The absolute value of a number \$x\$ is normally written as \$|x|\$. The left and right side of the absolute value uses the same symbol, so it is not immediately obvious how to parse nested absolute values e.g. \$||1-2|+|3-|4-5|||\$

Your goal is to parse such an expression containing nested absolute values:

The expression will be given as a string of characters.
For simplicity the expression will only contain single digit numbers (or letters if that is easier in your language), the operators + and - (you can use any two distinct characters to represent these operations) and the symbol | for the left and right side of a absolute value.
You do not need to handle the case where a number is directly adjacent to a absolute value (e.g. 2|3| or |2|3, this generalization will be handled in the companion challenge)

Your output should be the same expression in a form that allows to determine how the absolute values are bracketed.

The output has to satisfy the following rules:

• The expression within a absolute value must not end with an operator ( + or - )
• The expression within a absolute value cannot be empty
• Each | has to be part of exactly one absolute value

You may assume there is a valid way to parse the given input.

Examples:

|2|                ->  (2)
|2|+|3|            ->  (2)+(3)
||2||              ->  ((2))
||2|-|3||          ->  ((2)-(3))
|-|-2+3||          ->  (-(-2+3))
|-|-2+3|+|4|-5|    ->  (-(-2+3)+(4)-5)
|-|-2+|-3|+4|-5|   ->  (-(-2+(-3)+4)-5)
||1-2|+|3-|4-5|||  ->  ((1-2)+(3-(4-5)))

This is code-golf the shortest solution wins.

Parse nested absolute values 2

The absolute value of a number \$x\$ is normally written as \$|x|\$. The left and right side of the absolute value uses the same symbol, so it is not immediately obvious how to parse nested absolute values e.g. \$||1-2|+|3-|4-5|||\$

Your goal is to parse such an expression containing nested absolute values:

Follow up to my previous challenge about parsing nested absolute values

The expression will be given as a string of characters. For simplicity the expression will only contain single digit numbers (or letters if that is easier in your language), the operators + and - (you can use any two distinct characters to represent these operations) and the symbol | for the left and right side of a absolute value. To make the challenger not too easy, it is allowed for numbers to be directly adjacent to absolute values so (2|3| and |2|3 both are valid expressions)

Your output should be the same expression in a form that allows to determine how the absolute values are bracketed.

The output has to satisfy the following rules:

• The expression within a absolute value must not end with an operator ( + or - )
• The expression within a absolute value cannot be empty
• Each | has to be part of exactly one absolute value

You may assume there is a valid way to parse the given input. If there is more than one way to parse the expression you can choose any valid solution.

Examples (all possible outputs):

|2|                ->  (2)
|2|+|3|            ->  (2)+(3)
|2|3|-4|           ->  (2)3(-4)    
|2|3|-4|           ->  (2(3)-4)
|2|3-|4|           ->  (2)3-(4)
||2||              ->  ((2))
||2|-|3||          ->  ((2)-(3))
|-|-2+3||          ->  (-(-2+3))
|-|-2+3|+|4|-5|    ->  (-(-2+3)+(4)-5)
|-|-2+|-3|+4|-5|   ->  (-(-2+(-3)+4)-5)
||1-2|+|3-|4-5|||  ->  ((1-2)+(3-(4-5)))

This is code-golf the shortest solution wins.

code-golf parsing

Meta

• Is this a duplicate?

• Is the formulation clear?

• Should I post both versions, or only one of them (The firsts one is relatively easy, the second one is probably more difficult)?

Part1

Part2

The expression will be given as a string of characters. For simplicity the expression will only contain single digit numbers (or letters if that is easier in your language), the operators + and - (you can use any two distinct characters to represent these operations) and the symbol | for the left and right side of a absolute value.

Examples:

|2|                ->  (2)
|2|+|3|            ->  (2)+(3)
||2||              ->  ((2))
||2|-|3||          ->  ((2)-(3))
|-|-2+3||          ->  (-(-2+3))
|-|-2+3|+|4|-5|    ->  (-(-2+3)+(4)-5)
|-|-2+|-3|+4|-5|   ->  (-(-2+(-3)+4)-5)
||1-2|+|3-|4-5|||  ->  ((1-2)+(3-(4-5)))

• Is this a duplicate?

• Is the formulation clear?

• Should I allow implicit products ( 2|3| -> 2(3) )

The expression will be given as a string of characters.
For simplicity the expression will only contain single digit numbers (or letters if that is easier in your language), the operators + and - (you can use any two distinct characters to represent these operations) and the symbol | for the left and right side of a absolute value.
You do not need to handle the case where a number is directly adjacent to a absolute value (e.g. 2|3| or |2|3, this generalization will be handled in the companion challenge)

Your output should be the same expression in a form that allows to determine how the absolute values are bracketed.

The output has to satisfy the following rules:

• The expression within a absolute value must not end with an operator ( + or - )
• The expression within a absolute value cannot be empty
• Each | has to be part of exactly one absolute value

You may assume there is a valid way to parse the given input.

Examples:

|2|                ->  (2)
|2|+|3|            ->  (2)+(3)
||2||              ->  ((2))
||2|-|3||          ->  ((2)-(3))
|-|-2+3||          ->  (-(-2+3))
|-|-2+3|+|4|-5|    ->  (-(-2+3)+(4)-5)
|-|-2+|-3|+4|-5|   ->  (-(-2+(-3)+4)-5)
||1-2|+|3-|4-5|||  ->  ((1-2)+(3-(4-5)))

This is code-golf the shortest solution wins.

Parse nested absolute values 2

The absolute value of a number \$x\$ is normally written as \$|x|\$. The left and right side of the absolute value uses the same symbol, so it is not immediately obvious how to parse nested absolute values e.g. \$||1-2|+|3-|4-5|||\$

Your goal is to parse such an expression containing nested absolute values:

Follow up to my previous challenge about parsing nested absolute values

The expression will be given as a string of characters. For simplicity the expression will only contain single digit numbers (or letters if that is easier in your language), the operators + and - (you can use any two distinct characters to represent these operations) and the symbol | for the left and right side of a absolute value. To make the challenger not too easy, it is allowed for numbers to be directly adjacent to absolute values so (2|3| and |2|3 both are valid expressions)

Examples (all possible outputs):

|2|                ->  (2)
|2|+|3|            ->  (2)+(3)
|2|3|-4|           ->  (2)3(-4)    
|2|3|-4|           ->  (2(3)-4)
|2|3-|4|           ->  (2)3-(4)
||2||              ->  ((2))
||2|-|3||          ->  ((2)-(3))
|-|-2+3||          ->  (-(-2+3))
|-|-2+3|+|4|-5|    ->  (-(-2+3)+(4)-5)
|-|-2+|-3|+4|-5|   ->  (-(-2+(-3)+4)-5)
||1-2|+|3-|4-5|||  ->  ((1-2)+(3-(4-5)))

• Is this a duplicate?

• Is the formulation clear?

• Should I post both versions, or only one of them (The firsts one is relatively easy, the second one is probably more difficult)?