Complexity Analysis of isPalindrome Function

Code Overview

The provided code is a JavaScript function intended to check if a given number x is a palindrome. The function undergoes the following steps:

1. Converts the number to a string representation.
2. Checks if the first character is not a number (for NaN cases).
3. Returns true for single-character strings.
4. Iterates through the string to compare characters from the start and end moving towards the center.

Code Snippet

var isPalindrome = function(x) {
    strX = x.toString();
    if (isNaN(strX[0])) return false;
    if (strX.length === 1) return true;
    for (let i = 0; i < strX.length; i++) {
        if (i >= strX.length - i) return true;
        if (parseInt(strX[i]) === parseInt(strX[strX.length - 1 - i])) continue;
        else return false;
    }
};

Time Complexity

Analysis

1. Conversion to String: The operation x.toString() involves converting the entire number to a string. This can be considered O(n), where n is the number of digits in x.
2. Initial Checks:
   • isNaN(strX[0]): Constant time O(1).
   • Checking strX.length === 1: Constant time O(1).
3. Iteration through String: The loop iterates through the string to check characters:
   • In the worst case, it compares characters until reaching the middle of the string. Thus, up to n/2 comparisons occur, leading to O(n) complexity for the loop as well, since we generally express complexities in terms of the dominant factor.

Total Time Complexity

• Worst-case: O(n) for full iteration.
• Average-case: O(n), due to the linear nature of the scanning.
• Best-case: O(1) when it returns true for single-character input.

Space Complexity

Analysis

1. String Representation: Storing strX costs O(n) space for the string representation.
2. Additional Variables: Other variables used (i, parseInt, etc.) occupy constant space O(1).

Total Space Complexity

• Total: O(n) due to the string representation.

Bottlenecks and Optimization Insights

1. Unnecessary Character Parsing: The use of parseInt on characters could be avoided by directly comparing characters as strings, thus enhancing efficiency.

2. Loop Condition: The condition i >= strX.length - i inside the loop is theoretically extraneous since it is checked after the loop has validated that all pairs match. This may be optimized away, reducing redundant checks.

3. NaN Check: The check for NaN may not be necessary if we can assume that the input will always be valid since the function is designated for numeric input.

Conclusion

The function is straightforward but can be optimized for better performance, particularly in terms of unnecessary computations. Leveraging string comparisons directly instead of converting characters to integers can streamline the process and reduce execution time in practical scenarios.

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