【HDOJ】5564 Clarke and digits

DP+快速矩阵幂。注意base矩阵的初始化，不难。

/* 5564 */
#include <iostream>
#include <string>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <vector>
#include <deque>
#include <algorithm>
#include <cstdio>
#include <cmath>
#include <ctime>
#include <cstring>
#include <climits>
#include <cctype>
#include <cassert>
#include <functional>
#include <iterator>
#include <iomanip>
using namespace std;
//#pragma comment(linker,"/STACK:102400000,1024000")

#define sti                set<int>
#define stpii            set<pair<int, int> >
#define mpii            map<int,int>
#define vi                vector<int>
#define pii                pair<int,int>
#define vpii            vector<pair<int,int> >
#define rep(i, a, n)     for (int i=a;i<n;++i)
#define per(i, a, n)     for (int i=n-1;i>=a;--i)
#define clr                clear
#define pb                 push_back
#define mp                 make_pair
#define fir                first
#define sec                second
#define all(x)             (x).begin(),(x).end()
#define SZ(x)             ((int)(x).size())
#define lson            l, mid, rt<<1
#define rson            mid+1, r, rt<<1|1

const int mod = 1e9+7;
const int maxn = 75;
int ID[maxn][maxn];
int n;

typedef struct mat_t {
    __int64 m[maxn][maxn];

    mat_t() {
        memset(m, 0, sizeof(m));
    }

    void init() {
        memset(m, 0, sizeof(m));
    }

    void print() {
        rep(i, 0, n) {
            rep(j, 0, n) {
                printf("%I64d ", m[i][j]);
            }
            putchar('
');
        }
    }
} mat_t;

mat_t matMult(mat_t& a, mat_t& b) {
    mat_t c;

    rep(i, 0, n)
        rep(j, 0, n)
            rep(k, 0, n)
                c.m[i][j] = (c.m[i][j] + a.m[i][k]*b.m[k][j]%mod)%mod;

    return c;
}

mat_t matPow(mat_t a, int m) {
    mat_t ret;

    rep(i, 0, n)
        ret.m[i][i] = 1;
    while (m) {
        if (m & 1)
            ret = matMult(ret, a);
        a = matMult(a, a);
        m >>= 1;
    }

    return ret;
}

mat_t e;
mat_t base;

void init(int s) {
    // first column is one
    // first row is zero(accept first one)
    rep(j, 0, n) {
        e.m[0][j] = 0;
        if (j%7 == 1)
            e.m[j][0] = 1;
        else
            e.m[j][0] = 0;
    }
    e.m[0][0] = 1;
    
    rep(i, 0, 10) {
        rep(j, 0, 7) {
            rep(ii, 0, 10) {
                int jj = (10*j+ii)%7;
                int id = ID[i][j];
                int id_ = ID[ii][jj];
                if (i+ii == s)
                    e.m[id][id_] = 0;
                else
                    e.m[id][id_] = 1;
            }
        }
    }

    #ifndef ONLINE_JUDGE
        // e.print();
    #endif
}

void init_base() {
    int cnt = 1;
    n = 7*10+1;

    rep(i, 0, 10)
        rep(j, 0, 7)
            ID[i][j] = cnt++;
    rep(i, 1, 10)
        base.m[0][ID[i][i%7]] = 1;
}

__int64 cal(int len) {
    if (len == 0)
        return 0;

    __int64 ret = 0;
    mat_t res = matPow(e, len);

    rep(i, 0, n)
        ret = (ret + base.m[0][i]*res.m[i][0]%mod)%mod;
    return ret;
}

int main() {
    ios::sync_with_stdio(false);
    #ifndef ONLINE_JUDGE
        freopen("data.in", "r", stdin);
        freopen("data.out", "w", stdout);
    #endif

    int t;
    int l, r, s;
    __int64 nl, nr, ans;

    init_base();
    scanf("%d", &t);
    while (t--) {
        scanf("%d %d %d", &l, &r, &s);
        init(s);
        nl = cal(l-1);
        nr = cal(r);
        ans = (nr-nl+mod) % mod;
        #ifndef ONLINE_JUDGE
            printf("nl = %I64d, nr = %I64d
", nl, nr);
        #endif
        printf("%I64d
", ans);
    }

    #ifndef ONLINE_JUDGE
        printf("time = %d.
", (int)clock());
    #endif

    return 0;
}