#985932 (C++23) No.2907 Business Revealing Dora Tiles

提出ソース

結果

問題	No.2907 Business Revealing Dora Tiles
ユーザー	👑 獅子座じゃない人
提出日時	2024-06-06 10:28:00
言語	C++23 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	504 ms / 3,000 ms
コード長	10,231 bytes
コンパイル時間	12,213 ms
コンパイル使用メモリ	276,820 KB
実行使用メモリ	6,944 KB
最終ジャッジ日時	2024-09-23 11:39:35
合計ジャッジ時間	29,460 ms
ジャッジサーバーID （参考情報）	judge1 / judge2

このコードへのチャレンジ
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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	4 ms 6,812 KB
testcase_01	AC	4 ms 6,816 KB
testcase_02	AC	4 ms 6,816 KB
testcase_03	AC	4 ms 6,944 KB
testcase_04	AC	5 ms 6,940 KB
testcase_05	AC	5 ms 6,940 KB
testcase_06	AC	4 ms 6,944 KB
testcase_07	AC	25 ms 6,944 KB
testcase_08	AC	17 ms 6,940 KB
testcase_09	AC	5 ms 6,940 KB
testcase_10	AC	4 ms 6,944 KB
testcase_11	AC	32 ms 6,940 KB
testcase_12	AC	4 ms 6,944 KB
testcase_13	AC	4 ms 6,944 KB
testcase_14	AC	4 ms 6,940 KB
testcase_15	AC	5 ms 6,944 KB
testcase_16	AC	4 ms 6,940 KB
testcase_17	AC	4 ms 6,940 KB
testcase_18	AC	10 ms 6,940 KB
testcase_19	AC	4 ms 6,940 KB
testcase_20	AC	4 ms 6,944 KB
testcase_21	AC	32 ms 6,944 KB
testcase_22	AC	6 ms 6,944 KB
testcase_23	AC	60 ms 6,944 KB
testcase_24	AC	218 ms 6,944 KB
testcase_25	AC	212 ms 6,944 KB
testcase_26	AC	216 ms 6,944 KB
testcase_27	AC	217 ms 6,944 KB
testcase_28	AC	214 ms 6,944 KB
testcase_29	AC	242 ms 6,940 KB
testcase_30	AC	218 ms 6,940 KB
testcase_31	AC	225 ms 6,944 KB
testcase_32	AC	218 ms 6,940 KB
testcase_33	AC	217 ms 6,940 KB
testcase_34	AC	219 ms 6,944 KB
testcase_35	AC	225 ms 6,940 KB
testcase_36	AC	215 ms 6,944 KB
testcase_37	AC	214 ms 6,944 KB
testcase_38	AC	221 ms 6,940 KB
testcase_39	AC	215 ms 6,944 KB
testcase_40	AC	211 ms 6,944 KB
testcase_41	AC	223 ms 6,940 KB
testcase_42	AC	213 ms 6,940 KB
testcase_43	AC	224 ms 6,944 KB
testcase_44	AC	398 ms 6,944 KB
testcase_45	AC	484 ms 6,940 KB
testcase_46	AC	365 ms 6,944 KB
testcase_47	AC	97 ms 6,944 KB
testcase_48	AC	125 ms 6,944 KB
testcase_49	AC	136 ms 6,944 KB
testcase_50	AC	221 ms 6,944 KB
testcase_51	AC	33 ms 6,940 KB
testcase_52	AC	221 ms 6,944 KB
testcase_53	AC	464 ms 6,944 KB
testcase_54	AC	63 ms 6,940 KB
testcase_55	AC	476 ms 6,940 KB
testcase_56	AC	474 ms 6,940 KB
testcase_57	AC	468 ms 6,940 KB
testcase_58	AC	353 ms 6,944 KB
testcase_59	AC	504 ms 6,940 KB

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ソースコード

raw source code

#include <bits/stdc++.h>
using namespace std;

