Task — Summations

You are given a list of positive numbers, @n. Write a script to find out the summations as described below.

Examples

Example 1
Input: @n = (1, 2, 3, 4, 5)
Output: 42
    1 2 3  4  5
      2 5  9 14
        5 14 28
          14 42
             42
The nth row starts with the second element of the (n-1)th 
row. The following element is sum of all elements except 
first element of previous row. You stop once you have just
one element in the row.

Example 2
Input: @n = (1, 3, 5, 7, 9)
Output: 70
    1 3  5  7  9
      3  8 15 24
         8 23 47
           23 70
              70

Analysis

We are given a list of positive numbers and asked to generate a triangular array according to certain rules.

From the examples we can see that the first row of the output is just the input.

The nth row then has n - 1 blank columns, and subsequent columns contain the sum of the cell to the left and the cell above.

There is, as usual, the issue of producing pretty output, and I chose to output all the cells one character wider than the final cell, which is always going to be the largest number.

Try it 

#!/usr/bin/perl

# Peter Campbell Smith - 2022-05-03
# PWC 163 task 2

use v5.28;
use strict;
use warnings;
use utf8;

my (@tests, $test, @n, $rows, $row, $col, @grid, $width);

@tests = ([1, 2, 3, 4, 5], [1, 3, 5, 7, 9], [12, 32, 43, 72, 34, 99, 6, 50]);

# loop over tests
for $test (@tests) {
    @n = @$test;
    $rows = scalar @n;
    
    # create a grid of the output
    for $row (0 .. $rows - 1) {
        for $col (0 .. $rows - 1) {
            
            # the first row is just the input
            if ($row == 0) {
                $grid[0][$col] = $n[$col];
            
            # any cell where $col < $row is blank - so make it 0 for now
            } elsif ($col < $row) {
                $grid[$row][$col] = 0;
                
            # all the other cells are the sum of the cell to the left and the cell above
            } else {
                $grid[$row][$col] = $grid[$row - 1][$col] + $grid[$row][$col - 1];
            }
        }
    }
    
    # for a nice output the width of each column is the width of the final cell + 1
    $width = length($grid[$rows - 1][$rows - 1]) + 1;
    
    # output the result - padded to $width, or if zero, just $width spaces
    say '';
    for $row (0 .. $rows - 1) {
        for $col (0 .. $rows - 1) {
            print $grid[$row][$col] ? sprintf("\%${width}d", $grid[$row][$col]) : (' ' x $width);
        }
        say '';
    }   
}

Output

  1  2  3  4  5
     2  5  9 14
        5 14 28
          14 42
             42

  1  3  5  7  9
     3  8 15 24
        8 23 47
          23 70
             70

    12    32    43    72    34    99     6    50
          32    75   147   181   280   286   336
                75   222   403   683   969  1305
                     222   625  1308  2277  3582
                           625  1933  4210  7792
                                1933  6143 13935
                                      6143 20078
                                           20078