The parentheses in the "hard" expression represent order of evaluation. Rather than trying to generate the displayed form directly, just come up with a list of operators in random order, and derive the display form of the expression from that.

Numbers: 1 3 3 9 7 2

Operators: + * / + *

Result: ((1 + 3) * 3 / 9 + 7) * 2

Deriving the display form is a relatively simple recursive algorithm.

Update: here is an algorithm in Perl to generate the display form. It displays the components of the expression in a random order (without changing the value), so that the parentheses don't always end up on the left side.

use warnings;
use strict;

sub build_expression
{
    my ($num,$op) = @_;
    
    #Start with the final term.
    my $last_num = pop @$num; 
    my $last_op = pop @$op;

    #Base case: return the number if there is just a number 
    return $last_num unless defined $last_op;

    #Recursively call for the expression minus the final term.
    my $rest = build_expression($num,$op); 
    
    #Add parentheses if there is a bare + or - and this term is * or /
    $rest = "($rest)" if ($rest =~ /[+-][^)]+$|^[^)]+[+-]/ and $last_op !~ /[+-]/);
    
    #Return the two components in a random order.
    return rand(2) >= 1 ? "$rest $last_op $last_num" : "$last_num $last_op $rest";      
}

my @numbers   = qw/1 3 4 3 9 7 2 1 10/;
my @operators = qw|+ + * / + * * +|;

print build_expression([@numbers],[@operators]) , "\n";

The parentheses in the "hard" expression represent order of evaluation. Rather than trying to generate the displayed form directly, just come up with a list of operators in random order, and derive the display form of the expression from that.

Numbers: 1 3 3 9 7 2

Operators: + * / + *

Result: ((1 + 3) * 3 / 9 + 7) * 2

Deriving the display form is a relatively simple recursive algorithm.

Update: here is an algorithm in Perl to generate the display form. Because + and * are distributive, it randomizes the order of the terms for those operators. That helps keep the parentheses from all building up on one side.

use warnings;
use strict;

sub build_expression
{
    my ($num,$op) = @_;
    
    #Start with the final term.
    my $last_num = pop @$num; 
    my $last_op = pop @$op;

    #Base case: return the number if there is just a number 
    return $last_num unless defined $last_op;

    #Recursively call for the expression minus the final term.
    my $rest = build_expression($num,$op); 
    
    #Add parentheses if there is a bare + or - and this term is * or /
    $rest = "($rest)" if ($rest =~ /[+-][^)]+$|^[^)]+[+-]/ and $last_op !~ /[+-]/);
    
    #Return the two components in a random order for + or *.
    return $last_op =~ m|[-/]| || rand(2) >= 1 ? 
        "$rest $last_op $last_num" : "$last_num $last_op $rest";        
}

my @numbers   = qw/1 3 4 3 9 7 2 1 10/;
my @operators = qw|+ + * / + * * +|;

print build_expression([@numbers],[@operators]) , "\n";

The parentheses in the "hard" expression represent order of evaluation. Rather than trying to generate the displayed form directly, just come up with a list of operators in random order, and derive the display form of the expression from that.

Numbers: 1 3 3 9 7 2

Operators: + * / + *

Result: ((1 + 3) * 3 / 9 + 7) * 2

Deriving the display form is a relatively simple recursive algorithm.

The parentheses in the "hard" expression represent order of evaluation. Rather than trying to generate the displayed form directly, just come up with a list of operators in random order, and derive the display form of the expression from that.

Numbers: 1 3 3 9 7 2

Operators: + * / + *

Result: ((1 + 3) * 3 / 9 + 7) * 2

Deriving the display form is a relatively simple recursive algorithm.

Update: here is an algorithm in Perl to generate the display form. It displays the components of the expression in a random order (without changing the value), so that the parentheses don't always end up on the left side.

use warnings;
use strict;

sub build_expression
{
    my ($num,$op) = @_;
    
    #Start with the final term.
    my $last_num = pop @$num; 
    my $last_op = pop @$op;

    #Base case: return the number if there is just a number 
    return $last_num unless defined $last_op;

    #Recursively call for the expression minus the final term.
    my $rest = build_expression($num,$op); 
    
    #Add parentheses if there is a bare + or - and this term is * or /
    $rest = "($rest)" if ($rest =~ /[+-][^)]+$|^[^)]+[+-]/ and $last_op !~ /[+-]/);
    
    #Return the two components in a random order.
    return rand(2) >= 1 ? "$rest $last_op $last_num" : "$last_num $last_op $rest";      
}

my @numbers   = qw/1 3 4 3 9 7 2 1 10/;
my @operators = qw|+ + * / + * * +|;

print build_expression([@numbers],[@operators]) , "\n";