Yanghui triangle code implementation

1                                             

1  1

1  2  1

1  3  3  1

1  4  6  4  1

1  5  10  5  1

. . . . . . . . . .

law ：

1. The first row and the main diagonal are 1

2. Current value = The previous row is preceded by the previous column + Same column as previous row

Two dimensional array implementation ：

Thinking analysis ：

1. The first row and the main diagonal are 1

arr[0][n]=0;arr[i][i]=0

2. Current value = The previous row is preceded by the previous column + Same column as previous row

arr[i][j]=arr[i-1][j-1]+arr[i-1][j]

// Yang Hui triangle two-dimensional array implementation 
#include<stdio.h>
#define MAX 10
int main()
{
    int arr[MAX][MAX];
    for(int i=0;i<MAX;i++)
    {
        for(int j=0;j<=i;j++)
        {
            if(j==0||i==j)
                arr[i][j]=1;
            else 
                arr[i][j]=arr[i-1][j-1]+[i-1][j];
            printf("%-4d",arr[i][j]);
        }
        printf("\n");
    }
}

One dimensional array implementation ：

Thinking analysis ：

Each row of data is directly updated in this array

For example, the third line 1  2  1

On the fourth line 1 3 3 1, It's on the third line 1  2  1 On the basis of

We try to find rules from the front to the back ：

The third line 1  2 1

In the fourth row 1  1+2=3  ● 1 

The fifth row   1  

● Place should be violet 2+1 Got 3, But at this point I found , The second data in the fourth row updates the original data to 3,2 It is no longer possible to use , From this it is found that , Data cannot be updated from front to back

Find the rules from the back to the front ：

benefits ： The main diagonal is updated each time 1

The third line 1  2 1  

In the fourth row   1        2          1           1

             1  2+1=3   1+2= 3      1

The fifth row  1          3           3         1            1

            1    3 +1 =4       3+3=6         3+1=4     1

Code implementation ：

// One dimensional array to achieve Yang Hui triangle 
#include<stdio.h>
#define MAX 10
int main()
{
    for(int i=0;i<MAX;i++)
    {
        for(int j=i;j>=0;j--)// Traverse from back to front 
        {
            if(j==0||j==i)
            {
                arr[j]=1;
            }
            else
            {
                arr[j]+=arr[j-1];
            }
            printf("%-4d",arr[j]);
        }
    }
}

If there are any mistakes, please let me know in the comments section , thank you