0287-find-the-duplicate-number

287. Find the Duplicate Number

Problem Description

Given an array nums containing n + 1 integers where each integer is between 1 and n (inclusive), prove that at least one duplicate number must exist. Assume that there is only one duplicate number, find the duplicate one.

Example 1:

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

Example 2:

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

Solution

Approach 1: Binary Search

public int findDuplicate(int[] nums) {
    int lo = 1, hi = nums.length - 1;
    
    while (lo < hi) {
        int mid = lo + (hi - lo) / 2;
        int count = count(nums, mid);
        
        if (count <= mid)
            lo = mid + 1;
        else
            hi = mid;
    }
    return lo;
}

private helper methods

private int count(int[] nums, int key) {
    int count = 0;
    for (int i = 0; i < nums.length; i++) {
        if (nums[i] <= key)
            count++;
    }
    return count;
}

Test

Compile with javac Solution.java and run with java Solution.

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