Submission #251599

#	Time	Username	Problem	Language	Result	Execution time	Memory
251599		rqi	Duathlon (APIO18_duathlon)	C++14	31 / 100	326 ms	31988 KiB

count_triplets

#include <bits/stdc++.h>
using namespace std;
 
typedef long long ll;
typedef long double ld;
typedef double db; 
typedef string str; 

typedef pair<int,int> pi;
typedef pair<ll,ll> pl; 
typedef pair<db,db> pd; 

typedef vector<int> vi; 
typedef vector<ll> vl; 
typedef vector<db> vd; 
typedef vector<str> vs; 
typedef vector<pi> vpi;
typedef vector<pl> vpl; 
typedef vector<pd> vpd; 

#define mp make_pair
#define f first
#define s second
#define sz(x) (int)x.size()
#define all(x) begin(x), end(x)
#define rall(x) (x).rbegin(), (x).rend() 
#define rsz resize
#define ins insert 
#define ft front() 
#define bk back()
#define pf push_front 
#define pb push_back
#define eb emplace_back 
#define lb lower_bound 
#define ub upper_bound 

#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; 
const ld PI = acos((ld)-1);
const int xd[4] = {1,0,-1,0}, yd[4] = {0,1,0,-1}; 
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count()); 

template<class T> bool ckmin(T& a, const T& b) { 
    return b < a ? a = b, 1 : 0; }
template<class T> bool ckmax(T& a, const T& b) { 
    return a < b ? a = b, 1 : 0; } 
int pct(int x) { return __builtin_popcount(x); } 
int bits(int x) { return 31-__builtin_clz(x); } // floor(log2(x)) 
int cdiv(int a, int b) { return a/b+!(a<0||a%b == 0); } // division of a by b rounded up, assumes b > 0 
int fstTrue(function<bool(int)> f, int lo, int hi) {
    hi ++; assert(lo <= hi); // assuming f is increasing
    while (lo < hi) { // find first index such that f is true 
        int mid = (lo+hi)/2; 
        f(mid) ? hi = mid : lo = mid+1; 
    } 
    return lo;
}

// INPUT
template<class A> void re(complex<A>& c);
template<class A, class B> void re(pair<A,B>& p);
template<class A> void re(vector<A>& v);
template<class A, size_t SZ> void re(array<A,SZ>& a);

template<class T> 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); }
template<class H, class... T> void re(H& h, T&... t) { re(h); re(t...); }

template<class A> void re(complex<A>& c) { A a,b; re(a,b); c = {a,b}; }
template<class A, class B> void re(pair<A,B>& p) { re(p.f,p.s); }
template<class A> void re(vector<A>& x) { trav(a,x) re(a); }
template<class A, size_t SZ> void re(array<A,SZ>& x) { trav(a,x) re(a); }

// TO_STRING
#define ts to_string
str ts(char c) { return str(1,c); }
str ts(bool b) { return b ? "true" : "false"; }
str ts(const char* s) { return (str)s; }
str ts(str s) { return s; }
template<class A> str ts(complex<A> c) { 
    stringstream ss; ss << c; return ss.str(); }
str ts(vector<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; }
template<class A, class B> str ts(pair<A,B> p);
template<class T> str ts(T v) { // containers with begin(), end()
    bool fst = 1; str res = "{";
    for (const auto& x: v) {
        if (!fst) res += ", ";
        fst = 0; res += ts(x);
    }
    res += "}"; return res;
}
template<class A, class B> str ts(pair<A,B> p) {
    return "("+ts(p.f)+", "+ts(p.s)+")"; }

// OUTPUT
template<class A> void pr(A x) { cout << ts(x); }
template<class H, class... T> void pr(const H& h, const T&... t) { 
    pr(h); pr(t...); }
void ps() { pr("\n"); } // print w/ spaces
template<class H, class... T> void ps(const H& h, const T&... t) { 
    pr(h); if (sizeof...(t)) pr(" "); ps(t...); }

// DEBUG
void DBG() { cerr << "]" << endl; }
template<class H, class... T> void DBG(H h, T... t) {
    cerr << ts(h); if (sizeof...(t)) cerr << ", ";
    DBG(t...); }
#ifdef LOCAL // compile with -DLOCAL
#define dbg(...) cerr << "LINE(" << __LINE__ << ") -> [" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__)
#else
#define dbg(...) 0
#endif

// FILE I/O
void setIn(string s) { freopen(s.c_str(),"r",stdin); }
void setOut(string s) { freopen(s.c_str(),"w",stdout); }
void unsyncIO() { ios_base::sync_with_stdio(0); cin.tie(0); }
void setIO(string s = "") {
    unsyncIO();
    // 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
}

const int mx = 100005;
int n;
vi oadj[mx];
bool ovisited[mx];
vi olist;

void ogenList(int node){
    if(ovisited[node]) return;
    //dbg(node);
    ovisited[node] = 1;
    olist.pb(node);
    for(auto u: oadj[node]){
        ogenList(u);
    }
}

vi adj[mx];

int sub[mx];

void genSubs(int node, int prv = -1){
    sub[node] = 1;
    for(auto u: adj[node]){
        if(u == prv) continue;
        genSubs(u, node);
        sub[node]+=sub[u];
    }
}

ll treeSolve(int N){
    genSubs(1);
    ll ans = 0;
    for(int i = 1; i <= N; i++){
        ans+=ll(N-1)*ll(N-1);
        for(auto u: adj[i]){
            if(sub[u] > sub[i]){
                ans-=(ll(N)-ll(sub[i]))*(ll(N)-ll(sub[i]));
            }
            else{
                ans-=ll(sub[u])*ll(sub[u]);
            }
        }
    }
    return ans;
}

