帕斯卡三角函数

Question

我正在尝试编写一个函数来打印出 帕斯卡三角形 直到用户输入的步骤。该程序一直运行到第 5 步，并打印出 0 1 4 0 4 1 0 而不是预期的 0 1 4 6 1 0。它从另一个列表中获取两个值，当时都是3，然后添加它们，所以我不确定它如何更改为0。 代码：

static void PascalsTri(int input)
  {
    //Declare lists starting at 0 1 0
    int counter = 0;
    int[] start = { 0, 1, 0 };
    List<int> TriList = new List<int>(start);
    List<int> TempTriList = new List<int>();
    //Check if input is possible
    if(input < 1)
    {
      return;
    }
    //Write starting list to console
    Console.WriteLine(string.Join(" ", TriList));
    //Run the function as many times as the user input
    for(int i = 1; i < input; i++)
    {
      //Start off with the first two digits
      TempTriList.Add(0);
      TempTriList.Add(1);
      //Loop through writing the rule for as many numbers as there are
      while(counter < i)
      {
        //Takes the previous number and adds it to the correlating number
        TempTriList.Insert(counter+1, TriList[counter] + TriList[counter+1]);
        counter++;
      }
      TempTriList.Add(0);
      TriList.Clear();
      //Records the output in the permanent list, and prints it to the console
      foreach(int j in TempTriList)
      {
        TriList.Add(TempTriList[j]);
      }
      TempTriList.Clear();
      counter = 0;
      Console.WriteLine(string.Join(" ", TriList));
    }
  }

Answer 1

如果您想逐行打印 Pascal Triangle，您可以在计算 next 行时循环 (fiddle)

代码：

    static void PascalTri(int rowsToPrint) {
      // 1st current line
      int[] current = new int[] { 0, 1, 0 };
      
      Console.WriteLine(string.Join(" ", current));

      // we compute all the other lines in a simple loop
      for (int r = 1; r < rowsToPrint; ++r) {
        // next line is 1 number longer than current
        int[] next = new int[current.Length + 1];

        // compute next line items
        for (int c = 0; c < current.Length - 1; ++c)
          next[c + 1] = current[c] + current[c + 1];

        // after computation, next line becomes current one
        current = next;

        // finally, we print the line
        Console.WriteLine(string.Join(" ", current));
      }
    }

演示：

PascalTri(10);

结果：

0 1 0
0 1 1 0
0 1 2 1 0
0 1 3 3 1 0
0 1 4 6 4 1 0
0 1 5 10 10 5 1 0
0 1 6 15 20 15 6 1 0
0 1 7 21 35 35 21 7 1 0
0 1 8 28 56 70 56 28 8 1 0
0 1 9 36 84 126 126 84 36 9 1 0

Answer 2

这也让我难过一阵子。然后我意识到你foreach中的一行代码是错误的。

TriList.Add(TempTriList[j]);

应该是：

TriList.Add(j);

变量“j”不是索引，而是数组值本身。一旦你做出改变，一切都会奏效。

如果使用递归方法，此代码可能会更好地安排，但由于您拥有的工作（现在），我会留下它。使用递归进行更改可能很困难，并且远远超出了这个问题的范围。