#include <atcoder/modint>
using namespace atcoder;
using mint=modint998244353;

typedef   uint8_t     u8;
typedef   uint16_t    u16;
typedef   uint32_t    u32;
typedef   uint64_t    u64;
typedef __uint128_t   u128;
#define ctz32(a) ((a) ? __builtin_ctz((a)) : (32))
static const u32 fn[16] = {
    0x0001u, 0x0102u, 0x0183u, 0x8041u,
    0x015cu, 0x5f24u, 0xde2cu, 0x957eu,
    0x01f4u, 0xf7d8u, 0x76b0u, 0x5d52u,
    0xa977u, 0x20d1u, 0xc1a4u, 0x271fu};
static inline u32 to_nimber(u32 x) {
    u32 y = 0;
    for (; x; x &= x - 1)
        y ^= fn[ctz32(x)];
    return y;
}
static inline u32 to_double(u32 x) { return x << 1 ^ (x < 32768 ? 0 : 93099U); }
u16 ln[65536];
u16 expo[196605];
u16 *Hexpo = expo + 62133;
u16 *H2expo = expo + 58731;
__attribute__((constructor)) void _construct_nimber_product_() {
    *expo = 1;
    for (int i = 1; i < 65535; ++i)
        expo[i] = to_double(expo[i - 1]);
    for (int i = 1; i < 65535; ++i) {
        expo[i] = to_nimber(expo[i]);
        ln[expo[i]] = i;
    }
    memcpy(expo + 65535, expo, 131070);
    memcpy(expo + 131070, expo, 131070);
}
u16 product_16(u16 A, u16 B) { return A && B ? expo[ln[A] + ln[B]] : 0; }
u16 H_16(u16 A) { return A ? Hexpo[ln[A]] : 0; }
u16 H2_16(u16 A) { return A ? H2expo[ln[A]] : 0; }
u16 Hproduct_16(u16 A, u16 B) { return A && B ? Hexpo[ln[A] + ln[B]] : 0; }
u32 product_32(u32 A, u32 B) {
    u16 a = A & 65535;
    u16 b = B & 65535;
    u16 c = A >> 16;
    u16 d = B >> 16;
    u16 e = product_16(a, b);
    return (u32)(product_16((u16)(a ^ c), (u16)(b ^ d)) ^ e) << 16 | (Hproduct_16(c, d) ^ e);
}
u32 H_32(u32 A) {
    u16 a = A & 65535;
    u16 b = A >> 16;
    return H_16((u16)(a ^ b)) << 16 | H2_16(b);
}
u64 product(u64 A, u64 B) {
    u32 a = A & UINT_MAX;
    u32 b = B & UINT_MAX;
    u32 c = A >> 32;
    u32 d = B >> 32;
    u32 e = product_32(a, b);
    return (u64)(product_32(a ^ c, b ^ d) ^ e) << 32 | (H_32(product_32(c, d)) ^ e);
}

vector nim_prod_table(256, vector<unsigned long long>(256));
vector<unsigned long long> nim_inv_table(256);

void nim_prod_precalc() {
    nim_prod_table[0][0]=0;
    nim_prod_table[0][1]=0;
    nim_prod_table[1][0]=0;
    nim_prod_table[1][1]=1;
    for(int d=0;d<3;++d){
        int p=1<<d;
        for(int a=0;a<(1<<(2*p));++a){
            for(int b=(1<<p);b<(1<<(2*p));++b){
                unsigned long long a_h=a>>p;
                unsigned long long a_l=a-(a_h<<p);
                unsigned long long b_h=b>>p;
                unsigned long long b_l=b-(b_h<<p);
                unsigned long long al_bl=nim_prod_table[a_l][b_l];
                unsigned long long ahl_bhl=nim_prod_table[a_h^a_l][b_h^b_l];
                unsigned long long ah_bh=nim_prod_table[a_h][b_h];
                unsigned long long ah_bh_h=nim_prod_table[ah_bh][1ULL<<(p-1)];
                nim_prod_table[a][b]=nim_prod_table[b][a]=((al_bl^ahl_bhl)<<p)^(al_bl^ah_bh_h);
            }
        }
    }
}