ll cycSolve(int N){
    return ll(N)*ll(N-1)*ll(N-2);
}

int num[mx];
int par[mx];
vi children[mx];
bool visited[mx];

void dfs(int node, int prv = -1){
    visited[node] = 1;
    if(prv != -1){
        par[node] = prv;
        children[prv].pb(node);
    }
    for(auto u: adj[node]){
        if(u == prv) continue;
        if(visited[u]){
            if(num[u] == 1) continue;
            num[node]++;
            num[u]--;
            // dbg(node, u);
            continue;
        }
        dfs(u, node);
    }
}

void getnum(int node){
    for(auto u: children[node]){
        getnum(u);
        num[node]+=num[u];
    }
}

int cnt = 0;
map<int, int> m;
int csz[mx];

void genMap(int node){
    if(num[node] > 0){
        assert(num[node] == 1); //cactus
        m[node] = m[par[node]];
        csz[m[node]]++;
    }
    else{
        m[node] = ++cnt;
        csz[m[node]]++;
    }
    for(auto u: children[node]){
        genMap(u);
    }
}

vi tadj[mx];
int tsub[mx];

void genTsub(int node, int prv = -1){
    tsub[node]+=csz[node];
    for(auto u: tadj[node]){
        if(u == prv) continue;
        genTsub(u, node);
        tsub[node]+=tsub[u];
    }
}


ll tsolve(int N){
    genTsub(1);
    // for(int i = 1; i <= cnt; i++){
    //     dbg(i, tsub[i]);
    // }
    ll ans = 0;
    for(int i = 1; i <= cnt; i++){
        ans+=ll(csz[i])*ll(N-1)*ll(N-2);

        for(auto u: tadj[i]){
            if(tsub[u] > tsub[i]){
                ans-=ll(N-tsub[i])*ll(N-tsub[i]-1);
                ans-=ll(csz[i]-1)*ll(N-tsub[i]+1)*ll(N-tsub[i]);
            }
            else{
                ans-=ll(tsub[u])*ll(tsub[u]-1);
                ans-=ll(csz[i]-1)*ll(tsub[u]+1)*ll(tsub[u]);
            }
        }
        //dbg(i, ans);
    }
    return ans;
}

ll hardSolve(int N){ //CHANGE THIS! Do Cactus case as well
    cnt = 0;
    for(int i = 1; i <= N; i++){
        num[i] = par[i] = csz[i] = tsub[i] = 0;
        visited[i] = 0;
        children[i].clear();
        tadj[i].clear();
    }
    m.clear();

    dfs(1);
    // for(int i = 1; i <= N; i++){
    //     dbg(i, children[i]);
    // }
    // for(int i = 1; i <= N; i++){
    //     dbg(i, num[i]);
    // }
    getnum(1);
    // for(int i = 1; i <= N; i++){
    //     dbg(i, num[i]);
    // }
    genMap(1);
    // dbg(m);
    // for(int i = 1; i <= N; i++){
    //     dbg(i, csz[i]);
    // }
    for(int i = 1; i <= N; i++){
        for(auto u: adj[i]){
            if(m[i] != m[u]){
                tadj[m[i]].pb(m[u]);
            }
        }
    }
    // dbg(cnt);
    // for(int i = 1; i <= cnt; i++){
    //     dbg(tadj[i]);
    // }
    return tsolve(N);
}

ll solve(int N){
    bool isTree = 1;
    bool isCyc = 1;

    int tot = 0;
    for(int i = 1; i <= N; i++){
        tot+=sz(adj[i]);
        if(sz(adj[i]) > 2) isCyc = 0;
    }
    if(tot/2 != N-1){
        isTree = 0;
    }
    if(isTree){
        //dbg(hardSolve(N));
        //assert(hardSolve(N) == treeSolve(N));
        return treeSolve(N);
    }
    else if(isCyc){
        return cycSolve(N);
    }

    return hardSolve(N);
}

int main() {
    setIO();
    int m;
    cin >> n >> m;
    for(int i = 1; i <= m; i++){
        int u, v;
        cin >> u >> v;
        oadj[u].pb(v);
        oadj[v].pb(u);
    }
    ll ans = 0;
    for(int i = 1; i <= n; i++){
        if(ovisited[i]) continue;
        //dbg(i);
        olist.clear();
        ogenList(i);
        map<int, int> m;
        for(int i = 0; i < sz(olist); i++){
            m[olist[i]] = i+1;
        }
        int N = sz(olist);
        for(int i = 1; i <= N; i++){
            adj[i].clear();
        }
        for(auto u: olist){
            for(auto x: oadj[u]){
                adj[m[u]].pb(m[x]);
            }
        }
        ans+=solve(N);
    }
    ps(ans);
    // you should actually read the stuff at the bottom
}

/* stuff you should look for
    * int overflow, array bounds
    * special cases (n=1?)
    * do smth instead of nothing and stay organized
    * WRITE STUFF DOWN
*/

Compilation message (stderr)

count_triplets.cpp: In function 'void setIn(std::__cxx11::string)':
count_triplets.cpp:128:31: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
 void setIn(string s) { freopen(s.c_str(),"r",stdin); }
                        ~~~~~~~^~~~~~~~~~~~~~~~~~~~~
count_triplets.cpp: In function 'void setOut(std::__cxx11::string)':
count_triplets.cpp:129:32: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
 void setOut(string s) { freopen(s.c_str(),"w",stdout); }
                         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~

• Subtask 1: 0 / 5
• Subtask 2: 0 / 11
• Subtask 3: 8 / 8
• Subtask 4: 10 / 10
• Subtask 5: 13 / 13
• Subtask 6: 0 / 15
• Subtask 7: 0 / 20
• Subtask 8: 0 / 8
• Subtask 9: 0 / 10