Submission #102051

#	Time	Username	Problem	Language	Result	Execution time	Memory
102051		Benq	Gauss (COCI17_gauss)	C++14	160 / 160	1093 ms	108280 KiB

gauss

#pragma GCC optimize ("O3")
#pragma GCC target ("sse4")

#include <bits/stdc++.h>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/rope>

using namespace std;
using namespace __gnu_pbds;
using namespace __gnu_cxx;
 
typedef long long ll;
typedef long double ld;
typedef complex<ld> cd;

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

typedef vector<int> vi;
typedef vector<ld> vd;
typedef vector<ll> vl;
typedef vector<pi> vpi;
typedef vector<pl> vpl;
typedef vector<cd> vcd;

template <class T> using Tree = tree<T, null_type, less<T>, rb_tree_tag,tree_order_statistics_node_update>;

#define FOR(i, a, b) for (int i = (a); i < (b); i++)
#define F0R(i, a) for (int i = 0; i < (a); i++)
#define FORd(i,a,b) for (int i = (b)-1; i >= (a); i--)
#define F0Rd(i,a) for (int i = (a)-1; i >= 0; i--)
#define trav(a, x) for (auto& a : x)

#define mp make_pair
#define pb push_back
#define f first
#define s second
#define lb lower_bound
#define ub upper_bound

#define sz(x) (int)x.size()
#define beg(x) x.begin()
#define en(x) x.end()
#define all(x) beg(x), en(x)
#define resz resize

const int MOD = 1000000007; // 998244353
const ll INF = 1e18;
const int MX = 100001;
const ld PI = 4*atan((ld)1);

template<class T> void ckmin(T &a, T b) { a = min(a, b); }
template<class T> void ckmax(T &a, T b) { a = max(a, b); }

template<class A, class B> A operator+=(A& l, const B& r) { return l = l+r; }
template<class A, class B> A operator-=(A& l, const B& r) { return l = l-r; }
template<class A, class B> A operator*=(A& l, const B& r) { return l = l*r; }
template<class A, class B> A operator/=(A& l, const B& r) { return l = l/r; }

namespace input {
    template<class T> void re(complex<T>& x);
    template<class T1, class T2> void re(pair<T1,T2>& p);
    template<class T> void re(vector<T>& a);
    template<class T, size_t SZ> void re(array<T,SZ>& a);

    template<class T> void re(T& x) { cin >> x; }
    void re(double& x) { string t; re(t); x = stod(t); }
    void re(ld& x) { string t; re(t); x = stold(t); }
    template<class Arg, class... Args> void re(Arg& first, Args&... rest) { 
        re(first); re(rest...); 
    }

    template<class T> void re(complex<T>& x) { T a,b; re(a,b); x = cd(a,b); }
    template<class T1, class T2> void re(pair<T1,T2>& p) { re(p.f,p.s); }
    template<class T> void re(vector<T>& a) { F0R(i,sz(a)) re(a[i]); }
    template<class T, size_t SZ> void re(array<T,SZ>& a) { F0R(i,SZ) re(a[i]); }
}

using namespace input;

namespace output {
    template<class T1, class T2> void pr(const pair<T1,T2>& x);
    template<class T, size_t SZ> void pr(const array<T,SZ>& x);
    template<class T> void pr(const vector<T>& x);
    template<class T> void pr(const set<T>& x);
    template<class T1, class T2> void pr(const map<T1,T2>& x);

    template<class T> void pr(const T& x) { cout << x; }
    template<class Arg, class... Args> void pr(const Arg& first, const Args&... rest) { 
        pr(first); pr(rest...); 
    }

    template<class T1, class T2> void pr(const pair<T1,T2>& x) { 
        pr("{",x.f,", ",x.s,"}"); 
    }
    template<class T> void prContain(const T& x) {
        pr("{");
        bool fst = 1; trav(a,x) pr(!fst?", ":"",a), fst = 0; 
        pr("}");
    }
    template<class T, size_t SZ> void pr(const array<T,SZ>& x) { prContain(x); }
    template<class T> void pr(const vector<T>& x) { prContain(x); }
    template<class T> void pr(const set<T>& x) { prContain(x); }
    template<class T1, class T2> void pr(const map<T1,T2>& x) { prContain(x); }
    
