java - 如何将其变成帕斯卡三角形而不是直角三角形？

Question

我需要一个用于制作帕斯卡三角形的代码。此代码适用于直角三角形，但我需要它是帕斯卡三角形。它需要有 10 行，并且顶部和底部中间有一个间隙。有人可以帮我解决这个问题吗？ for 循环就可以了。

public static int get_pascal(int row, int col) {
    if (col == 0 || col == row) {
        return 1;
    } else {
        return get_pascal(row - 1, col - 1) + get_pascal(row - 1, col);
    }
}

public static void main(String[] args) {
    //row size variable
    int rowNum = 5;

    levels = new String[rowNum];

    int i = 0;
    int arIndex = 0;
    System.out.println(recurseRow(i, rowNum, arIndex));
    System.out.println("                                 ");
    System.out.println(upsideDown(rowNum - 1));
}

//Recursion for row
public static String recurseRow(int i, int rowNum, int arrayIndex) {
    if (i == rowNum)
        return "";
    else {
        int k = 0;
        int next = i + 1;
        String str = recurseCol(i, k);
        levels[arrayIndex] = str;
        arrayIndex += 1;
        return str + "\n" + recurseRow(next, rowNum, arrayIndex);
    }
}

//Recursion for column
public static String recurseCol(int i, int k) {
    if (k > i)
        return "";
    else {
        int next = k + 1;
        return get_pascal(i, k) + " " + recurseCol(i, next);
    }
}

//upside down recursion
public static String upsideDown(int index) {
    if (index < 0) {
        return "";
    } else {
        String str = levels[index];
        index -= 1;
        return str + "\n" + upsideDown(index);
    }
}

Answer 1

帕斯卡三角形 - 是二项式系数的三角形数组，其中第一行和第一列的元素等于 1，所有其他元素是该行和列中前一个元素的总和。

T[i][j] = T[i][j-1] + T[i-1][j];

您可以创建一个迭代方法来填充这样的数组:

public static int[][] pascalsTriangle(int n) {
    // an array of 'n' rows
    int[][] arr = new int[n][];
    // iterate over the rows of the array
    for (int i = 0; i < n; i++) {
        // a row of 'n-i' elements
        arr[i] = new int[n - i];
        // iterate over the elements of the row
        for (int j = 0; j < n - i; j++) {
            if (i == 0 || j == 0) {
                // elements of the first row
                // and column are equal to one
                arr[i][j] = 1;
            } else {
                // all other elements are the sum of the
                // previous element in the row and column
                arr[i][j] = arr[i][j - 1] + arr[i - 1][j];
            }
        }
    }
    return arr;
}

public static void main(String[] args) {
    int n = 10;
    System.out.println("n = " + n);
    System.out.println("Pascal's triangle:");
    int[][] arr = pascalsTriangle(n);
    for (int[] row : arr) {
        for (int element : row)
            System.out.printf("%2d ", element);
        System.out.println();
    }
}

输出:

n = 10
Pascal's triangle:
 1  1  1  1  1  1  1  1  1  1 
 1  2  3  4  5  6  7  8  9 
 1  3  6 10 15 21 28 36 
 1  4 10 20 35 56 84 
 1  5 15 35 70 126 
 1  6 21 56 126 
 1  7 28 84 
 1  8 36 
 1  9 
 1 

<小时/>

^{另请参阅:Array of binomial coefficients}