<p>Given an unsorted integer array <code>nums</code>. Return the <em>smallest positive integer</em> that is <em>not present</em> in <code>nums</code>.</p>

<p>You must implement an algorithm that runs in <code>O(n)</code> time and uses <code>O(1)</code> auxiliary space.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,2,0]
<strong>Output:</strong> 3
<strong>Explanation:</strong> The numbers in the range [1,2] are all in the array.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [3,4,-1,1]
<strong>Output:</strong> 2
<strong>Explanation:</strong> 1 is in the array but 2 is missing.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums = [7,8,9,11,12]
<strong>Output:</strong> 1
<strong>Explanation:</strong> The smallest positive integer 1 is missing.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>-2<sup>31</sup> &lt;= nums[i] &lt;= 2<sup>31</sup> - 1</code></li>
</ul>

#pragma GCC target("tune=native")
#pragma GCC optimize("Ofast")
//#pragma GCC optimize("Os")
// Code here is optimized for size

static const auto fastIO = []() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    std::cout.tie(nullptr);
    return 0;
}();
class Solution {
public:
    Solution() {
        ios_base::sync_with_stdio(false);
        cin.tie(nullptr);
    }
    int firstMissingPositive(vector<int>& arr) {
        int n = arr.size();

        // Place each number in its correct position
        for (int i = 0; i < n; i++) {
            while (arr[i] > 0 && arr[i] <= n && arr[arr[i] - 1] != arr[i]) {
                swap(arr[i], arr[arr[i] - 1]);
            }
        }

        // Find the first missing positive integer
        for (int i = 0; i < n; i++) {
            if (arr[i] != i + 1) {
                return i + 1;
            }
        }

        // If all positions are correct, return n + 1
        return n + 1;
    }
};

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