    void ps() { pr("\n"); } 
    template<class Arg, class... Args> void ps(const Arg& first, const Args&... rest) { 
        pr(first," "); ps(rest...); // print w/ spaces
    }
}

using namespace output;

namespace io {
    void setIn(string s) { freopen(s.c_str(),"r",stdin); }
    void setOut(string s) { freopen(s.c_str(),"w",stdout); }
    void setIO(string s = "") {
        ios_base::sync_with_stdio(0); cin.tie(0); // fast I/O
        if (sz(s)) { setIn(s+".in"), setOut(s+".out"); } // for USACO
    }
}

using namespace io;

template<class T> T invGeneral(T a, T b) {
    a %= b; if (a == 0) return b == 1 ? 0 : -1;
    T x = invGeneral(b,a); 
    return x == -1 ? -1 : ((1-(ll)b*x)/a+b)%b;
}

template<class T> struct modInt {
    T val;
    T mod = 0;
    // static const T mod = MOD;

    void normalize() {
        if (mod == 0) return;
        val %= mod; if (val < 0) val += mod;
    }
    modInt(T v = 0, T m = 0) : val(v), mod(m) { normalize(); }
    // modInt(T v = 0, T m = 0) : val(v) { normalize(); }

    explicit operator T() const { return val; }
    friend ostream& operator<<(ostream& os, const modInt& a) { return os << a.val; }
    friend bool operator==(const modInt& a, const modInt& b) { return a.val == b.val; }
    friend bool operator!=(const modInt& a, const modInt& b) { return !(a == b); }

    friend void check(modInt& a, modInt& b) { // make sure all operations are valid
        // comment out if mod is static const
        if (a.mod > 0 && b.mod > 0) { assert(a.mod == b.mod); return; }
        T mod = max(a.mod,b.mod); if (mod == 0) mod = MOD;
        if (a.mod != mod) { a.mod = mod; a.normalize(); }
        if (b.mod != mod) { b.mod = mod; b.normalize(); }
    }
    friend modInt operator+(modInt a, modInt b) {
        check(a,b); a.val += (T)b;
        if (a.val >= a.mod) a.val -= a.mod;
        return a;
    }
    friend modInt operator-(modInt a, modInt b) {
        check(a,b); a.val -= (T)b; 
        if (a.val < 0) a.val += a.mod; 
        return a;
    }
    friend modInt operator-(const modInt& a) { return modInt(0)-a; }

    friend modInt operator*(modInt a, modInt b) {
        check(a,b); a.val = (ll)a.val*(T)b%a.mod; return a;
    }
    friend modInt exp(modInt a, ll p) {
        modInt ans(1,a.mod);
        for (; p; p /= 2, a *= a) if (p&1) ans *= a;
        return ans;
    }
    friend modInt inv(const modInt& a) {
        return {invGeneral(a.val,a.mod),a.mod};
        // return exp(b,b.mod-2) if prime
    }
    friend modInt operator/(modInt a, modInt b) { 
        check(a,b); return a*inv(b); 
    }
};

typedef modInt<int> mi;
typedef pair<mi,mi> pmi;
typedef vector<mi> vmi;
typedef vector<pmi> vpmi;

int K, M, F[10001], T;
vi divi[1000001];
array<int,20> dist[1000001];
map<vi,array<int,20>> m;
bitset<1000001> done;
vi L;
vpi lucky;

void search(vi ori, vi cur, int ind, int numDivi, array<int,20>& cans) {
    if (ind == sz(ori)) {
        if (numDivi == 1) return;
        vi CUR; trav(t,cur) if (t) CUR.pb(t);
        sort(all(CUR)); reverse(all(CUR));
        // ps("HUH",ori,CUR);
        FOR(i,1,20) ckmin(cans[i],m[CUR][i-1]+F[numDivi]);
        return;
    }
    cur.pb(-1);
    F0R(i,ori[ind]+1) {
        cur[ind] = i;
        search(ori,cur,ind+1,numDivi*(ori[ind]+1-i),cans);
    }
}

array<int,20> inf;

array<int,20> getDist(int x) {
    if (!done[x]) {
        done[x] = 1;
        dist[x] = m[divi[x]];
    }
    return dist[x];
}

array<int,20> conv(array<int,20> a, array<int,20> b) {
    auto c = inf;
    F0R(i,20) F0Rd(j,20-i) ckmin(c[i+j],a[i]+b[j]);
    return c;
}

