287. Find the Duplicate Number

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.

 

Example 1:

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

Example 2:

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

Example 3:

Input: nums = [1,1]
Output: 1

Example 4:

Input: nums = [1,1,2]
Output: 1

 

Constraints:

  • 2 <= n <= 3 * 104
  • 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 without modifying the array nums?
  • Can you solve the problem using only constant, O(1) extra space?
  • Can you solve the problem with runtime complexity less than O(n2)?

287. Find the Duplicate Number
struct Solution;

impl Solution {
    fn find_duplicate(nums: Vec<i32>) -> i32 {
        let n = (nums.len() - 1) as i32;
        let mut low = 1;
        let mut high = n;
        while low < high {
            let mid = low + (high - low) / 2;
            let mut count = 0;
            for &x in &nums {
                if x <= mid {
                    count += 1;
                }
            }
            if count <= mid {
                low = mid + 1;
            } else {
                high = mid;
            }
        }
        low
    }
}

#[test]
fn test() {
    let nums = vec![1, 3, 4, 2, 2];
    let res = 2;
    assert_eq!(Solution::find_duplicate(nums), res);
    let nums = vec![3, 1, 3, 4, 2];
    let res = 3;
    assert_eq!(Solution::find_duplicate(nums), res);
}