number_triangle_pattern_from_top.c

/*

    number_triangle_pattern_interesting.c

https://www.facebook.com/groups/3092811364081112/permalink/7605244639504406/

numbers           indexes           matrix

1                 00                00 01 02 03 04
2 6               10 11             10 11 12 13 14
3 7 10            20 21 22          20 21 22 23 24
4 8 11 13         30 31 32 33       30 31 32 33 34
5 9 12 14 15      40 41 42 43 44    40 41 42 43 44

r - row
c - column

There are n rows and at most n columns.

The number of columns in a row is the row number (r)

The number in the first  column is the row number (r)

The number in the n-th   column is ...

In order to calculate the corresponding number to be written
in the place whose indices are r1,c1,
we will use the indices of the virtual matrix M[n][n].

See separation_of_matrix_elements.c
https://pastebin.com/7AbM4rB1

An square matrix M[r][c] of characters of dimension 5 x 5 is given.
Separate various elements of matrix to an array.

r is index of rows.
c is index of columns.

elements of the main diagonal have the property:    r = c


elements above the main diagonal have the property: r < c


elements of the first diagonal above the main diagonal have the property:      r-c = -1

elements of the second diagonal above the main diagonal have the property:     r-c = -2

elements of the third diagonal above the main diagonal have the property:      r-c = -3

the elements of the fourth diagonal above the main diagonal have the property: r-c = -4


elements below the main diagonal have the property: r > c


elements of the first diagonal below the main diagonal have the property:  r-c = 1

elements of the second diagonal below the main diagonal have the property: r-c = 2

elements of the third diagonal below the main diagonal have the property:  r-c = 3

elements of the fourth diagonal below the main diagonal have the property: r-c = 4




elements of the side diagonal have the property: r+c = n-1


elements above the side diagonal have the property: r+c < n-1


elements of the first diagonal above the side diagonal have the property:  r+c = n-1

elements of the second diagonal above the side diagonal have the property: r+c = n-2

elements of the third diagonal above the side diagonal have the property:  r+c = n-3

elements of the fourth diagonal above the side diagonal have the property: r+c = n-4


elements below the side diagonal have the property: r+c >= n


elements of the first diagonal below the side diagonal have the property:  r+c = 5

elements of the second diagonal below the side diagonal have the property: r+c = 6

elements of the third diagonal below the side diagonal have the property:  r+c = 7

elements of the fourth diagonal below the side diagonal have the property: r+c = 8




    You can find all my C programs at Dragan Milicev's pastebin:

    https://pastebin.com/u/dmilicev

*/

#include <stdio.h>

/*
numbers           indexes           matrix
1                 00                00 01 02 03 04
2 6               10 11             10 11 12 13 14
3 7 10            20 21 22          20 21 22 23 24
4 8 11 13         30 31 32 33       30 31 32 33 34
5 9 12 14 15      40 41 42 43 44    40 41 42 43 44
*/
// counts elements up to element r1,c1
int calculate_num(int n, int r1, int c1){
    int r, c, num=0, fromWhichRow=0;

    for(c=0;c<=c1;c++){ // for all columns up to the column in which the requested element is
        if(c<c1){
            for(r=fromWhichRow;r<n;r++) // from which row to count elements
                num++;
            fromWhichRow++;             // the next first row from which it is counted
        }
        else if(c==c1)  // for the column in which the requested element is
            for(r=fromWhichRow;r<=r1;r++)
                num++;
    }
    return num;
}

// print triangle of numbers
void number_triangle_pattern_interesting(int n){
    int r, c, num;          // r - row, c - column, num - number to be printed

    for(r=0;r<n;r++){       // for all rows
        for(c=0;c<n;c++)    // for all columns
            if(r>=c){       // elements on the main diagonal and below the main diagonal have a property r >= c
                num = calculate_num(n,r,c);
                printf("%3d",num);  // calculate and print the corresponding number num
            }
        printf("\n");       // new row
    }
}


int main(void){
    int n;                  // number of rows and columns

    for(n=3;n<7;n++){       // a few examples
        printf("\n  n = %d \n\n",n);
        number_triangle_pattern_interesting(n);
    }

    printf("\n\n");
    return 0;
} // main()