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41. First Missing Positive

Hard

Given an unsorted integer array nums, return the smallest missing positive integer.

You must implement an algorithm that runs in O(n) time and uses constant extra space.

Example 1:

Input: nums = [1,2,0]

Output: 3

Explanation: The numbers in the range [1,2] are all in the array.

Example 2:

Input: nums = [3,4,-1,1]

Output: 2

Explanation: 1 is in the array but 2 is missing.

Example 3:

Input: nums = [7,8,9,11,12]

Output: 1

Explanation: The smallest positive integer 1 is missing.

Constraints:

• 1 <= nums.length <= 105
• -231 <= nums[i] <= 231 - 1

Solution

(define/contract (first-missing-positive nums)
  (-> (listof exact-integer?) exact-integer?)
  (let* ((len (length nums))
         (vec (list->vector nums)))
    (define (swap i j)
      (let ((temp (vector-ref vec i)))
        (vector-set! vec i (vector-ref vec j))
        (vector-set! vec j temp)))
    (for ([i (in-range len)])
      (let loop ()
        (let* ((num (vector-ref vec i))
               (pos (- num 1)))
          (when (and (> num 0) (<= num len) (not (= (vector-ref vec pos) num)))
            (swap i pos)
            (loop)))))
    (let find-missing ((i 0))
      (cond
        ((= i len) (+ len 1))
        ((not (= (vector-ref vec i) (+ i 1))) (+ i 1))
        (else (find-missing (+ i 1)))))))