UVA10334 Ray through glasses large number __uva10334

Suppose we put two panes of glass back-to-back. How many ways a are there for light rays to pass through or is reflected after changing direction n times? Following figure shows the situations when the value of n is 0, 1 and 2.

Input

It is a set of lines with an integer n where 0≤n≤1000 in each of them.

Output

For every one of the integers a line containing a as described above.

Sample Input

0

1

2

Sample Output

1

2

3

Title Link: UVA10334 Ray through glasses

Question brief: (slightly)

Problem Analysis:

The problem is actually the Fibonacci sequence, but the starting item values are different. The recurrence type is as follows:

F0=0

f1=2

......

Fn=fn-2 + fn-1 (n>=2)

The large number calculation is realized by the simulation method, see the program.

Program Description:

It is most convenient to use Java program to complete the calculation of large numbers.

Preface: (slightly)

Reference link: (slightly)

The C + + language program for AC is as follows:

AC's C + + Language Program (analog method) is as follows:

/* UVA10334 Ray through glasses

/* #include <bits/stdc++.h>

using namespace std;

typedef unsigned long long ull;

const int N = 1000;
const int N2 = 1000/17;
Const ULL BASE = 1e17;
Ull fib[n + 1][n2 + 1];

void Setfib ()
{
    fib[0][0] = 1;
    Fib[1][0] = 2;
    int len = 1;
    for (int i = 2; I <= N; i++) {
        int carry = 0;
        for (int j = 0; J < Len; J +) {
            fib[i][j] = Fib[i-2][j] + fib[i-1][j] + carry;
            carry = fib[i][j]/BASE;
            FIB[I][J]%= BASE;
        if (carry)
            fib[i][len++] = Carry
    }
}

int main ()
{
    memset (fib, 0, sizeof (FIB));

    Setfib ();

    int n;
    while (~SCANF ("%d", &n)) {
        int k = N2;
        while (fib[n][k] = = 0)
            k--;
        printf ("%lld", Fib[n][k]);
        for (int i = k-1 i >= 0; i--)
            printf ("%017lld", Fib[n][i));
        printf ("\ n");
    }

    return 0;
}

The Java language Program for AC is as follows:

/* UVA10334 Ray through glasses * *

import Java.math.BigInteger;
Import Java.util.Scanner;

public class Main {public
    static void Main (string[] args) {
        Scanner cin = new Scanner (system.in);
        biginteger[] fib = new biginteger[1001];
        Fib[0] = new BigInteger ("1");
        FIB[1] = new BigInteger ("2");
        for (int i = 2; I <= 1000 i + +)
            fib[i] = Fib[i-1].add (fib[i-2));
        while (Cin.hasnext ())
        {
            int N = Cin.nextint ();
            System.out.println (Fib[n]);}}