斐波那契数列——简单例子背后的通用思想和技巧

暴力递归

import java.util.*;
public class Fib1 {
    public static void main(String[] args){
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();

        int []arr = new int[n+1];
        System.out.println(help(arr,n));


    }
    static int help(int[] arr,int n){
        if(n == 0||n==1){
            return n;
        }
        else{
            arr[n] = help(arr,n-1)+help(arr,n-2);
            return arr[n];
        }
    }
}

带备忘录的递归

import java.util.*;
public class Fib2 {
    public static void main(String[] args){
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int []arr = new int[n+1];
        System.out.println(help(arr,n));
    }

    static int help(int[] arr,int n){
        if(n == 0||n==1){
            return n;
        }
        if(arr[n] != 0){        //其值不等于原始值0，则说明这个数已经运算出结果了(f(0)不用考虑)
            return arr[n];
        }
        arr[n] = help(arr,n-1)+help(arr,n-2);
        return arr[n];
    }
}

迭代法

import java.util.*;
public class Fib3 {
    public static void main(String[] args){
        Scanner in = new Scanner(System.in);

        int n = in.nextInt();
        int []arr = new int[n+1];

        arr[0] = 0;
        arr[1] = 1;

        for(int i = 2;i

滚动更新

import java.util.*;
public class Fib4 {
    public static void main(String[] args){
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        if(n == 0||n==1){
            System.out.println(n);
        }
        int a = 0;
        int b = 1;

        int c = 0;
        for(int i = 2;i<=n;i++){
            c = a + b;
            a = b;
            b = c;
        }
        System.out.println(c);
    }
}