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What's the sense of initiating a extra Int inputX?
https://github.com/diwu/LeetCode-Solutions-in-Swift/blob/master/Solutions/Solutions/Easy/Easy_009_Palindrome_Number.swift#L29
I think return palindromeX == x just works.

The implementation of brute force will fail on haystakc: "mississippi" needle: "issispi"

Missing reset j = 0 on haystack[i+j] != needle[j]

ni niubi

In case you ignored the requirements:

The function first discards as many whitespace characters as necessary until the first non-whitespace character is found. Then, starting from this character, takes an optional initial plus or minus sign followed by as many numerical digits as possible, and interprets them as a numerical value.

Thus, atoi("123-") must be 123. But with your solution, the output is -123.

https://github.com/diwu/LeetCode-Solutions-in-Swift/blob/master/Solutions/Solutions/Easy/Easy_008_String_to_Integer_atoi.swift#L47

I think this is the proper answer:
https://github.com/haoel/leetcode/blob/master/algorithms/stringToIntegerAtoi/stringToIntegerAtoi.cpp#L51-L57

My translation in Swift:
https://github.com/lexrus/LeetCode.swift/blob/master/StringToIntegerAtoi/StringToIntegerAtoi.swift