Final Value of Variable After Performing Operations

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ArraysStrings

There is a programming language with only four operations and one variable X:

++X and X++ increments the value of the variable X by 1.
--X and X-- decrements the value of the variable X by 1.

Initially, the value of X is 0.

Given an array of strings operations containing a list of operations, return the final value of X after performing all the operations.

Example 1:

Input: operations = ["--X","X++","X++"]
Output: 1
Explanation: The operations are performed as follows:
Initially, X = 0.
--X: X is decremented by 1, X =  0 - 1 = -1.
X++: X is incremented by 1, X = -1 + 1 =  0.
X++: X is incremented by 1, X =  0 + 1 =  1.

Example 2:

Input: operations = ["++X","++X","X++"]
Output: 3
Explanation: The operations are performed as follows:
Initially, X = 0.
++X: X is incremented by 1, X = 0 + 1 = 1.
++X: X is incremented by 1, X = 1 + 1 = 2.
X++: X is incremented by 1, X = 2 + 1 = 3.

Example 3:

Input: operations = ["X++","++X","--X","X--"]
Output: 0
Explanation: The operations are performed as follows:
Initially, X = 0.
X++: X is incremented by 1, X = 0 + 1 = 1.
++X: X is incremented by 1, X = 1 + 1 = 2.
--X: X is decremented by 1, X = 2 - 1 = 1.
X--: X is decremented by 1, X = 1 - 1 = 0.

Constraints:

1 <= operations.length <= 100
operations[i] will be either "++X", "X++", "--X", or "X--".

Try coding it in LeetCode

Solution

Clarifying Questions

When you get asked this question in a real-life environment, it will often be ambiguous (especially at FAANG). Make sure to ask these questions in that case:

What is the range of possible values for the variable and the operations?
Are there any invalid or unexpected operations that I should handle?
Is the input list of operations guaranteed to be non-empty?
What data type should the final value be (e.g., integer, float)?
Should I assume the operations are always valid and will not cause an overflow or other errors?

Brute Force Solution

Approach

We start with a variable and a list of actions to perform on it. The brute-force way is to go through the list of actions one by one and apply each action to the variable in the order they appear.

Here's how the algorithm would work step-by-step:

Begin with the initial value of the variable.
Look at the first action in the list.
Perform that action on the variable; this changes the variable's value.
Now, look at the next action in the list.
Perform that action on the variable, again updating its value.
Keep repeating this process for every action in the list, always using the variable's current value.
Once you've performed every action, the final value of the variable is the answer.

Code Implementation

def final_value_after_operations_brute_force(operations):
    variable_value = 0

    # Iterate through the list of operations.
    for operation in operations:

        # Check if the operation is incrementing or decrementing.
        if operation == "--X" or operation == "X--":

            # Apply the decrement to the variable.
            variable_value -= 1

        elif operation == "++X" or operation == "X++":

            # Apply the increment to the variable.
            variable_value += 1

    return variable_value

Big(O) Analysis

Time Complexity

O(n) – The algorithm iterates through the list of operations exactly once. The number of operations is directly proportional to the number of operations in the input list, where n represents the number of operations. Each operation is applied sequentially, taking constant time. Therefore, the time complexity is O(n).

Space Complexity

O(1) – The algorithm iterates through a list of actions, modifying a single variable in place. It does not create any additional data structures, such as arrays, lists, or hash maps, to store intermediate results or track visited states. The space used is limited to storing the variable itself, which takes up constant space regardless of the input size N (the number of actions). Therefore, the auxiliary space complexity is O(1).

Optimal Solution

Approach

The key idea is to keep track of the current value of the variable. Since we only need the final result, we can process each operation one at a time, immediately updating the variable's value based on whether the operation increases or decreases it.

Here's how the algorithm would work step-by-step:

Begin with a variable that starts at zero.
Go through each operation in the order they are given.
If an operation adds one to the variable, increase the variable by one.
If an operation subtracts one from the variable, decrease the variable by one.
After processing all operations, the variable will hold the final value. This is your answer.

Code Implementation

def final_value_after_operations(operations):
    variable_value = 0

    # Iterate through each operation.
    for operation in operations:

        # Check for increment operations.
        if "++" in operation:
            variable_value += 1

        # Otherwise, it must be a decrement operation.
        else:
            variable_value -= 1

    # Return the final value of the variable.
    return variable_value

Big(O) Analysis

Time Complexity

O(n) – The algorithm iterates through the input array of operations once. The input size n represents the number of operations in the array. Each operation involves a constant-time update to the variable. Therefore, the time complexity is directly proportional to the number of operations, resulting in a linear time complexity of O(n).

Space Complexity

O(1) – The algorithm initializes a single integer variable to zero and updates its value based on the input operations. No additional data structures like arrays, lists, or hashmaps are used. Therefore, the space used remains constant regardless of the number of operations (N), resulting in O(1) space complexity.

Edge Cases

Case	How to Handle
Null or empty operations array	Return 0 if operations is null or empty as there are no operations to perform.
Operations array contains invalid operations (not ++X, X++, --X, X--)	Throw an IllegalArgumentException or return an error value to indicate invalid input.
Very large number of operations (approaching memory limits)	The solution should still perform correctly as each operation is processed independently, but memory usage should be monitored for extremely large inputs.
Integer overflow during increment/decrement	The problem statement does not mention overflow, but consider using a larger data type (long) or modulo arithmetic if the problem statement explicitly mentions possible overflows.
Operations with leading or trailing whitespace	Trim whitespace from each operation string before processing it.
Operations are a mix of increment and decrement, resulting in a final value of zero	The solution should correctly handle cancellations resulting in 0.
Operations array contains only increment or only decrement operations	The solution should perform as expected even when operations are homogeneous.
Read-only input operations array	The solution only reads from the input array, so it handles read-only arrays without issue.

Null or empty operations array

How to Handle:

Return 0 if operations is null or empty as there are no operations to perform.

Operations array contains invalid operations (not ++X, X++, --X, X--)

How to Handle:

Throw an IllegalArgumentException or return an error value to indicate invalid input.

Very large number of operations (approaching memory limits)

How to Handle:

The solution should still perform correctly as each operation is processed independently, but memory usage should be monitored for extremely large inputs.

Integer overflow during increment/decrement

How to Handle:

The problem statement does not mention overflow, but consider using a larger data type (long) or modulo arithmetic if the problem statement explicitly mentions possible overflows.

Operations with leading or trailing whitespace

How to Handle:

Trim whitespace from each operation string before processing it.

Operations are a mix of increment and decrement, resulting in a final value of zero

How to Handle:

The solution should correctly handle cancellations resulting in 0.

Operations array contains only increment or only decrement operations

How to Handle:

The solution should perform as expected even when operations are homogeneous.

Read-only input operations array

How to Handle:

The solution only reads from the input array, so it handles read-only arrays without issue.