【HDOJ】5564 Clarke and digits

DP+快速矩阵幂。注意base矩阵的初始化，不难。

  1 /* 5564 */
  2 #include <iostream>
  3 #include <string>
  4 #include <map>
  5 #include <queue>
  6 #include <set>
  7 #include <stack>
  8 #include <vector>
  9 #include <deque>
 10 #include <algorithm>
 11 #include <cstdio>
 12 #include <cmath>
 13 #include <ctime>
 14 #include <cstring>
 15 #include <climits>
 16 #include <cctype>
 17 #include <cassert>
 18 #include <functional>
 19 #include <iterator>
 20 #include <iomanip>
 21 using namespace std;
 22 //#pragma comment(linker,"/STACK:102400000,1024000")
 23
 24 #define sti                set<int>
 25 #define stpii            set<pair<int, int> >
 26 #define mpii            map<int,int>
 27 #define vi                vector<int>
 28 #define pii                pair<int,int>
 29 #define vpii            vector<pair<int,int> >
 30 #define rep(i, a, n)     for (int i=a;i<n;++i)
 31 #define per(i, a, n)     for (int i=n-1;i>=a;--i)
 32 #define clr                clear
 33 #define pb                 push_back
 34 #define mp                 make_pair
 35 #define fir                first
 36 #define sec                second
 37 #define all(x)             (x).begin(),(x).end()
 38 #define SZ(x)             ((int)(x).size())
 39 #define lson            l, mid, rt<<1
 40 #define rson            mid+1, r, rt<<1|1
 41
 42 const int mod = 1e9+7;
 43 const int maxn = 75;
 44 int ID[maxn][maxn];
 45 int n;
 46
 47 typedef struct mat_t {
 48     __int64 m[maxn][maxn];
 49
 50     mat_t() {
 51         memset(m, 0, sizeof(m));
 52     }
 53
 54     void init() {
 55         memset(m, 0, sizeof(m));
 56     }
 57
 58     void print() {
 59         rep(i, 0, n) {
 60             rep(j, 0, n) {
 61                 printf("%I64d ", m[i][j]);
 62             }
 63             putchar(‘\n‘);
 64         }
 65     }
 66 } mat_t;
 67
 68 mat_t matMult(mat_t& a, mat_t& b) {
 69     mat_t c;
 70
 71     rep(i, 0, n)
 72         rep(j, 0, n)
 73             rep(k, 0, n)
 74                 c.m[i][j] = (c.m[i][j] + a.m[i][k]*b.m[k][j]%mod)%mod;
 75
 76     return c;
 77 }
 78
 79 mat_t matPow(mat_t a, int m) {
 80     mat_t ret;
 81
 82     rep(i, 0, n)
 83         ret.m[i][i] = 1;
 84     while (m) {
 85         if (m & 1)
 86             ret = matMult(ret, a);
 87         a = matMult(a, a);
 88         m >>= 1;
 89     }
 90
 91     return ret;
 92 }
 93
 94 mat_t e;
 95 mat_t base;
 96
 97 void init(int s) {
 98     // first column is one
 99     // first row is zero(accept first one)
100     rep(j, 0, n) {
101         e.m[0][j] = 0;
102         if (j%7 == 1)
103             e.m[j][0] = 1;
104         else
105             e.m[j][0] = 0;
106     }
107     e.m[0][0] = 1;
108
109     rep(i, 0, 10) {
110         rep(j, 0, 7) {
111             rep(ii, 0, 10) {
112                 int jj = (10*j+ii)%7;
113                 int id = ID[i][j];
114                 int id_ = ID[ii][jj];
115                 if (i+ii == s)
116                     e.m[id][id_] = 0;
117                 else
118                     e.m[id][id_] = 1;
119             }
120         }
121     }
122
123     #ifndef ONLINE_JUDGE
124         // e.print();
125     #endif
126 }
127
128 void init_base() {
129     int cnt = 1;
130     n = 7*10+1;
131
132     rep(i, 0, 10)
133         rep(j, 0, 7)
134             ID[i][j] = cnt++;
135     rep(i, 1, 10)
136         base.m[0][ID[i][i%7]] = 1;
137 }
138
139 __int64 cal(int len) {
140     if (len == 0)
141         return 0;
142
143     __int64 ret = 0;
144     mat_t res = matPow(e, len);
145
146     rep(i, 0, n)
147         ret = (ret + base.m[0][i]*res.m[i][0]%mod)%mod;
148     return ret;
149 }
150
151 int main() {
152     ios::sync_with_stdio(false);
153     #ifndef ONLINE_JUDGE
154         freopen("data.in", "r", stdin);
155         freopen("data.out", "w", stdout);
156     #endif
157
158     int t;
159     int l, r, s;
160     __int64 nl, nr, ans;
161
162     init_base();
163     scanf("%d", &t);
164     while (t--) {
165         scanf("%d %d %d", &l, &r, &s);
166         init(s);
167         nl = cal(l-1);
168         nr = cal(r);
169         ans = (nr-nl+mod) % mod;
170         #ifndef ONLINE_JUDGE
171             printf("nl = %I64d, nr = %I64d\n", nl, nr);
172         #endif
173         printf("%I64d\n", ans);
174     }
175
176     #ifndef ONLINE_JUDGE
177         printf("time = %d.\n", (int)clock());
178     #endif
179
180     return 0;
181 }