Find the first missing positive number in an array.

Focus on developing an efficient algorithm to identify the first missing positive integer in an unsorted array. Start by discussing the constraints of the problem, particularly the need to handle negative numbers and zeroes, as they are not relevant to the solution. Consider using a linear time complexity approach, such as placing each number in its corresponding index position (i.e., number 1 at index 0, number 2 at index 1, etc.). Be prepared to explain your thought process clearly, including edge cases like empty arrays or arrays with all negative numbers. Finally, discuss the space complexity of your solution and how it can be optimized.