C#递归计算数列a(n)=a(n-1)+a(n-2)的第n项

目录

一、关于递归

二、示例

三、生成效果

一、关于递归

????????递归算法在程序设计中被广泛应用，递归是方法在运行中直接或间接调用自身而产生的重入现象，它是计算机科学的一个重要概念，而且在算法的世界中占有着重要的位置，使用递归方法可以使代码变得更加简洁和清晰。?

????????在C#中，每建立一条线程都会被分配大约1MB大小的地址空间，由于线程栈有固定的大小，如果进行递归的层次太深，有可能会出现溢出。

二、示例

// 递归计算数列a(n)=a(n-1)+a(n-2)
namespace _032
{
    public partial class Form1 : Form
    {
        private Label? label1;
        private TextBox? textBox2;
        private TextBox? textBox1;
        private Button? button1;
        private GroupBox? groupBox1;
        public Form1()
        {
            InitializeComponent();
            Load += Form1_Load;
        }
        private void Form1_Load(object? sender, EventArgs e)
        {
            // 
            // label1
            // 
            label1 = new Label
            {
                AutoSize = true,
                Location = new Point(12, 22),
                Name = "label1",
                Size = new Size(43, 17),
                TabIndex = 0,
                Text = "输入数列第n项："
            };
            // 
            // textBox1
            // 
            textBox1 = new TextBox
            {
                Location = new Point(115, 22),
                Name = "textBox1",
                Size = new Size(100, 23),
                TabIndex = 1
            };
            // 
            // textBox2
            // 
            textBox2 = new TextBox
            {
                Location = new Point(12, 51),
                Name = "textBox2",
                Size = new Size(180, 23),
                TabIndex = 3,
                Visible = false
            };

            // 
            // button1
            //                
            button1 = new Button
            {
                Location = new Point(230, 22),
                Name = "button1",
                Size = new Size(70, 23),
                TabIndex = 2,
                Text = "计算",
                UseVisualStyleBackColor = true
            };
            button1.Click += Button1_Click;
            // 
            // groupBox1
            // 
            groupBox1 = new GroupBox
            {
                Location = new Point(12, 12),
                Name = "groupBox1",
                Size = new Size(310, 87),
                TabIndex = 3,
                TabStop = false,
                Text = "递归计算数列a(n)=a(n-1)+a(n-2)"
            };          
            groupBox1.Controls.Add(label1);
            groupBox1.Controls.Add(button1);
            groupBox1.Controls.Add(textBox1);
            groupBox1.Controls.Add(textBox2);
            groupBox1.SuspendLayout();
            // 
            // Form1
            // 
            AutoScaleDimensions = new SizeF(7F, 17F);
            AutoScaleMode = AutoScaleMode.Font;
            ClientSize = new Size(334, 111);           
            Controls.Add(groupBox1);
            Name = "Form1";
            StartPosition = FormStartPosition.CenterScreen;
            Text = "递归算法";
            groupBox1.ResumeLayout(false);
            groupBox1.PerformLayout();
        }

        private void Button1_Click(object? sender, EventArgs e)
        {
            textBox2!.Visible = true;
            if (int.TryParse(textBox1!.Text, out int Input_int))//为变量赋值
            {
                textBox2!.Text =                                //输出计算结果
                   "计算结果为：" + Get(Input_int).ToString();
            }
            else
            {
                MessageBox.Show("请输入正确的数值！", "提示！");  //提示输入正确数值                                
            }
        }

        /// <summary>
        /// 递归算法
        /// </summary>
        /// <param name="i">数列的第n项n值</param>
        /// <returns>计算结果</returns>
        static int Get(int i)
        {
            if (i <= 0)							//判断数值是否小于0
                return 0;						//返回数值0
            else if (i >= 1 && i <= 2)			//判断位数是否大于等于0并且小于等于2
                return 1;						//返回数值1
            else								//如果不满足上述条件执行下面语句
                return Get(i - 1) + Get(i - 2);	//返回指定位数前两位数的和
        }
    }
}

三、生成效果

?