C#使用迭代算法计算斐波那契数列通项

目录

1.斐波纳契数列

2.迭代一次产生1个新的通项

3.迭代一次产生2个新的通项

---

1.斐波纳契数列

        斐波纳契数列的定义是，它的第一项和第二项均为1，以后各项都为前两项之和。        

        公式如下：

        F(n) = F(n-1) + F(n-2)

        其中，F(1) = 0, F(2) = 1。

2.迭代一次产生1个新的通项

// 用迭代的方法求斐波那契数列通项

namespace _147_1
{
    class Program
    {
        static void Main(string[] args)
        {
            ArgumentNullException.ThrowIfNull(args);

            int n = 10;
            int a = 0, b = 1, c = 0;
            string fibSequence = "";

            for (int i = 1; i <= n; i++)
            {
                c = a + b;
                a = b;
                b = c;
                fibSequence += c.ToString() + (i < n ? ", " : "");
            }

            Console.WriteLine("第{0}项斐波那契数列的值为：{1}", n, c);
            Console.WriteLine("斐波那契数列的前{0}项为：{1}", n, fibSequence);
        }
    }
}
//运行结果：
/*
第10项斐波那契数列的值为：89
斐波那契数列的前10项为：1, 2, 3, 5, 8, 13, 21, 34, 55, 89

*/

3.迭代一次产生2个新的通项

 

// 斐波纳契数列通项
namespace _147
{
    public partial class Form1 : Form
    {
        private ListBox? listBox1;
        private Label? label1;
        private TextBox? textBox1;
        private Button? button1;

        public Form1()
        {
            InitializeComponent();
            StartPosition = FormStartPosition.CenterScreen;
            Load += Form1_Load;
        }

        private void Form1_Load(object? sender, EventArgs e)
        {
            // 
            // listBox1
            // 
            listBox1 = new ListBox
            {
                FormattingEnabled = true,
                ItemHeight = 17,
                Location = new Point(12, 12),
                Name = "listBox1",
                Size = new Size(250, 191),
                TabIndex = 0
            };
            // 
            // label1
            // 
            label1 = new Label
            {
                AutoSize = true,
                Location = new Point(12, 217),
                Name = "label1",
                Size = new Size(44, 17),
                TabIndex = 1,
                Text = "数字："
            };
            // 
            // textBox1
            // 
            textBox1 = new TextBox
            {
                Location = new Point(71, 211),
                Name = "textBox1",
                Size = new Size(100, 23),
                TabIndex = 2
            };
            // 
            // button1
            // 
            button1 = new Button
            {
                Location = new Point(186, 211),
                Name = "button1",
                Size = new Size(75, 23),
                TabIndex = 3,
                Text = "计算",
                UseVisualStyleBackColor = true
            };
            button1.Click += Button1_Click;
            // 
            // Form1
            // 
            AutoScaleDimensions = new SizeF(7F, 17F);
            AutoScaleMode = AutoScaleMode.Font;
            ClientSize = new Size(274, 246);
            Controls.Add(button1);
            Controls.Add(textBox1);
            Controls.Add(label1);
            Controls.Add(listBox1);
            Name = "Form1";
            Text = "Form1";
        }

        private void Button1_Click(object? sender, EventArgs e)
        {
            listBox1?.Items.Clear();//清空ListBox控件
            int a = 1, b = 1;          //定义变量
            int p;                     //循环次数
            try
            {
                p = Convert.ToInt32(textBox1!.Text);
            }
            catch                      //出现错误
            {
                MessageBox.Show("请输入数值型数据");
                textBox1!.Text = "15";
                return;
            }

            int n;
            for (n = 1; n <= p; n++)//每次遍历添加2个项目
            {
                listBox1!.Items.Add(a.ToString());//输出数值
                listBox1.Items.Add(b.ToString());//输出数值
                a += b;//获取前两个数的和
                b += a;//获取前两个数的和
            }
        }
    }
}