unsigned long long nim_product(unsigned long long a, unsigned long long b, int p=64) {
    if(a==0 || b==0){
        return 0;
    }
    if(a==1){
        return b;
    }
    if(b==1){
        return a;
    }
    if(p==64){
        if(a<(1ULL<<8) && b<(1ULL<<8)){
            p=8;
        } else if(a<(1ULL<<16) && b<(1ULL<<16)){
            p=16;
        } else if(a<(1ULL<<32) && b<(1ULL<<32)){
            p=32;
        }
    }
    if(p==8){
        return nim_prod_table[a][b];
    }
    p/=2;
    unsigned long long a_h=a>>p;
    unsigned long long a_l=a-(a_h<<p);
    unsigned long long b_h=b>>p;
    unsigned long long b_l=b-(b_h<<p);
    unsigned long long al_bl=nim_product(a_l, b_l, p);
    unsigned long long ahl_bhl=nim_product(a_h^a_l, b_h^b_l, p);
    unsigned long long ah_bh=nim_product(a_h, b_h, p);
    unsigned long long ah_bh_h=nim_product(ah_bh, 1ULL<<(p-1), p);
    return ((al_bl^ahl_bhl)<<p)^(al_bl^ah_bh_h);
}

void nim_inv_precalc() {
    for(int i=0;i<256;++i){
        for(int j=i;j<256;++j){
            if(nim_prod_table[i][j]==1){
                nim_inv_table[i]=j;
                nim_inv_table[j]=i;
                break;
            }
        }
    }
}

unsigned long long nim_inv(unsigned long long a, int p=64) {
    if(p==64){
        if(a<(1ULL<<8)){
            p=8;
        } else if(a<(1ULL<<16)){
            p=16;
        } else if(a<(1ULL<<32)){
            p=32;
        }
    }
    if(p==8){
        return nim_inv_table[a];
    }
    p/=2;
    unsigned long long a_h=a>>p;
    unsigned long long a_l=a-(a_h<<p);
    unsigned long long half_inv=nim_inv(product(a_h^a_l, a_l)^product(product(a_h, a_h), 1ULL<<(p-1)), p);
    return (product(half_inv, a_h)<<p)^product(half_inv, a_h^a_l);
}

tuple<int,vector<int>,vector<int>> gauss_jordan(int r, int c, vector<vector<unsigned long long>> & m) {
    vector<int> members;
    vector<int> not_members;
    int rank=0;
    for(int i=0;i<c;++i){
        int pivot=-1;
        for(int j=rank;j<r;++j){
            if(m[j][i]>0){
                pivot=j;
                break;
            }
        }
        if(pivot==-1){
            not_members.emplace_back(i);
            continue;
        }
        members.emplace_back(i);
        swap(m[pivot], m[rank]);
        auto inv=nim_inv(m[rank][i]);
        m[rank][i]=1;
        for(int k=i+1;k<c;++k){
            m[rank][k]=product(m[rank][k], inv);
        }
        for(int j=0;j<r;++j){
            if(j==rank){
                continue;
            }
            auto factor=m[j][i];
            m[j][i]=0;
            for(int k=i+1;k<c;++k){
                m[j][k]^=product(m[rank][k], factor);
            }
        }
        ++rank;
        if(rank==r){
            for(int j=i+1;j<c;++j){
                not_members.emplace_back(j);
            }
            break;
        }
    }
    return tuple{rank,members,not_members};
}

bool dynamic_matrix_rank(int rank, int a_col, int from_col, int to_col, vector<vector<unsigned long long>> & u, vector<vector<unsigned long long>> & m){
    vector<unsigned long long> v(rank);
    for(int i=0;i<rank;++i){
        v[i]=m[i][from_col]^m[i][to_col];
    }
    vector<unsigned long long> v2(rank);
    for(int i=0;i<rank;++i){
        for(int j=0;j<rank;++j){
            v2[i]^=product(u[i][j], v[j]);
        }
    }
    if(v2[a_col]==1){
        return false;
    }
    vector<unsigned long long> clean(rank);
    unsigned long long inv=nim_inv(v2[a_col]^1);
    for(int i=0;i<rank;++i){
        if(i==a_col){
            clean[i]=inv^1;
        } else {
            clean[i]=product(v2[i], inv);
        }
    }
    auto u_row=u[a_col];
    for(int i=0;i<rank;++i){
        for(int j=0;j<rank;++j){
            u[i][j]^=product(clean[i], u_row[j]);
        }
    }
    return true;
}

