Absent smallest positive

You are given an array of integers. Write a script to return the smallest absent positive integer such that it is strictly greater than the average of all elements in the given array.

Examples

Example 1
Input: @arr = (1, 2, 4, 5, 6)
Output: 7
Average: (1 + 2 + 4 + 5 + 6) / 5 = 3.6
We need the smallest positive integer absent from nums that is
   strictly greater than 3.6.
The positive integers greater than 3.6 are 4, 5, 6, 7, ....
4 is in the given array.
5 is in the given array.
6 is in the given array.
7 is not in.

Example 2
Input: @arr = (-5, -2, -1, 3)
Output: 1
Average: (-5 -2 -1 + 3) / 4 = -1.25
We need the smallest absent positive integer strictly greater than
   -1.25.
Positive integers are 1, 2, 3, 4, ... (all are strictly greater than
   -1.25).
1 is positive and absent from the given array.

Example 3
Input: @arr = (1, 2, 3)
Output: 4
Average: (1 + 2 + 3) / 3 = 2.0
We need an integer strictly greater than 2.0.
3 is in the given array.
4 is not in.

Example 4
Input: @arr = (2, 3, 7, 8)
Output: 6
Average: (2 + 3 + 7 + 8) / 4 = 5.0
We need an integer strictly greater than 5.0.
6 is not in the given array.

Example 5
Input: @arr = (1, 1, 1, 10)
Output: 4
Average: (1 + 1 + 1 + 10) / 4 = 3.25
Positive integers strictly greater than 3.25: 4, 5, 6, ...
4 is not in the given array.

Analysis

Perhaps my mind has been dulled by the clocks going back, but I couldn't think of a shortcut to the obvious stepwise solution.

First I go through the array, summing the numbers and recording their presence in %present - a hash rather than an array as some of the numbers may be negative.

Then I start with the smallest integer which is larger than the average and no less than 1 and increment that until it doesn't appear in %present.

And that's the answer. It only takes 2 seconds to handle an array of a million numbers.

Try it 

Your input:

#!/usr/bin/perl

# Blog: http://ccgi.campbellsmiths.force9.co.uk/challenge/397/1

use v5.28;    # The Weekly Challenge - 2026-10-26
use utf8;     # Week 397 - task 1 - Absent smallest positive
use warnings; # Peter Campbell Smith
binmode STDOUT, ':utf8';
use Encode;

absent_smallest_positive(1, 2, 4, 5, 6);
absent_smallest_positive(-5, -2, -1, 3);
absent_smallest_positive(1, 2, 3);
absent_smallest_positive(2, 3, 7, 8);
absent_smallest_positive(1, 1, 1, 10);

my @array;
push @array, int(rand(10000)) for 1 .. 500;
absent_smallest_positive(@array);

sub absent_smallest_positive {
    
    my (@array, $total, %present, $answer);
    
    # find total and record presence
    @array = @_;
    for (@array) {
        $total += $_;
        $present{$_} = 1;
    }
    
    # find minimum answer and increment until not present
    $answer = int($total / $#array) + 1;
    $answer = 1 if $answer < 1;
    $answer ++ while $present{$answer};
    
