41. First Missing Positive

Problem:

Given an unsorted integer array, find the smallest missing positive integer.

Example 1:

Input: [1,2,0]
Output: 3

Example 2:

Input: [3,4,-1,1]
Output: 2

Example 3:

Input: [7,8,9,11,12]
Output: 1

Note:

Your algorithm should run in O(n) time and uses constant extra space.

Solution:

The last requirement is why this problem is marked “hard”. Though the solution feels like cheating: it modifies the array to mark numbers.

So the algorithm still requires O(n) space but O(1) extra space.

The core idea of the solution is, if the length of the array is n, then the smallest missing positive integer must be within [1, n+1].

Consider an edge-case scenario where the array is [1,2,...,n]. The smallest missing positive integer is n+1.

Now if one of these integers is missing in the array, that integer is the smallest missing positive integer.

If more than one are missing, pick the smallest.

So here we reuse the array and keep trying to put integer k into the slot indexed k-1 (via swapping).

/**
 * @param {number[]} nums
 * @return {number}
 */
let firstMissingPositive = function (nums) {
  const n = nums.length;

  for (let i = 1; i < n; i++) {
    while (nums[i] <= n && nums[i] !== nums[nums[i] - 1]) {
      const t = nums[i];
      nums[i] = nums[t - 1];
      nums[t - 1] = t;
    }
  }

  for (let i = 0; i < n; i++) {
    if (nums[i] !== i + 1) {
      return i + 1;
    }
  }

  return n + 1;
};

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