Smallest Missing Positive Integer

Write a C# program to find the smallest missing positive integer in an unsorted array of integers. Your algorithm should run in O(n) time and use constant extra space.

Example 1

        
Input: nums = [1, 2, 0]
        
Output: 3
        
Explanation:
            

                
Step 1: Replace all non-positive numbers and numbers greater than the array length (n=3) with a value outside the valid range (e.g., 4).
                
Step 2: Use the array itself as a hash table by marking the presence of each valid positive number by making the value at index (i-1) negative.
                
Step 3: After marking, the array would have presence of 1 and 2 indicated.
                
Step 4: Find the first index i where the value is positive, which corresponds to the first missing positive integer i+1.
                
Step 5: Since 1 and 2 are present, 3 is the smallest missing positive integer.
            
        
    

Example 2

        
Input: nums = [3, 4, -1, 1]
        
Output: 2
        
Explanation:
            

                
Step 1: Replace all non-positive numbers (-1) and numbers greater than the array length (n=4), which are 3 and 4, with a value outside the valid range (e.g., 5).
                
Step 2: Use the array itself as a hash table by marking the presence of each valid positive number.
                
Step 3: After marking, the array would have presence of 1 indicated but not 2.
                
Step 4: Find the first index i where the value is positive, which corresponds to index 1 (for number 2).
                
Step 5: Since 1 is present but 2 is not, 2 is the smallest missing positive integer.
            
        
    

Constraints

        
1 ≤ nums.length ≤ 10⁵
        
-2³¹ ≤ nums[i] ≤ 2³¹ - 1
        
Time Complexity: O(n)
        
Space Complexity: O(1)