Submission #241640

#	Time	Username	Problem	Language	Result	Execution time	Memory
241640		rqi	Skyscraper (JOI16_skyscraper)	C++14	100 / 100	272 ms	3840 KiB

skyscraper

#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: modular arithmetic operations 
 * Source: 
    * KACTL
    * https://codeforces.com/blog/entry/63903
    * https://codeforces.com/contest/1261/submission/65632855 (tourist)
    * https://codeforces.com/contest/1264/submission/66344993 (ksun)
 * Verification: 
    * https://open.kattis.com/problems/modulararithmetic
 */

struct mi {
    typedef decay<decltype(MOD)>::type T; 
     /// don't silently convert to T
    T v; explicit operator T() const { return v; }
    mi() { v = 0; }
    mi(ll _v) { 
        v = (-MOD < _v && _v < MOD) ? _v : _v % MOD;
        if (v < 0) v += MOD;
    }
    friend bool operator==(const mi& a, const mi& b) { 
        return a.v == b.v; }
    friend bool operator!=(const mi& a, const mi& b) { 
        return !(a == b); }
    friend bool operator<(const mi& a, const mi& b) { 
        return a.v < b.v; }
    friend void re(mi& a) { ll x; re(x); a = mi(x); }
    friend str ts(mi a) { return ts(a.v); }
   
    mi& operator+=(const mi& m) { 
        if ((v += m.v) >= MOD) v -= MOD; 
        return *this; }
    mi& operator-=(const mi& m) { 
        if ((v -= m.v) < 0) v += MOD; 
        return *this; }
    mi& operator*=(const mi& m) { 
        v = (ll)v*m.v%MOD; return *this; }
    mi& operator/=(const mi& m) { return (*this) *= inv(m); }
    friend mi pow(mi a, ll p) {
        mi ans = 1; assert(p >= 0);
        for (; p; p /= 2, a *= a) if (p&1) ans *= a;
        return ans;
    }
    friend mi inv(const mi& a) { assert(a.v != 0); 
        return pow(a,MOD-2); }
        
    mi operator-() const { return mi(-v); }
    mi& operator++() { return *this += 1; }
    mi& operator--() { return *this -= 1; }
    friend mi operator+(mi a, const mi& b) { return a += b; }
    friend mi operator-(mi a, const mi& b) { return a -= b; }
    friend mi operator*(mi a, const mi& b) { return a *= b; }
    friend mi operator/(mi a, const mi& b) { return a /= b; }
};
typedef vector<mi> vmi;
typedef pair<mi,mi> pmi;
typedef vector<pmi> vpmi;

vector<vmi> scmb; // small combinations
void genComb(int SZ) {
    scmb.assign(SZ,vmi(SZ)); scmb[0][0] = 1;
    FOR(i,1,SZ) F0R(j,i+1) 
        scmb[i][j] = scmb[i-1][j]+(j?scmb[i-1][j-1]:0);
}

/**
 * Description: pre-compute factorial mod inverses,
     * assumes $MOD$ is prime and $SZ < MOD$.
 * Time: O(SZ)
 * Source: KACTL
 * Verification: https://dmoj.ca/problem/tle17c4p5
 */

vi invs, fac, ifac;
void genFac(int SZ) {
    invs.rsz(SZ), fac.rsz(SZ), ifac.rsz(SZ); 
    invs[1] = fac[0] = ifac[0] = 1; 
    FOR(i,2,SZ) invs[i] = MOD-(ll)MOD/i*invs[MOD%i]%MOD;
    FOR(i,1,SZ) {
        fac[i] = (ll)fac[i-1]*i%MOD;
        ifac[i] = (ll)ifac[i-1]*invs[i]%MOD;
    }
}

mi comb(int a, int b) {
    if (a < b || b < 0) return 0;
    return mi((ll)fac[a]*ifac[b]%MOD*ifac[a-b]%MOD);
}



int N, L;
int A[105];
mi dp[2][2][105][1005]; //number of components, total weight so far
mi ndp[2][2][105][1005]; 

void update(int s1, int s2, int j, int newval, mi ways){
    //dbg(s1, s2, j, newval, ways);
    if(s1 > 1) return;
    if(s2 > 1) return;
    if(j < 0) return;
    if(newval > L){
        //if(ways != 0) dbg(s1, s2, j, newval, ways);
        return;
    }
    if(newval < 0) return;
    if(ways != mi(0)) assert(newval >= 0);
    ndp[s1][s2][j][newval]+=ways;
}

void transition(int i, int s1, int s2, int j, int k){

    //dbg(i, s1, s2, j, k);

