Different Ways To Add Parentheses - Leetcode Solution

The problem "Different Ways to Add Parentheses" on Leetcode is a recursion-based problem that involves implementing a program that takes an arithmetic expression string as input, and then returns all possible combinations of ways to add parentheses to the expression to obtain different values.

The problem statement can be summarised as follows:

Given a string s representing an arithmetic expression consisting of integers and operators (+, -, *), return all possible ways to add parentheses to the expression to evaluate it differently.

To solve this problem, we will use the following approach:

1. Parse the input string and identify the operators and operands.
2. Recursively break the expression into all possible sub-expressions by placing parentheses at different positions.
3. Evaluate each sub-expression and return the set of unique values obtained.

Now, let's look at each of these steps in more detail.

1. Parsing the Input String

We start by parsing the input string and separating the operands and operators. To do this, we can use a regular expression to split the input string into a list of tokens, where each token is either an operator (+, -, *) or an operand (a positive integer).

For example, the input string "2+3*4-5" can be split into the following tokens:

["2", "+", "3", "*", "4", "-", "5"]

We can then use these tokens to generate all possible sub-expressions by placing parentheses at different positions.

2. Breaking the Expression into Sub-Expressions

We can use a recursive approach to break the expression into all possible sub-expressions by placing parentheses at different positions. We can start by considering the entire input string as a single sub-expression and then recursively break it down into smaller sub-expressions by placing parentheses at different positions.

For example, consider the input string "2+34-5". We can place parentheses around the "+" operator to break it down into two sub-expressions: "2" and "34-5". We can then recursively break down the second sub-expression by placing parentheses around the "*" operator to obtain two more sub-expressions: "3" and "4-5". Next, we can recursively break down "4-5" into "4" and "5".

At each step, we evaluate each sub-expression and return the set of unique values obtained. In this way, we can generate all possible ways to add parentheses to the expression to obtain different values.

3. Evaluating Sub-Expressions

To evaluate a sub-expression, we can use a simple algorithm that iterates over the operators and operands in the sub-expression and applies the operators to the operands. For example, the sub-expression "3*4-5" can be evaluated as follows:

1. Initialize the result to the first operand: result = 3
2. Iterate over the remaining tokens in the sub-expression: a. If the token is an operator, apply it to the current result and the next operand b. If the token is an operand, update the current operand
3. Return the final result

Using this algorithm, we can evaluate each sub-expression and return the set of unique values obtained.

Overall, the Different Ways to Add Parentheses problem on Leetcode can be solved using a recursive approach that involves parsing the input string, breaking it down into all possible sub-expressions by placing parentheses at different positions, and evaluating each sub-expression to obtain the set of unique values.

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