287. Find the Duplicate Number

Problem

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 <= 10^5

• 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 (Java)

class Solution {
    public int findDuplicate(int[] nums) {
        int[] arr = new int[nums.length + 1];
        for (int num : nums) {
            arr[num] += 1;
            if (arr[num] == 2) {
                return num;
            }
        }
        return 0;
    }
}

Solution (Javascript)

/**
 * @param {number[]} nums
 * @return {number}
 */
var findDuplicate = function(nums) {
  for (const val of nums) {
    const num = Math.abs(val);
    if (nums[num - 1] < 0) {
      return num;
    }
    nums[num - 1] *= -1;
  }
};

Explain:

nope.

Complexity:

• Time complexity : O(n).
• Space complexity : O(n).