Java数据结构（递归执行顺序、杨辉三角、斐波那契篇）

13-04-12 来源：[db:作者]

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递归：程序调用自身的编程技巧称为递归（ recursion）。递归做为一种算法在程序设计语言中广泛应用。一个过程或函数在其定义或说明中有直接或间接调用自身的一种方法，它通常把一个大型复杂的问题层层转化为一个与原问题相似的规模较小的问题来求解，递归策略只需少量的程序就可描述出解题过程所需要的多次重复计算，大大地减少了程序的代码量。递归的能力在于用有限的语句来定义对象的无限集合。一般来说，递归需要有边界条件、递归前进段和递归返回段。当边界条件不满足时，递归前进；当边界条件满足时，递归返回。

[java]
package ch05Recursion;

public class Recursion {

    public static void main(String[] args) {
        test(0);
    }

    public static void test(int i){
        if(i < 100){
            System.out.println("Hello world! " + i);
            test(++i);
            System.out.println("Hello java! " + i);
        }
    }
}

package ch05Recursion;

public class Recursion {

public static void main(String[] args) {
  test(0);
}

public static void test(int i){
  if(i < 100){
   System.out.println("Hello world! " + i);
   test(++i);
   System.out.println("Hello java! " + i);
  }
}
}

执行顺序大意图：

[java]
Hello world! 0
Hello world! 1
Hello world! 2
Hello world! 3
Hello world! 4
Hello world! 5
Hello world! 6
Hello world! 7
Hello world! 8
Hello world! 9
Hello world! 10
Hello world! 11
Hello world! 12
Hello world! 13
Hello world! 14
Hello world! 15
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Hello world! 90
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Hello world! 94
Hello world! 95
Hello world! 96
Hello world! 97
Hello world! 98
Hello world! 99
Hello java! 100
Hello java! 99
Hello java! 98
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Hello java! 8
Hello java! 7
Hello java! 6
Hello java! 5
Hello java! 4
Hello java! 3
Hello java! 2
Hello java! 1

Hello world! 0
Hello world! 1
Hello world! 2
Hello world! 3
Hello world! 4
Hello world! 5
Hello world! 6
Hello world! 7
Hello world! 8
Hello world! 9
Hello world! 10
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Hello world! 90
Hello world! 91
Hello world! 92
Hello world! 93
Hello world! 94
Hello world! 95
Hello world! 96
Hello world! 97
Hello world! 98
Hello world! 99
Hello java! 100
Hello java! 99
Hello java! 98
Hello java! 97
Hello java! 96
Hello java! 95
Hello java! 94
Hello java! 93
Hello java! 92
Hello java! 91
Hello java! 90
Hello java! 89
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Hello java! 4
Hello java! 3
Hello java! 2
Hello java! 1

三角数字：

[java]
package ch05Recursion;

public class Trigo {

    public static void main(String[] args) {
        System.out.println(trigo(1));
        System.out.println(trigo(2));
        System.out.println(trigo(3));
        System.out.println(trigo(4));

        System.out.println("---");

        System.out.println(trigoRecursion(1));
        System.out.println(trigoRecursion(2));
        System.out.println(trigoRecursion(3));
        System.out.println(trigoRecursion(4));
    }

    /**
     * 三角数字循环相加
     * @param n
     * @return
     */
    public static int trigo(int n){
        int total = 0;
        while(n > 0){
            total = total + n;
            n--;
        }
        return total;
    }

    /**
     * 三角数字递归相加
     * @param n
     * @return
     */
    public static int trigoRecursion(int n){
        if(n == 1)
            return 1;
        else
            return n + trigoRecursion(--n);
    }
}

package ch05Recursion;

public class Trigo {

public static void main(String[] args) {
  System.out.println(trigo(1));
  System.out.println(trigo(2));
  System.out.println(trigo(3));
  System.out.println(trigo(4));

  System.out.println("---");

  System.out.println(trigoRecursion(1));
  System.out.println(trigoRecursion(2));
  System.out.println(trigoRecursion(3));
  System.out.println(trigoRecursion(4));
}

