斐波那契數列

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斐波納契數列（Fibonacci Sequence），又稱黃金分割數列，指的是這樣一個數列：1、1、2、3、5、8、13、21、……在數學上，斐波納契數列以如下被以遞歸的方法定義：F0=0，F1=1，Fn=F(n-1)+F(n-2)（n>=2，n∈N*）在現代物理、準晶體結構、化學等領域，斐波納契數列都有直接的應用。

Java版

//main方法

public static void main(String[] args)
{        
        ArrayList<Integer> result = new ArrayList<Integer>();
        result.add(1);
        result.add(1);
        addNewValue(result);
        System.out.println(result);

        System.out.println(addNum(5));

        System.out.println(fibonacci(5));
}

//1

public static void addNewValue(ArrayList<Integer> array)
{
      if (array.size() <= 5)
      {
            array.add(array.get(array.size() - 1) + array.get(array.size() - 2));
            addNewValue(array);
      }
}

// 2

public static long addNum(int num)
{
      if (num <= 1)
      {
            return 1;
      }
      else
      {
            return addNum(num - 1) + addNum(num - 2);
      }
}

//3

public static BigInteger fibonacci(int num)
{
      if (num == 0)
      {
            return new BigInteger("0");
      }
      else if (num == 1)
      {
            return new BigInteger("1");
      }
      else
      {
            BigInteger b0 = BigInteger.ZERO;
            BigInteger b1 = BigInteger.ONE;
            BigInteger fn = BigInteger.ZERO;
            for (int i = 1; i <= num; i++)
            {
                fn = b0.add(b1);
                b0 = b1;
                b1 = fn;
            }
            return fn;
      }
}

Shell版

#1

#!/bin/bash

echo "Fibonacci script"

echo "Press a number here..."
read number

if [ $number -le 0 ]
then
   echo "You have something wrong.The number must be great then 0."
   exit 1
fi

for((i=0;i<$number;i++))
do
  if(($i-2>=0))
    then
      ((array[$i]=${array[$i-1]}+${array[$i-2]}))
    else
      ((array[$i]=$i))
  fi
  echo array[$i]=${array[$i]}
done
sum=0
for((j=0;j<10;j++))
do
  sum=$(($sum+${array[$j]}))
done

echo "$sum"

#2

#!/bin/bash
#Fibonacci Sequence

echo "Press a number here..."
read number

if [ $number -le 0 ]
then
   echo "You have something wrong.The number must be great then 0."
   exit 1
fi
echo "Well, you wanna print between 1 and $number, and count them."

fibonacci(){
  arg1=0
  arg2=1
  for((i=1;i<=$number;i++))
  do
    ((arg3=$arg1+$arg2))

    echo "Seq: $arg1+$arg2=$(($arg1+$arg2))"

    sum=$(($sum+$arg3))
    arg1=$arg2
    arg2=$arg3
  done

  echo "$sum"
}
fibonacci