Step by step

You are given an array of integers, @ints. Write a script to find the minimum positive start value such that the step-by-step sum is never less than one.

Examples

Example 1
Input: @ints = (-3, 2, -3, 4, 2)
Output: 5
For start value 5.
5 + (-3) = 2
2 + (+2) = 4
4 + (-3) = 1
1 + (+4) = 5
5 + (+2) = 7

Example 2
Input: @ints = (1, 2)
Output: 1

Example 3
Input: @ints = (1, -2, -3)
Output: 5

Analysis

Unless I have misunderstood, this seems quite easy.

Do a trial run with a starting value of 0, and call the final value $least. The answer is then 1 - $least.

The only slight twist is that we are asked for the minimum positive value, so if 1 - $least < 1 then we return 1.

Using the CPAN power, the job becomes cake walk for anyone. See it yourself to believe.

Try it 

#!/usr/bin/perl

# Blog: http://ccgi.campbellsmiths.force9.co.uk/challenge

use v5.26;    # The Weekly Challenge - 2024-12-30
use utf8;     # Week 302 - task 2 - Step by step
use warnings; # Peter Campbell Smith
binmode STDOUT, ':utf8';

step_by_step(-3, 2, -3, 4, 2);
step_by_step(1, -2, -3);
step_by_step(6, 7, 8, 9, 10);

# larger example
my @ints;
push @ints, int(rand(50)) - 25 for 0 .. 99;
step_by_step(@ints);

sub step_by_step {
    
    my (@ints, $i, $sum, $least);
    @ints = @_;
    
    # find the smallest sum ($least) if we start with 0
    $least = 1e6;
    for $i (@ints) {
        $sum += $i;
        $least = $sum if $sum < $least;
    }
    
    # the answer is (1 - $least)
    say qq[\nInput:  \@ints = (] . join(', ', @ints) . qq[)];
    say qq[Output: ] . ((1 - $least) > 0 ? (1 - $least) : 1);
}

9 lines of code

Output from script

Input:  @ints = (-3, 2, -3, 4, 2)
Output: 5

Input:  @ints = (1, -2, -3)
Output: 5

Input:  @ints = (6, 7, 8, 9, 10)
Output: 1

Input:  @ints = (-7, 8, 10, -12, -22, -15, 18, 1, -8, 6,
5, 20, 19, -12, -18, 14, -22, -14, 3, -19, -23, 20, 6,
-18, 10, -24, 17, -22, -15, 16, 2, 2, -1, 17, -24, 14,
-21, 15, 13, 13, 24, 5, -16, 15, -11, 13, 10, 20, 8, -15,
11, -21, 8, 3, -2, 17, -6, 0, 7, 14, 16, -9, -2, -10, -2,
-18, 19, -18, 0, -8, 23, 7, -8, 15, -18, 7, 22, -2, 21,
-18, 3, 20, -14, 19, 2, 17, -6, -9, 1, 2, -24, 1, 24, -1,
6, -9, -11, 23, 16, -2)
Output: 95