对于递归的个人理解

递归

条件

1. 可以通过递归调用来缩小问题规模，且新问题与原问题有着相同的形式。（自身调用）

2. 存在一种简单情境，可以使递归在简单情境下退出。（递归出口）

递归三要素

1. 一定有一种可以退出程序的情况；

2. 总是在尝试将一个问题化简到更小的规模

3. 父问题与子问题不能有重叠的部分

例子

public class Factorial {

    public static void main(String[] args) {
        printNum(5);
    }

    public static void printNum(int num){
        if (num > 1){							//------>如果num<=1 就退出，递归的出口
            num = num - 1;						//将num逐渐变小，逐渐靠近退出的情况
            printNum(num);						//------>调用自己
        }
        System.out.print(num + ",");
    }
}

执行结果：1,1,2,3,4,

流程分析

public static void printNum(5){
        if (num > 1){           //--->num = 5,成立
            num = num - 1;		//--->num = 4
            printNum(num);
        }
        System.out.print(num + ",");
    }

public static void printNum(5){
    
   public static void printNum(4){
        if (num > 1){           //--->num = 4,成立
            num = num - 1;		//--->num = 3
            printNum(num);
        }
        System.out.print(num + ",");
    }
    
    
    System.out.print(num + ",");   //--->num:4
}

public static void printNum(5){
   public static void printNum(4){
    	public static void printNum(3){
            if (num > 1){           //--->num = 3,成立
                num = num - 1;		//--->num = 2
                printNum(num);
            }
            System.out.print(num + ",");
    	}
        System.out.print(num + ","); //------3
    } 
   System.out.print(num + ",");  //----->4
}

public static void printNum(int num){
   public static void printNum(int num){
    	public static void printNum(int num){
            	public static void printNum(int num){
                    if (num > 1){           //--->num = 2,成立
                        num = num - 1;		//--->num = 1
                        printNum(num);
                    }
                    System.out.print(num + ",");
                }
            System.out.print(num + ","); //------>2
    	}
        System.out.print(num + ",");//------->3
    } 
   System.out.print(num + ","); // ------>4
}

public static void printNum(int num){
   public static void printNum(int num){
    	public static void printNum(int num){
            	public static void printNum(int num){
                    	public static void printNum(int num){
                            if (num > 1){           //--->num = 1,不成立
                                num = num - 1;	
                                printNum(num);
                            }
                            System.out.print(num + ",");					//当前打印:1,
                        }
                    System.out.print(num + ","); //-------->1
                }
            System.out.print(num + ","); // ------->2
    	}
        System.out.print(num + ","); // ------->3
    } 
   System.out.print(num + ","); // ----->4
}

public static void printNum(int num){
   public static void printNum(int num){
    	public static void printNum(int num){
            	public static void printNum(int num){
                    	public static void printNum(int num){
                            System.out.print(num + ","); //--->打印当前的num：1
                        }
                    System.out.print(num + ","); // -------->1				//当前打印:1,
                }
            System.out.print(num + ",");//-------->2
    	}
        System.out.print(num + ",");//-------->3
    } 
   System.out.print(num + ",");//-------->4
}

public static void printNum(int num){
   public static void printNum(int num){
    	public static void printNum(int num){
            	public static void printNum(int num){
                    System.out.print(num + ","); //--->打印当前的num：1		
                }															//当前打印:1,1,
            System.out.print(num + ",");
    	}
        System.out.print(num + ",");
    } 
   System.out.print(num + ",");
}

public static void printNum(int num){
   public static void printNum(int num){
    	public static void printNum(int num){
            System.out.print(num + ",");//--->打印当前的num：2			//当前打印:1,1,2,
    	}
        System.out.print(num + ",");
    } 
   System.out.print(num + ",");
}

public static void printNum(int num){
   public static void printNum(int num){
        System.out.print(num + ",");//--->打印当前的num：3			//当前打印:1,1,2,3
    } 
   System.out.print(num + ",");
}

public static void printNum(int num){ 
   System.out.print(num + ",");//--->打印当前的num：4					//当前打印:1,1,2,3,4
}