Kickstart Round B 2018

A. No Nine

数位dp

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

int d[22];
LL po[22], f[22][2][9];
LL cal(LL x){
    int b = 0;
    while(x) d[++b] = x % 10, x /= 10;
    memset(f, 0, sizeof(f));
    f[b+1][1][0] = 1;
    for(int i = b + 1; i >= 2; i--){
        for(int j = 0; j <= 1; j++){
            for(int k = 0; k < 9; ++k){
                if(!f[i][j][k]) continue;
                for(int nxt = 0; nxt < 9; ++nxt){
                    if(j && nxt > d[i-1]) continue;
                    int nj = j && (nxt == d[i-1]);
                    int nk = (k + po[i-2] * nxt) % 9;
                    f[i-1][nj][nk] += f[i][j][k];
                }
            }
        }
    }
    LL ret = 0;
    for(int i = 1; i < 9; ++i) ret += f[1][0][i] + f[1][1][i];
    return ret;
}

int main(){
    freopen("A-large.in", "r", stdin);
    freopen("A-large.out", "w", stdout);
    po[0] = 1;
    for(int i = 1; i < 22; i++) po[i] = po[i-1] * 10 % 9;
    int T;
    scanf("%d", &T);
    for(int kase = 1; kase <= T; ++kase){
        LL F, L;
        cin >> F >> L;
        LL ans = cal(L) - cal(F) + 1;
        printf("Case #%d: %lld
", kase, ans);
    }
    return 0;
}

B. Sherlock and the Bit Strings

两边dp枚举中间

#include <bits/stdc++.h>
using namespace std;
typedef long long LL;
const LL INF = 1e18;
typedef pair<int, int> pii;
vector<pii> A[111], B[111];
LL pre[111][1<<16], suf[111][1<<16];
int d[111];

bool check_pre(int b, int msk){
    bool ret = true;
    for(int i = 0; i < B[b].size(); ++i){
        int a = B[b][i].first, c = B[b][i].second;
        int tmp = msk & ((1 << (b - a + 1)) - 1);
        if(__builtin_popcount(tmp) != c) ret = false;
    }
    return ret;
}

bool check_suf(int a, int msk){
    bool ret = true;
    for(int i = 0; i < A[a].size(); ++i){
        int b = A[a][i].first, c = A[a][i].second;
        int tmp = msk >> (15 - b + a);
        if(__builtin_popcount(tmp) != c) ret = false;
    }
    return ret;
}

int main(){
    freopen("B-large-practice.in", "r", stdin);
    freopen("B-large-practice.out", "w", stdout);
    int T;
    scanf("%d", &T);
    for(int kase = 1; kase <= T; ++kase){
        int N, K;
        LL P;
        scanf("%d %d %lld", &N, &K, &P);
        for(int i = 0; i <= N + 1; ++i) A[i].clear(), B[i].clear();
        for(int i = 1; i <= K; ++i){
            int a, b, c;
            scanf("%d %d %d", &a, &b, &c);
            A[a].push_back(pii(b, c));
            B[b].push_back(pii(a, c));
        }
        if(N < 16){
            for(int i = 0; i < (1 << N); ++i){
                for(int j = 1; j <= N; ++j) d[j] = i & (1 << (N - j)) ? 1 : 0;
                int ok = 1;
                for(int j = 1; j <= N; ++j){
                    for(int k = 0; k < A[j].size(); ++k){
                        int tmp = 0;
                        for(int p = j; p <= A[j][k].first; ++p) tmp += d[p];
                        if(tmp != A[j][k].second) ok = 0;
                    }
                    for(int k = 0; k < B[j].size(); ++k){
                        int tmp = 0;
                        for(int p = B[j][k].first; p <= j; ++p) tmp += d[p];
                        if(tmp != B[j][k].second) ok = 0;
                    }
                }
                P -= ok;
                if(P == 0){
                    printf("Case #%d: ", kase);
                    for(int i = 1; i <= N; i++) printf("%d", d[i]); puts("");
                    break;
                }
            }
            continue;
        }
        memset(pre, 0, sizeof(pre));
        for(int j = 0; j < (1 << 16); ++j){
            int ok = 1;
            for(int k = 1; k <= 16; ++k)
                if(!check_pre(k, j >> (16 - k))) ok = 0;
            pre[0][j] = ok;
        }
        for(int i = 0; i < N - 16; ++i){
            for(int j = 0; j < (1 << 16); j++){
                if(!pre[i][j]) continue;
                for(int k = 0; k <= 1; ++k){
                    int nj = (j << 1) & ((1 << 16) - 1);
                    nj |= k;
                    if(!check_pre(i + 17, nj)) continue;
                    if(!check_suf(i + 1, j)) continue;
                    pre[i+1][nj] += pre[i][j];
                    pre[i+1][nj] = min(pre[i+1][nj], INF);
                }
            }
        }
        memset(suf, 0, sizeof(suf));
        for(int j = 0; j < (1 << 16); ++j){
            int ok = 1;
            for(int k = 1; k <= 16; ++k)
                if(!check_suf(N - 16 + k, (j << (k - 1)) & ((1 << 16) - 1))) ok = 0;
            suf[N+1][j] = ok;
        }
        for(int i = N + 1; i > 17; --i){
            for(int j = 0; j < (1 << 16); j++){
                if(!suf[i][j]) continue;
                for(int k = 0; k <= 1; ++k){
                    int nj = (j >> 1) | (k << 15);
                    if(!check_suf(i - 17, nj)) continue;
                    if(!check_pre(i - 1, j)) continue;
                    suf[i-1][nj] += suf[i][j];
                    suf[i-1][nj] = min(suf[i-1][nj], INF);
                }
            }
        }
        int msk;
        for(int j = 0; j < (1 << 16); ++j){
            LL tmp = pre[0][j] * suf[17][j];
            if(tmp >= P){
                msk = j;
                break;
            }
            P -= tmp;
        }
        for(int i = 1; i <= N - 16; ++i){
            d[i] = msk >> 15;
            msk = (msk << 1) & ((1 << 16) - 1);
            if(pre[i][msk] && suf[i+17][msk] >= P) continue;
            P -= suf[i+17][msk];
            msk ^= 1;
        }
        for(int i = N; i >= N - 15; --i) d[i] = msk % 2, msk /= 2;
        printf("Case #%d: ", kase);
        for(int i = 1; i <= N; i++) printf("%d", d[i]); puts("");
    }
    return 0;
}

C. King's Circle