今天我们学习如何有效地求表达式的值。对于这个问题,用二分解决比较好。
(1)当时,
(2)当时,那么有
(3)当时,那么有
代码:
#include <iostream> #include <string.h> #include <stdio.h> using namespace std; const int M = 1000000007; typedef long long LL; LL power(LL a,LL b) { LL ans = 1; a %= M; while(b) { if(b & 1) { ans = ans * a % M; b--; } b >>= 1; a = a * a % M; } return ans; } LL sum(LL a,LL n) { if(n == 1) return a; LL t = sum(a,n/2); if(n & 1) { LL cur = power(a,n/2+1); t = (t + t * cur % M) % M; t = (t + cur) % M; } else { LL cur = power(a,n/2); t = (t + t * cur % M) % M; } return t; } int main() { LL a,n; while(cin>>a>>n) cout<<sum(a,n)<<endl; return 0; }
题目:http://poj.org/problem?id=3233
题意:矩阵求和
代码:
#include <iostream> #include <string.h> #include <stdio.h> using namespace std; const int N = 35; struct Matrix { int m[N][N]; }; Matrix I; int n,k,M; Matrix add(Matrix a,Matrix b) { Matrix c; for(int i=0; i<n; i++) { for(int j=0; j<n; j++) { c.m[i][j] = a.m[i][j] + b.m[i][j]; c.m[i][j] %= M; } } return c; } Matrix multi(Matrix a,Matrix b) { Matrix c; for(int i=0; i<n; i++) { for(int j=0; j<n; j++) { c.m[i][j] = 0; for(int k=0; k<n; k++) c.m[i][j] += a.m[i][k] * b.m[k][j]; c.m[i][j] %= M; } } return c; } Matrix power(Matrix A,int n) { Matrix ans = I,p = A; while(n) { if(n & 1) { ans = multi(ans,p); n--; } n >>= 1; p = multi(p,p); } return ans; } Matrix sum(Matrix A,int k) { if(k == 1) return A; Matrix t = sum(A,k/2); if(k & 1) { Matrix cur = power(A,k/2+1); t = add(t,multi(t,cur)); t = add(t,cur); } else { Matrix cur = power(A,k/2); t = add(t,multi(t,cur)); } return t; } int main() { while(scanf("%d%d%d",&n,&k,&M)!=EOF) { Matrix A; for(int i=0; i<n; i++) { for(int j=0; j<n; j++) { scanf("%d",&A.m[i][j]); A.m[i][j] %= M; I.m[i][j] = (i==j); } } Matrix ans = sum(A,k); for(int i=0; i<n; i++) { for(int j=0; j<n; j++) printf("%d ",ans.m[i][j]); puts(""); } } return 0; }