Submission #240063

#	Time	Username	Problem	Language	Result	Execution time	Memory
240063		rqi	Construction of Highway (JOI18_construction)	C++14	100 / 100	462 ms	16248 KiB

construction

#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
}




/**
 * Description: Link-Cut Tree. Given a function $f(1\ldots N)\to 1\ldots N,$ 
     * evaluates $f^b(a)$ for any $a,b.$ \texttt{sz} is for path queries; 
     * \texttt{sub}, \texttt{vsub} are for subtree queries. \texttt{x->access()} 
     * brings \texttt{x} to the top and propagates it; its left subtree will be 
     * the path from \texttt{x} to the root and its right subtree will be empty. 
     * Then \texttt{sub} will be the number of nodes in the connected component
     * of \texttt{x} and \texttt{vsub} will be the number of nodes under \texttt{x}.
     * Use \texttt{makeRoot} for arbitrary path queries.
 * Time: O(\log N)
 * Usage: FOR(i,1,N+1)LCT[i]=new snode(i); link(LCT[1],LCT[2],1);
 * Source: Dhruv Rohatgi, Eric Zhang
    * https://sites.google.com/site/kc97ble/container/splay-tree/splaytree-cpp-3
    * https://codeforces.com/blog/entry/67637
 * Verification: (see README for links)
    * ekzhang Balanced Tokens
    * Dynamic Tree Test (Easy)
    * https://probgate.org/viewproblem.php?pid=578 (The Applicant)
 */

typedef struct snode* sn;
struct snode { //////// VARIABLES
    sn p, c[2]; // parent, children
    sn extra; // extra cycle node for "The Applicant"
    bool flip = 0; // subtree flipped or not
    int val, sz; // value in node, # nodes in current splay tree
    int sub, vsub = 0; // vsub stores sum of virtual children
    snode(int _val) : val(_val) {
        p = c[0] = c[1] = extra = NULL; calc(); }
    friend int getSz(sn x) { return x?x->sz:0; }
    friend int getSub(sn x) { return x?x->sub:0; }
    void prop() { // lazy prop
        //if (!flip) return;
        if(c[0]) c[0]->val = val;
        if(c[1]) c[1]->val = val;
        /*swap(c[0],c[1]); flip = 0;
        F0R(i,2) if (c[i]) c[i]->flip ^= 1;*/
    }
    void calc() { // recalc vals
        F0R(i,2) if (c[i]) c[i]->prop();
        sz = 1+getSz(c[0])+getSz(c[1]);
        sub = 1+getSub(c[0])+getSub(c[1])+vsub;
    }
    //////// SPLAY TREE OPERATIONS
    int dir() {
        if (!p) return -2;
        F0R(i,2) if (p->c[i] == this) return i;
        return -1; // p is path-parent pointer
    } // -> not in current splay tree
    // test if root of current splay tree
    bool isRoot() { return dir() < 0; } 
    friend void setLink(sn x, sn y, int d) {
        if (y) y->p = x;
        if (d >= 0) x->c[d] = y; }
    void rot() { // assume p and p->p propagated
        assert(!isRoot()); int x = dir(); sn pa = p;
        setLink(pa->p, this, pa->dir());
        setLink(pa, c[x^1], x); setLink(this, pa, x^1);
        pa->calc(); calc();
    }
    void splay() {
        while (!isRoot() && !p->isRoot()) {
            p->p->prop(), p->prop(), prop();
            dir() == p->dir() ? p->rot() : rot();
            rot();
        }
        if (!isRoot()) p->prop(), prop(), rot();
        prop();
    }
    sn fbo(int b) { // find by order
        prop(); int z = getSz(c[0]); // of splay tree
        if (b == z) { splay(); return this; }
        return b < z ? c[0]->fbo(b) : c[1] -> fbo(b-z-1);
    }
    //////// BASE OPERATIONS

    //return vector of mp(val, sz)
    vpi access(sn b, int num) { // bring this to top of tree, propagate
        vpi rval; //return value
        for (sn v = this, pre = NULL; v; v = v->p) {
            v->splay(); // now switch virtual children
            if (pre) v->vsub -= pre->sub;
            if (v->c[1]) v->vsub += v->c[1]->sub;
            pi valsz;
            valsz.f = v->val;
            valsz.s = 1;
            if(v->c[0]) valsz.s += v->c[0]->sz;
            rval.pb(valsz);
            v->c[1] = pre; v->calc(); pre = v;
        }
        splay(); assert(!c[1]); // right subtree is empty
        setLink(this, b, 1);
        b->calc();
        calc();
        b->splay();
        b->val = num;
        b->prop();
        return rval;
    }
};


/**
 * Description: range sum queries and point updates for $D$ dimensions
 * Source: https://codeforces.com/blog/entry/64914
 * Verification: SPOJ matsum
 * Usage: \texttt{BIT<int,10,10>} gives 2D BIT
 * Time: O((\log N)^D)
 */

template <class T, int ...Ns> struct BIT {
    T val = 0; void upd(T v) { val += v; }
    T query() { return val; }
};
template <class T, int N, int... Ns> struct BIT<T, N, Ns...> {
    BIT<T,Ns...> bit[N+1];
    template<typename... Args> void upd(int pos, Args... args) {
        for (; pos<=N; pos+=pos&-pos) bit[pos].upd(args...); }
    template<typename... Args> T sum(int r, Args... args) {
        T res=0; for (;r;r-=r&-r) res += bit[r].query(args...); 
        return res; }
    template<typename... Args> T query(int l, int r, Args... 
        args) { return sum(r,args...)-sum(l-1,args...); }
}; 


const int mx = 100005;
int C[mx];
sn LCT[mx];
BIT<ll, 100005> bit;

int main() {
    setIO();
    int N;
    cin >> N;
    map<int, int> m;
    for(int i = 1; i <= N; i++){
        cin >> C[i];
        m[C[i]];
    }

    int cnt = 0;
    for(auto &u: m){
        cnt++;
        u.s = cnt;
    }
        
    for(int i = 1; i <= N; i++){
        C[i] = m[C[i]];
        LCT[i] = new snode(C[i]);
    }

    for(int i = 1; i <= N-1; i++){
        int A, B;
        cin >> A >> B;
        
        vpi nums = LCT[A]->access(LCT[B], C[B]);
        //dbg(A, B, C[B]);
        //dbg(nums);
        ll ans = 0;
        for(auto u: nums){
            bit.upd(u.f, u.s);
            ans+=ll(u.s)*bit.query(1, u.f-1);
        }
        for(auto u: nums){
            bit.upd(u.f, -u.s);
        }
        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)

construction.cpp: In function 'void setIn(std::__cxx11::string)':
construction.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); }
                        ~~~~~~~^~~~~~~~~~~~~~~~~~~~~
construction.cpp: In function 'void setOut(std::__cxx11::string)':
construction.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: 7 / 7
• Subtask 2: 9 / 9
• Subtask 3: 84 / 84