    mi ways = dp[s1][s2][j][k];
    if(ways == 0) return;
    int newval = k-A[i]*(s1+s2+2*(j));
    // if(i == 2 && s1 == 1 && s2 == 0 && j == 0 && k == 1){
    //     dbg(newval, ways);
    //     dbg(newval-A[i+1]+A[i+1]*(s1+s2+1+j-1));
    // }
    // if(i == 2 && s1 == 0 && s2 == 1 && j == 0 && k == 1){
    //     dbg(newval, ways);
    //     dbg(newval-A[i+1]+A[i+1]*(s1+1+s2+2*(j)));
    // }
    //start a new middle component
    update(s1, s2, j+1, newval-2*A[i+1]+A[i+1]*(s1+s2+2*(j+1)), ways);
    //add to an existing middle component
    update(s1, s2, j, newval+A[i+1]*(s1+s2+2*(j)), ways*j*2);
    //join together two middle components
    update(s1, s2, j-1, newval+2*A[i+1]+A[i+1]*(s1+s2+2*(j-1)), ways*comb(j, 2)*2);
    //join left and middle components
    if(s1 == 1) update(s1, s2, j-1, newval+2*A[i+1]+A[i+1]*(s1+s2+2*(j-1)), ways*j);
    //join middle and right components
    if(s2 == 1) update(s1, s2, j-1, newval+2*A[i+1]+A[i+1]*(s1+s2+2*(j-1)), ways*j);
    //add to an existing left component
    if(s1 == 1) update(s1, s2, j, newval+A[i+1]*(s1+s2+2*(j)), ways);
    //add to an existing right component
    if(s2 == 1) update(s1, s2, j, newval+A[i+1]*(s1+s2+2*(j)), ways);
    //start a left component
    update(s1+1, s2, j, newval-A[i+1]+A[i+1]*(s1+1+s2+2*(j)), ways);
    //start a right component
    update(s1, s2+1, j, newval-A[i+1]+A[i+1]*(s1+s2+1+2*(j)), ways);
    //transform a middle component into a left component
    update(s1+1, s2, j-1, newval+A[i+1]+A[i+1]*(s1+1+s2+2*(j-1)), ways*j);
    //transform a middle component into a right component
    update(s1, s2+1, j-1, newval+A[i+1]+A[i+1]*(s1+s2+1+2*(j-1)), ways*j);
}

int main() {
    setIO();
    cin >> N >> L;
    genFac(205);
    if(N == 1){
        ps(1);
        return 0;
    }
    for(int i = 1; i <= N; i++){
        cin >> A[i];
    }
    sort(A+1, A+1+N);

    dp[1][0][0][0] = 1;
    dp[0][1][0][0] = 1;
    dp[0][0][1][0] = 1;

    for(int i = 1; i+1 <= N-1; i++){ //place i+1th building
        for(int s1 = 0; s1 < 2; s1++){ //left present
            for(int s2 = 0; s2 < 2; s2++){ // right present 
                for(int j = 0; j <= N; j++){  //middle components
                    for(int k = 0; k <= L; k++){ //current weight
                        transition(i, s1, s2, j, k);
                    }
                } 
            }
        }

        //move to dp, reset ndp

        for(int s1 = 0; s1 < 2; s1++){ //left present
            for(int s2 = 0; s2 < 2; s2++){ // right present 
                for(int j = 0; j <= N; j++){  //middle components
                    for(int k = 0; k <= L; k++){ //current weight
                        dp[s1][s2][j][k] = ndp[s1][s2][j][k];
                        ndp[s1][s2][j][k] = 0;
                    }
                } 
            }
        }

        // if(i+1 == 2){
        //     dbg(dp[1][0][0][1]);
        //     dbg(dp[0][1][0][1]);
        // }
    }

    //dbg(dp[1][1][0][4]);
    mi ans = 0;
    //for answer, we could put N on the sides or the middle
    for(int k = 0; k <= L; k++){
        int newval = k-A[N-1]+A[N];
        mi ways = dp[0][1][0][k]; //N on the left
        if(newval <= L){
            //if(ways != 0) dbg(k, ways, "Ans1");
            ans+=ways;
        }

        newval = k-A[N-1]+A[N];
        ways = dp[1][0][0][k]; //N on the right
        if(newval <= L){
            //if(ways != 0) dbg(k, ways, "Ans2");
            ans+=ways;
        }

        newval = k-2*A[N-1]+2*A[N];
        ways = dp[1][1][0][k];
        if(newval <= L){
            //if(ways != 0) dbg(k, ways, "Ans3");
            ans+=ways;
        }
    }
    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)

skyscraper.cpp: In function 'void setIn(std::__cxx11::string)':
skyscraper.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); }
                        ~~~~~~~^~~~~~~~~~~~~~~~~~~~~
skyscraper.cpp: In function 'void setOut(std::__cxx11::string)':
skyscraper.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: 5 / 5
• Subtask 2: 15 / 15
• Subtask 3: 80 / 80