Find the Duplicate Number

ID: 633; medium; 寻找重复的数

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Solution 1 (Java)

public class Solution {
    /**
     * @param nums: an array containing n + 1 integers which is between 1 and n
     * @return: the duplicate one
     */
    public int findDuplicate(int[] nums) {
        int left = 1, right = nums.length;

        while (left + 1 < right) {
            int mid = left + (right - left) / 2;
            if (countSmallerNums(mid, nums) <= mid) {
                left = mid;
            } else {
                right = mid;
            }
        }

        if (countSmallerNums(left, nums) <= left)
            return right;
        return left;
    }

    private int countSmallerNums(int num, int[] nums) {
        int count = 0;
        for (int n : nums) {
            if (n <= num) count++;
        }
        return count;
    }
}

Notes

• The array is not sorted

• Time complexity should be less than

$$O(n^2)$$

• Space complexity should be

$$O(1)$$

We know that the range of the numbers is initially [1, n]. We take the middle element inside the range mid. If count ≤ mid, where count is the number of elements that are less than or equal to mid, then we are certain that the duplicated number is not inside the range [left, mid]. The reason is the following:

Example 1

Original array: [3, 1, 4, 6, 5, 8, 8, 9]

Range: [1, 9]

left	right	mid	count	Result
1	9	5	4 bc the smaller number are 3, 1, 4, 5	count ≤ mid

New range is [5, 9] and 8 is inside that range.✅

Example 2

Maybe think about [3, 8, 8, 4, 6, 1, 5, 9]. Length - 1?

• Time complexity for this solution is

$$O(n\log{n})$$

• Space complexity should be

$$O(1)$$

Solution 2 (Java)

Notes (Sort)

• Time complexity: O(nlogn)

• Space complexity: O(logn) or O(n), does not meet the requirement for this problem but indeed a solution

Solution 3 (Java)

Notes (Set)

• Use a set to find the duplicated number

• If the set already contains a number when adding it, it is the duplicated one.

Solution 4 (Java)

Notes (Array as HashMap)

Solution 5 (Java)

Notes (Floyd's Algorithm)

• A similar idea as used in Linked Cycle II.