HDU 1250 Hat's Fibonacci

题目描述：

A Fibonacci sequence is calculated by adding the previous two members the sequence, with the first two members being both 1.
F(1) = 1, F(2) = 1, F(3) = 1,F(4) = 1, F(n>4) = F(n - 1) + F(n-2) + F(n-3) + F(n-4)
Your task is to take a number as input, and print that Fibonacci number.

Input

Each line will contain an integers. Process to end of file.

Output

For each case, output the result in a line.

Sample Input

100

Sample Output

4203968145672990846840663646

 

Note:
No generated Fibonacci number in excess of 2005 digits will be in the test data, ie. F(20) = 66526 has 5 digits.

解题报告：

1：大数求和，上java。其实可以用矩阵快速幂写，但也没快多少。

代码1：

import java.math.BigInteger;
import java.util.Scanner;

public class Main{

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n;
        while(scanner.hasNext()){
            n = scanner.nextInt();
            BigInteger f1 = new BigInteger("1");
            BigInteger f2 = new BigInteger("1");
            BigInteger f3 = new BigInteger("1");
            BigInteger f4 = new BigInteger("1");
            if (n <= 4){
                System.out.println(1);
                continue;
            }
            BigInteger ans = new BigInteger("0");
            for (int i = 5; i <= n; i++) {
                ans = f1.add(f2).add(f3).add(f4);
                f1 = f2;
                f2 = f3;
                f3 = f4;
                f4 = ans;
            }
            System.out.println(ans);
        }
    }
}

代码2：

import java.math.BigInteger;
import java.util.Scanner;

public class Main{

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        while(scanner.hasNext()){
            int n = scanner.nextInt();
            if(n <= 4){
                System.out.println(1);
                continue;
            }
            Node A = new Node();
            A = Init(A);
            BigInteger ans = Pow(n - 4, A);
            System.out.println(ans);
        }
    }

    public static Node Init(Node A){
        for (int i = 0; i < 4; i++) {
            for (int j = 0; j < 4; j++) {
                A.num[i][j] = new BigInteger("0");
            }
        }
        for (int i = 0; i < 4; i++) {
            A.num[0][i] = new BigInteger("1");
        }
        A.num[1][0] = new BigInteger("1");
        A.num[2][1] = new BigInteger("1");
        A.num[3][2] = new BigInteger("1");

        return A;
    }

    public static Node Mul(Node A, Node B){
        Node C = new Node();
        for (int i = 0; i < 4; i++) {
            for (int j = 0; j < 4; j++) {
                C.num[i][j] = new BigInteger("0");
                for (int k = 0; k < 4; k++) {
                    C.num[i][j] = C.num[i][j].add(A.num[i][k].multiply(B.num[k][j]));
                }
            }
        }
        return C;
    }

    public static BigInteger Pow(int n, Node A){
        Node B = new Node();
        for (int i = 0; i < 4; i++) {
            for (int j = 0; j < 4; j++) {
                B.num[i][j] = new BigInteger("0");
            }
        }
        for (int i = 0; i < 4; i++) {
            B.num[i][0] = new BigInteger("1");
        }
        while(n > 0){
            if(n % 2 == 1)B = Mul(A, B);
            A = Mul(A, A);
            n = n/2;
        }
        return B.num[0][0];
    }
}

class Node{
    public BigInteger num[][] = new BigInteger[4][4];
}