    # report
    say qq[\nInput:  (] . join(', ', @array) . ')';
    say qq[Output: $answer];
}

11 lines of code

Output from script

Input:  (1, 2, 4, 5, 6)
Output: 7

Input:  (-5, -2, -1, 3)
Output: 1

Input:  (1, 2, 3)
Output: 4

Input:  (2, 3, 7, 8)
Output: 9

Input:  (1, 1, 1, 10)
Output: 5

Input:  (9666, 5416, 1918, 2300, 8750, 5620, 6396, 933, 2782, 2295,
   567, 1023, 5617, 5044, 8860, 4595, 4675, 4812, 597, 8533, 9402,
   2178, 5788, 829, 4709, 3471, 7122, 3586, 5760, 8240, 9426, 2788,
   1774, 9609, 2921, 7624, 9193, 1822, 9292, 9028, 4058, 3297, 4170,
   6681, 1087, 5257, 7553, 1198, 2344, 4793, 5786, 7455, 1851, 1354,
   8046, 1562, 7684, 9239, 4149, 7005, 9490, 7911, 3543, 796, 4522,
   1598, 1566, 2623, 7922, 9846, 4456, 5071, 4592, 9037, 9861, 878,
   8402, 9160, 2283, 226, 5256, 911, 209, 2577, 6535, 1069, 2785, 34,
   8328, 2291, 2486, 3430, 5509, 575, 7160, 4978, 1905, 5622, 244,
   8588, 3460, 7517, 4257, 7769, 8217, 6456, 6727, 2898, 9128, 9720,
   3280, 1905, 5120, 3485, 3273, 7717, 5358, 3240, 4368, 9977, 7462,
   107, 3917, 9431, 4419, 5887, 3914, 9132, 7289, 4620, 9024, 4443,
   2591, 5240, 2593, 2146, 8612, 8822, 6406, 332, 4025, 5185, 6643,
   3883, 3277, 240, 516, 3118, 5490, 5620, 7193, 4569, 9397, 1534,
   9032, 6141, 4303, 8451, 8125, 3278, 2735, 1712, 1436, 6910, 1452,
   9244, 312, 7298, 4453, 7699, 6032, 4483, 761, 7961, 8942, 5632,
   5738, 1554, 267, 1407, 2752, 4123, 1056, 7799, 929, 8146, 4169,
   1085, 8843, 1411, 2469, 2294, 5999, 468, 8263, 3526, 7455, 4240,
   6762, 2613, 8500, 4941, 5433, 9882, 8689, 4160, 4208, 2573, 8420,
   7005, 821, 8920, 8314, 7071, 5137, 6804, 6777, 8135, 5116, 6625,
   5010, 3195, 536, 6778, 248, 8974, 4338, 3514, 7023, 494, 2473,
   7478, 5636, 9733, 3584, 2901, 5699, 8805, 8308, 4927, 7573, 8194,
   3109, 7368, 3725, 6344, 5626, 184, 6467, 7746, 2574, 9992, 5325,
   2434, 9266, 1143, 1454, 2678, 3349, 1501, 4148, 314, 7966, 9455,
   4847, 5670, 9326, 4465, 2134, 1701, 5694, 6298, 403, 2870, 3891,
   861, 9252, 450, 1977, 7300, 7659, 5249, 4376, 9931, 9688, 6042,
   6268, 3931, 8498, 1025, 5656, 9094, 4774, 8952, 3712, 5937, 147,
   2871, 1335, 1871, 6784, 8976, 3544, 6978, 892, 5333, 4441, 3281,
   548, 4511, 6802, 3536, 925, 2450, 9460, 4946, 1778, 5454, 7028,
   5363, 953, 2893, 4111, 9303, 1992, 4919, 6202, 4283, 5453, 139,
   2354, 4709, 9946, 5275, 8280, 6978, 5815, 8136, 9756, 1005, 8632,
   2158, 4386, 6546, 968, 8742, 8603, 8136, 5025, 6039, 6989, 7102,
   9581, 5802, 2889, 8815, 7060, 4715, 5166, 5424, 8404, 2153, 2679,
   9877, 8553, 1627, 9472, 3786, 5948, 67, 3256, 5986, 8197, 4340,
   2850, 8480, 9285, 2696, 6917, 3650, 3151, 4667, 3530, 9256, 4507,
   3924, 4322, 3124, 1248, 6970, 6919, 5946, 8118, 6702, 7907, 703,
   8377, 3974, 6125, 9858, 7472, 5425, 2008, 4175, 9235, 55, 4931,
   9177, 3278, 6186, 3094, 9728, 280, 444, 2807, 9600, 6104, 9875,
   8750, 9509, 3489, 1005, 8837, 3659, 1904, 6963, 5937, 5174, 8299,
   7361, 344, 4823, 8578, 9588, 7445, 4305, 6980, 3986, 2408, 5345,
   6811, 6063, 416, 3351, 5621, 3615, 6497, 29, 3563, 5302, 2367,
   2862, 8870, 4799, 9973, 1628, 5917, 3805, 8234, 8251, 1653, 792,
   3390, 7429, 6258, 5860, 6601, 2023, 5177, 6054, 9154, 710, 7211,
   8355, 4519, 1492, 7720, 7623, 3411, 5229, 6160, 5252, 8090, 9372,
   2924, 7379, 2800, 5692, 4751, 3149, 346, 3303, 9637, 7756, 9108,
   2203, 8300, 8620, 8848, 4367)
Output: 5121