int main(void)
{
    nim_prod_precalc();
    nim_inv_precalc();
    int n,t;
    cin >> n >> t;
    vector h(t, vector<unsigned long long>(n));
    for(int i=0;i<t;++i){
        for(int j=0;j<n;++j){
            cin >> h[i][j];
            --h[i][j];
        }
    }
    auto m=h;
    auto [rank,members,not_members]=gauss_jordan(t, n, m);
    int s=0;
    for(int i: members){
        s+=1<<i;
    }
    vector<bool> seen(1<<n);
    vector<int> ranks(1<<n);
    stack<tuple<int,int,int>> st;
    seen[s]=true;
    ranks[s]=rank;
    vector u(rank, vector<unsigned long long>(rank));
    for(int i=0;i<rank;++i){
        u[i][i]=1;
    }
    st.emplace(tuple{s+(1<<n),n,n});
    st.emplace(tuple{s,n,n});
    while(!st.empty()){
        auto [s,i,j]=st.top();
        st.pop();
        if(s<(1<<n)){
            if(i<n){
                if(dynamic_matrix_rank(rank, i, members[i], not_members[j], u, m)){
                    ranks[s]=rank;
                    swap(members[i], not_members[j]);
                } else {
                    continue;
                }
            }
            for(int i=0;i<(int)members.size();++i){
                for(int j=0;j<(int)not_members.size();++j){
                    int new_s=s-(1<<members[i])+(1<<not_members[j]);
                    if(seen[new_s]){
                        continue;
                    }
                    seen[new_s]=true;
                    st.emplace(tuple{new_s+(1<<n),i,j});
                    st.emplace(tuple{new_s,i,j});
                }
            }
        } else {
            s-=1<<n;
            if(i<n && ranks[s]>0){
                swap(members[i], not_members[j]);
                dynamic_matrix_rank(rank, i, members[i], not_members[j], u, m);
            }
        }
    }
    for(int r=rank-1;r>=0;--r){
        vector<bool> is_member(n);
        for(int i=n-r;i<n;++i){
            is_member[i]=true;
        }
        do {
            int s=0;
            for(int i=0;i<n;++i){
                if(is_member[i]){
                    s+=1<<i;
                }
            }
            for(int i=0;i<n;++i){
                if(is_member[i]){
                    continue;
                }
                if(ranks[s+(1<<i)]>0){
                    ranks[s]=r;
                    break;
                }
            }
        } while(next_permutation(is_member.begin(), is_member.end()));
    }
    for(int r=0;r<n;++r){
        vector<bool> is_member(n);
        for(int i=n-r;i<n;++i){
            is_member[i]=true;
        }
        do {
            int s=0;
            for(int i=0;i<n;++i){
                if(is_member[i]){
                    s+=1<<i;
                }
            }
            for(int i=0;i<n;++i){
                if(is_member[i]){
                    continue;
                }
                ranks[s+(1<<i)]=max(ranks[s], ranks[s+(1<<i)]);
            }
        } while(next_permutation(is_member.begin(), is_member.end()));
    }
    mint ans=0;
    mint p=932051910;
    for(unsigned int s=0;s<(1U<<n);++s){
        int count=popcount(s);
        if(n%2>0){
            if(count%2>0){
                ans+=p.pow(count-ranks[s]);
            } else {
                ans-=p.pow(count-ranks[s]);
            }
        } else {
            if(count%2>0){
                ans-=p.pow(count-ranks[s]);
            } else {
                ans+=p.pow(count-ranks[s]);
            }
        }
    }
    cout << ans.val() << endl;
    return 0;
}

yukicoder

結果

テストケース

ソースコード