void init() {
    setIO(); re(K); FOR(i,1,K+1) re(F[i]);
    re(M); L.resz(M); re(L,T);
    lucky.resz(T); re(lucky);
    FOR(i,2,1000001) if (!sz(divi[i])) {
        for (int j = i; j < 1000001; j += i) {
            int cur = 0;
            int J = j; while (J % i == 0) { cur ++; J /= i; }
            divi[j].pb(cur);
        }
    }
    F0R(i,20) inf[i] = MOD;
    FOR(i,1,1000001) {
        sort(all(divi[i])); reverse(all(divi[i]));
        m[divi[i]] = {};
    }
    auto t = inf; t[0] = 0; m[divi[0]] = t;
    trav(t,m) if (sz(t.f)) {
        t.s = inf;
        search(t.f,{},0,1,t.s);
        // ps("HUH",t.f,t.s);
    }
    // trav(t,m) ps(t);
}

bool Q;
struct Line {
	mutable ll k, m, p; // slope, y-intercept, last optimal x
	bool operator<(const Line& o) const {
		return Q ? p < o.p : k < o.k;
	}
};

struct LineContainer : multiset<Line> { 
	const ll inf = LLONG_MAX;
	ll div(ll a, ll b) { // floored division
	    if (b < 0) a *= -1, b *= -1;
	    if (a >= 0) return a/b;
	    return -((-a+b-1)/b);
	}
	
	// updates x->p, determines if y is unneeded
	bool isect(iterator x, iterator y) { 
		if (y == end()) { x->p = inf; return 0; }
		if (x->k == y->k) x->p = x->m > y->m ? inf : -inf;
		else x->p = div(y->m - x->m, x->k - y->k);
		return x->p >= y->p;
	}
	
	void add(ll k, ll m) {
	    k *= -1, m *= -1;
		auto z = insert({k, m, 0}), y = z++, x = y;
		while (isect(y, z)) z = erase(z);
		if (x != begin() && isect(--x, y)) isect(x, y = erase(y));
		while ((y = x) != begin() && (--x)->p >= y->p) isect(x, erase(y));
	}
	
	ll query(ll x) { 
		assert(!empty());
		Q = 1; auto l = *lb({0,0,x}); Q = 0;
		return -(l.k * x + l.m);
	}
};

int smallAns[20];

int main() {
    init();
    int Q; re(Q);
    F0R(i,Q) {
        int A,B; re(A,B);
        
        F0R(j,20) smallAns[j] = MOD;
        if (A % B == 0) {
            auto dist = getDist(A/B);
            F0R(j,20) if (dist[j] != MOD) ckmin(smallAns[j],dist[j]);
           //  ps("HA",dist);
        }
        LineContainer LL;
        // no lucky numbers
        trav(t,lucky) if (A % t.f == 0 && t.f % B == 0) {
            // ps(A,B,t);
            auto dist = conv(getDist(A/t.f),getDist(t.f/B));
            int minAdd = MOD;
            F0R(j,20) if (dist[j] != MOD) {
                FOR(k,j,20) ckmin(smallAns[k],t.s*(k-j)+dist[j]);
                ckmin(minAdd,dist[j]-t.s*j);
            }
            if (minAdd != MOD) LL.add(t.s,minAdd);
            // lucky.s*(x-k)+dist[k]
        }
        ll ret = 0;
        trav(t,L) {
            if (t < 20) {
                if (smallAns[t] == MOD) ret --;
                else ret += smallAns[t];
            } else {
                if (sz(LL)) ret += LL.query(t);
                else ret --;
            }
        }
        ps(ret);
        // exit(0);
    }
}

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

Compilation message (stderr)

gauss.cpp: In function 'void io::setIn(std::__cxx11::string)':
gauss.cpp:117:35: 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); }
                            ~~~~~~~^~~~~~~~~~~~~~~~~~~~~
gauss.cpp: In function 'void io::setOut(std::__cxx11::string)':
gauss.cpp:118:36: 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: 16 / 16
• Subtask 2: 16 / 16
• Subtask 3: 16 / 16
• Subtask 4: 16 / 16
• Subtask 5: 16 / 16
• Subtask 6: 16 / 16
• Subtask 7: 16 / 16
• Subtask 8: 16 / 16
• Subtask 9: 16 / 16
• Subtask 10: 16 / 16