LeetCode-in-All

287. Find the Duplicate Number

Medium

Given an array of integers nums containing n + 1 integers where each integer is in the range [1, n] inclusive.

There is only one repeated number in nums, return this repeated number.

You must solve the problem without modifying the array nums and uses only constant extra space.

Example 1:

Input: nums = [1,3,4,2,2]

Output: 2

Example 2:

Input: nums = [3,1,3,4,2]

Output: 3

Constraints:

• 1 <= n <= 105
• nums.length == n + 1
• 1 <= nums[i] <= n
• All the integers in nums appear only once except for precisely one integer which appears two or more times.

Follow up:

• How can we prove that at least one duplicate number must exist in nums?
• Can you solve the problem in linear runtime complexity?

Solution

(require racket/hash)

(define/contract (find-duplicate nums)
  (-> (listof exact-integer?) exact-integer?)
  (letrec
      ([find-recurse
           (lambda (ns seen)
             (cond [(null? ns) -1]
                   [(hash-has-key? seen (car ns)) (car ns)]
                   [else (find-recurse
                           (cdr ns)
                           (hash-union
                             seen
                             (make-immutable-hash (list (cons (car ns) #t)))))]))])
    (find-recurse nums (make-immutable-hash))))

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