_}; while (sz(st)) { int x = st.bk; vis[x] = 1; if (ST[x] == EN[x]) { sum += used[x]; if (sz(st) > 1) if (!used[x]) used[st[sz(st) - 2]] = 1; st.pop_back(); continue; } int t = adj[ST[x]++]; if (!vis[t]) st.pb(t); } } int main() { setIO(); re(n); FOR(i, 1, n + 1) { re(spy[i]); assert(spy[i] != i); ST[spy[i]]++; } int ind = 0; FOR(i, 1, n + 1) { int tmp = ind; ind += ST[i]; ST[i] = tmp; EN[i] = ind; } FOR(i, 1, n + 1) adj[ST[spy[i]]++] = i; FOR(i, 1, n + 1) ST[spy[i]]--; FOR(i, 1, n + 1) if (!vis[i]) { int x = i, y = spy[i]; while (x != y) x = spy[x], y = spy[spy[y]]; vi cyc = {x}; while (spy[cyc.bk] != x) cyc.pb(spy[cyc.bk]); trav(t, cyc) vis[t] = 1; vector<bool> v; trav(t, cyc) { dfs(t); v.pb(used[t]); } F0R(j, sz(v)) if (v[j] == 1) { rotate(begin(v), begin(v) + j, end(v)); break; } int cur = 0; F0R(j, sz(v)) { if (v[j] == 0) cur++; else sum += cur / 2, cur = 0; } sum += cur / 2; } ps(sum); }