/**
* 三角数字循环相加
* @param n
* @return
*/
public static int trigo(int n){
  int total = 0;
  while(n > 0){
   total = total + n;
   n--;
  }
  return total;
}

/**
* 三角数字递归相加
* @param n
* @return
*/
public static int trigoRecursion(int n){
  if(n == 1)
   return 1;
  else
   return n + trigoRecursion(--n);
}
}

杨辉三角：

[java]
package ch05Recursion;

import java.util.Scanner;

public class YangHui {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        System.out.println("请输入将要显示的杨辉三角的行数（>=3）：");
        int i = sc.nextInt();
        if(i <= 3){
            System.out.println("请输入正确的值！");
            System.exit(-1);
        }
        // 建立杨辉三角形模型
        int yh[][] = new int[i][i];
        // 根据杨辉三角形特点，先录入两条边上的值，皆为1；
        for(int j = 0; j < i; j++){
            yh[j][0] = 1;
            yh[j][j] = 1;
        }
        // 根据杨辉三角形特点，填写其他值，完成整个杨辉三角形；
        for(int j = 2; j < i; j++){
            for(int n = 1; n < j; n++)
                yh[j][n] = yh[j - 1][n - 1] + yh[j - 1][n];
        }
        // 打印杨辉三角形
        for(int j = 0; j < i; j++){
            for(int n = 0; n <= j; n++)
                System.out.print(yh[j][n] + " ");
            System.out.println();
        }
    }
}

package ch05Recursion;

import java.util.Scanner;

public class YangHui {

public static void main(String[] args) {
  Scanner sc = new Scanner(System.in);
  System.out.println("请输入将要显示的杨辉三角的行数（>=3）：");
  int i = sc.nextInt();
  if(i <= 3){
   System.out.println("请输入正确的值！");
   System.exit(-1);
  }
  // 建立杨辉三角形模型
  int yh[][] = new int[i][i];
  // 根据杨辉三角形特点，先录入两条边上的值，皆为1；
  for(int j = 0; j < i; j++){
   yh[j][0] = 1;
   yh[j][j] = 1;
  }
  // 根据杨辉三角形特点，填写其他值，完成整个杨辉三角形；
  for(int j = 2; j < i; j++){
   for(int n = 1; n < j; n++)
    yh[j][n] = yh[j - 1][n - 1] + yh[j - 1][n];
  }
  // 打印杨辉三角形
  for(int j = 0; j < i; j++){
   for(int n = 0; n <= j; n++)
    System.out.print(yh[j][n] + " ");
   System.out.println();
  }
}
}

[java]
请输入将要显示的杨辉三角的行数（>=3）：
8
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1

请输入将要显示的杨辉三角的行数（>=3）：
8
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1

Fibonacci：比萨的列奥纳多，又称斐波那契（Leonardo Pisano ,Fibonacci, Leonardo Bigollo，1175年-1250年），意大利数学家，西方第一个研究斐波那契数，并将现代书写数和乘数的位值表示法系统引入欧洲。

[java]
package ch05Recursion;

public class Fibonacci {

    public static void main(String[] args) {
        System.out.println(fibonacci(1));
        System.out.println(fibonacci(2));
        System.out.println(fibonacci(3));
        System.out.println(fibonacci(4));
        System.out.println(fibonacci(5));
    }

    public static int fibonacci(int n){
        if(n == 0 || n == 1)
            return 1;
        else
            return fibonacci(n - 1) + fibonacci(n - 2);
    }
}

package ch05Recursion;

public class Fibonacci {

public static void main(String[] args) {
  System.out.println(fibonacci(1));
  System.out.println(fibonacci(2));
  System.out.println(fibonacci(3));
  System.out.println(fibonacci(4));
  System.out.println(fibonacci(5));
}

public static int fibonacci(int n){
  if(n == 0 || n == 1)
   return 1;
  else
   return fibonacci(n - 1) + fibonacci(n - 2);
}
}
[java] view plaincopyprint?1
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