ZOJ Problem Set–1828 Fibonacci Numbers

Time Limit: 2 Seconds      Memory Limit: 65536 KB

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A Fibonacci sequence is calculated by adding the previous two members of the sequence, with the first two members being both 1.

f(1) = 1, f(2) = 1, f(n > 2) = f(n - 1) + f(n - 2)

Your task is to take a number as input, and print that Fibonacci number.

Sample Input

100

Sample Output

354224848179261915075

Note:

No generated Fibonacci number in excess of 1000 digits will be in the test data, i.e. f(20) = 6765 has 4 digits.

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Source: University of Waterloo Local Contest 1996.10.05

#include<iostream>
#include<vector>
#include<string>
using namespace std;
const short NUMLENGTH = 1001;
class BigInteger
{
private:
  unsigned short *num;
  size_t size;
  BigInteger& addBigInteger(const BigInteger& pre1, const BigInteger& pre2) const
  {
    BigInteger *result = new BigInteger();
    size_t loop = pre1.size > pre2.size ? pre1.size:pre2.size;
    bool carry = false;//标记运算是否有进位
    short tempResult;
    size_t i = 0;
    for(i = 0; i < loop; i++)
    {
      tempResult = *(pre1.num + i)*(i < pre1.size) + *(pre2.num + i)*(i < pre2.size) + (short)carry;
      carry = (tempResult >= 10);
      *(result->num + i) = tempResult - 10*carry;
    }
    *(result->num + i) = (short)carry;
    result->size = loop + (int)carry;
    return *result;
  }
public:
  BigInteger()
  {
    num = new unsigned short[NUMLENGTH];
    for(int i = 0; i < NUMLENGTH; i++)
      *(this->num + i) = 0;
    size = 0;
  }
  BigInteger(const BigInteger& bi)
  {
    num = new unsigned short[NUMLENGTH];
    this->size = bi.size;
    for(int i = 0; i < NUMLENGTH;i++)
      *(this->num + i) = *(bi.num + i);
  }
  BigInteger(const string& bi)
  {
    this->size = bi.length();
    num = new unsigned short[NUMLENGTH];
    for(int i = size - 1; i >= 0; i--)
    {
      *(this->num + i) = bi[i] - '0';
    }
    for(int j = size; j < NUMLENGTH; j++)
    {
      *(this->num + j) = 0;
    }
  }
  BigInteger& operator+(const BigInteger& op) const
  {
    return addBigInteger(*this, op);
  }
  
  void printInteger()
  {
    for(int i = size - 1; i >= 0; i--)
      cout<<*(num + i);
  }
  void printDataArr()
  {
    for(int i = 0; i < NUMLENGTH; i++)
      cout<<*(num + i);
  }
  ~BigInteger()
  {
    delete [] num;
  }
};
int main(void)
{
  vector<BigInteger> fabonacci;
  fabonacci.push_back(BigInteger("0"));
  fabonacci.push_back(BigInteger("1"));
  fabonacci.push_back(BigInteger("1"));
  int num;
  while(cin>>num)
  {
    if(fabonacci.size() <= num)
    {
      for(int i = fabonacci.size() - 1;i < num; i++)
        fabonacci.push_back(fabonacci[i] + fabonacci[i - 1]);
    }
    fabonacci[num].printInteger();
    cout<<endl;
  }
  return 0;
}