Bzoj 1009: [HNOI2008]GT Exam (DP + matrix fast Power + KMP)

Wrote a morning ... Because the length of the M is also counted in the ...

DP (i, j) indicates that the ticket number before I character matches the number of scenarios for the first J of the unlucky number. KMP preprocessing, and then for J enumeration, the number 0~9 is also enumerated to calculate that f (i, j) represents DP (X-1, J) Contribution to DP (x, i). Then use the matrix to quickly power. Time complexity O (M^{3Logn + m)}

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#include <bits/stdc++.h>using namespace std;const int MAXN =;int FAIL[MAXN], S[MAXN], N, M, MOD; struct Matrix {int n, m;int A[MAXN][MAXN];matrix (int _n = 0, int _m = 0): N (_n), M (_m) {memset (A, 0, sizeof a);}void Unit () {for (int i = 0; i < n; i++)A[i][i] = 1;}matrix operator * (Matrix O) {matrix ret (n, O.M);for (int i = 0; i < n; i++)for (int k = 0; k < m; k++)For (int j = 0; J < o.m; J + +)Ret.a[i][j] = (Ret.a[i][j] + a[i][k] * o.a[k][j])% MOD;return ret;}matrix operator = (Matrix O) {for (int i = 0; i < n; i++)For (int j = 0; J < N; j + +)A[i][j] = o.a[i][j];return *this;}matrix operator ^ (int k) {matrix ret (n, m), t = *this; Ret.unit ();For (; k; k >>= 1) {if (K & 1) ret = ret * t;t = t * t;}return ret;}};void Kmp () {fail[0] = fail[1] = 0;for (int i = 1; i < M; i++) {int p = fail[i];while (P && s[i] = s[p]) p = fail[p];fail[i + 1] = s[i] = = s[p]? p + 1:0;}}int main () {scanf ("%d%d%d", &n, &m, &mod);for (int i = 0; i < M; i++) {char C = getchar ();For (;!isdigit (c); c = GetChar ());S[i] = C-' 0 ';}KMP ();Matrix Q (M, m);for (int i = 0; i < M; i++)For (int j = 0; J <; J + +) {int p = i;while (P && s[p]! = j) p = fail[p];if (s[p] = = j) p++;q.a[p][i]++;}matrix ans (M, 1);ans.a[0][0] = 1;ans = (Q ^ N) * ans;int tot = 0;for (int i = 0; i < M; i++)if (tot + = ans.a[i][0]) >= mod) tot-= mod;printf ("%d\n", tot);return 0;}

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1009: [HNOI2008]GT exam Time limit:1 Sec Memory limit:162 MB
submit:2236 solved:1368
[Submit] [Status] [Discuss] Description

Ashen ready to enroll in the GT exam, the ticket number is n-digit x1x2 .... Xn (0<=xi<=9), he does not want to appear on the ticket number of unlucky figures. His unlucky math a1a2 ... AM (0<=ai<=9) has M-bit, does not appear to refer to x1x2 ... The xn does not have exactly a paragraph equal to A1A2 ... Am. A1 and X1 can be 0

Input

The first line enters N,m,k. The next line is to enter the number of M bits. 100% data n<=10^9,m<=20,k<=1000 40% data n<=1000 10% data n<=6

Output

Ashen want to know how many kinds of numbers do not appear unlucky numbers, the result of output modulus K redundancy.

Sample Input4 3 100
111Sample OutputBayiHINT

Source

Bzoj 1009: [HNOI2008]GT Exam (DP + matrix fast Power + KMP)