Java數據結構（遞歸執行順序、楊輝三角、斐波那契篇）

遞歸：程序調用自身的編程技巧稱爲遞歸（ recursion）。遞歸做爲一種算法在程序設計語言中廣泛應用。 一個過程或函數在其定義或說明中有直接或間接調用自身的一種方法，它通常把一個大型複雜的問題層層轉化爲一個與原問題相似的規模較小的問題來求解，遞歸策略只需少量的程序就可描述出解題過程所需要的多次重複計算，大大地減少了程序的代碼量。遞歸的能力在於用有限的語句來定義對象的無限集合。一般來說，遞歸需要有邊界條件、遞歸前進段和遞歸返回段。當邊界條件不滿足時，遞歸前進；當邊界條件滿足時，遞歸返回。

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);
		}
	}
}

執行順序大意圖：

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
Hello world! 16
Hello world! 17
Hello world! 18
Hello world! 19
Hello world! 20
Hello world! 21
Hello world! 22
Hello world! 23
Hello world! 24
Hello world! 25
Hello world! 26
Hello world! 27
Hello world! 28
Hello world! 29
Hello world! 30
Hello world! 31
Hello world! 32
Hello world! 33
Hello world! 34
Hello world! 35
Hello world! 36
Hello world! 37
Hello world! 38
Hello world! 39
Hello world! 40
Hello world! 41
Hello world! 42
Hello world! 43
Hello world! 44
Hello world! 45
Hello world! 46
Hello world! 47
Hello world! 48
Hello world! 49
Hello world! 50
Hello world! 51
Hello world! 52
Hello world! 53
Hello world! 54
Hello world! 55
Hello world! 56
Hello world! 57
Hello world! 58
Hello world! 59
Hello world! 60
Hello world! 61
Hello world! 62
Hello world! 63
Hello world! 64
Hello world! 65
Hello world! 66
Hello world! 67
Hello world! 68
Hello world! 69
Hello world! 70
Hello world! 71
Hello world! 72
Hello world! 73
Hello world! 74
Hello world! 75
Hello world! 76
Hello world! 77
Hello world! 78
Hello world! 79
Hello world! 80
Hello world! 81
Hello world! 82
Hello world! 83
Hello world! 84
Hello world! 85
Hello world! 86
Hello world! 87
Hello world! 88
Hello world! 89
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
Hello java! 88
Hello java! 87
Hello java! 86
Hello java! 85
Hello java! 84
Hello java! 83
Hello java! 82
Hello java! 81
Hello java! 80
Hello java! 79
Hello java! 78
Hello java! 77
Hello java! 76
Hello java! 75
Hello java! 74
Hello java! 73
Hello java! 72
Hello java! 71
Hello java! 70
Hello java! 69
Hello java! 68
Hello java! 67
Hello java! 66
Hello java! 65
Hello java! 64
Hello java! 63
Hello java! 62
Hello java! 61
Hello java! 60
Hello java! 59
Hello java! 58
Hello java! 57
Hello java! 56
Hello java! 55
Hello java! 54
Hello java! 53
Hello java! 52
Hello java! 51
Hello java! 50
Hello java! 49
Hello java! 48
Hello java! 47
Hello java! 46
Hello java! 45
Hello java! 44
Hello java! 43
Hello java! 42
Hello java! 41
Hello java! 40
Hello java! 39
Hello java! 38
Hello java! 37
Hello java! 36
Hello java! 35
Hello java! 34
Hello java! 33
Hello java! 32
Hello java! 31
Hello java! 30
Hello java! 29
Hello java! 28
Hello java! 27
Hello java! 26
Hello java! 25
Hello java! 24
Hello java! 23
Hello java! 22
Hello java! 21
Hello java! 20
Hello java! 19
Hello java! 18
Hello java! 17
Hello java! 16
Hello java! 15
Hello java! 14
Hello java! 13
Hello java! 12
Hello java! 11
Hello java! 10
Hello java! 9
Hello java! 8
Hello java! 7
Hello java! 6
Hello java! 5
Hello java! 4
Hello java! 3
Hello java! 2
Hello java! 1

三角數字：

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));
	}
	
	/**
	 * 三角數字循環相加
	 * @param n
	 * @return
	 */
	public static int trigo(int n){
		int total = 0;
		while(n > 0){
			total = total + n;
			n--;
		}
		return total;
	}
	
	/**
	 * 三角數字遞歸相加
	 * @param n
	 * @return
	 */
	public static int trigoRecursion(int n){
		if(n == 1)
			return 1;
		else
			return n + trigoRecursion(--n);
	}
}

楊輝三角：

package ch05Recursion;

import java.util.Scanner;

public class YangHui {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		System.out.println("請輸入將要顯示的楊輝三角的行數（>=3）：");
		int i = sc.nextInt();
		if(i <= 3){
			System.out.println("請輸入正確的值！");
			System.exit(-1);
		}
		// 建立楊輝三角形模型
		int yh[][] = new int[i][i];
		// 根據楊輝三角形特點，先錄入兩條邊上的值，皆爲1；
		for(int j = 0; j < i; j++){
			yh[j][0] = 1;                      
			yh[j][j] = 1;
		}
		// 根據楊輝三角形特點，填寫其他值，完成整個楊輝三角形；
		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];
		}
		// 打印楊輝三角形
		for(int j = 0; j < i; j++){
			for(int n = 0; n <= j; n++)
				System.out.print(yh[j][n] + " ");
			System.out.println();
		}
	}
}

請輸入將要顯示的楊輝三角的行數（>=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：比薩的列奧納多，又稱斐波那契（Leonardo Pisano ,Fibonacci, Leonardo Bigollo，1175年-1250年），意大利數學家，西方第一個研究斐波那契數，並將現代書寫數和乘數的位值表示法系統引入歐洲。

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);
	}
}

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