【矩阵快速幂-求平方根表达式的值】HDU Problem of Precision 2256

Problem of Precision

Time Limit: 1000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 1055    Accepted Submission(s): 622

Problem Description

 

Input

The first line of input gives the number of cases, T. T test cases follow, each on a separate line. Each test case contains one positive integer n. (1 <= n <= 10^9)

 

Output

For each input case, you should output the answer in one line.

 

Sample Input

3125

 

Sample Output

997841

 

Source

HDOJ 2008 Summer Exercise（4）- Buffet Dinner

 

题意：

简单明了。不再解释。

解题思路：

盗图。。这图讲的足够了。

矩阵：

AC代码：

#include <stdio.h>#include <string.h>#include <algorithm>#define MOD 1024using namespace std;typedef int LL;LL Mat[2][2];LL res[2][2];void init(){    for(int i=0;i<2;i++){        for(int j=0;j<2;j++){            res[i][j]=(i==j);        }    }    Mat[0][0]=5;Mat[0][1]=2;    Mat[1][0]=12;Mat[1][1]=5;}void Matmul(LL a[2][2],LL b[2][2]){    LL t[2][2]={0};    for(int i=0;i<2;i++){        for(int k=0;k<2;k++){            if(a[i][k]){                for(int j=0;j<2;j++){                   t[i][j]=(t[i][j]+a[i][k]*b[k][j]%MOD)%MOD;                }            }        }    }    for(int i=0;i<2;i++)        for(int j=0;j<2;j++)            a[i][j]=t[i][j];}void Matrix(LL x[2][2],LL n){    while(n){        if(n&1) Matmul(res,x);        Matmul(x,x);        n>>=1;    }}int main(){    int t;    scanf("%d",&t);    while(t--){        LL n;        scanf("%d",&n);        init();        Matrix(Mat,n-1);        LL ans[2];        LL cnt=0;        ans[0]=5;ans[1]=2;        for(int i=0;i<2;i++){            cnt=(cnt+ans[i]*res[i][0]%MOD)%MOD;        }        printf("%d\n",(2*cnt-1)%MOD);    }    return 0;}

Problem of Precision

Time Limit: 1000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 1055    Accepted Submission(s): 622

Problem Description

 

Input

The first line of input gives the number of cases, T. T test cases follow, each on a separate line. Each test case contains one positive integer n. (1 <= n <= 10^9)

 

Output

For each input case, you should output the answer in one line.

 

Sample Input

3125

 

Sample Output

997841

 

Source

HDOJ 2008 Summer Exercise（4）- Buffet Dinner