Find the Duplicate Number

class Solution {
public:
    int findDuplicate(vector<int>& nums) {
        int n = nums.size();
        for(int i = 0; i < n; i++) {
            for(int j = i + 1; j < n; j++) {
                if((nums[i] ^ nums[j]) == 0) {
                    return nums[i];
                }
            }
        }
    }
};

class Solution {
public:
    int findDuplicate(vector<int>& nums) {
        int i = 0;
        int j = 0;
        while(true) {
            i = nums[i];
            j = nums[nums[j]];
            if(i == j) {
                break;
            }
        }
        i = 0;
        while(true) {
            i = nums[i];
            j = nums[j];
            if(i == j) {
                return i;
            }
        }
    }
};

class Solution {
public:
    int findDuplicate(vector<int>& nums) {
        int low = 1;
        int high = nums.size() - 1;
        while(low < high) {
            int mid = (low + high) / 2;
            int count = 0;
            for(int i = 0; i < nums.size(); i++) {
                if(nums[i] <= mid) {
                    count++;
                }
            }
            if(count <= mid) {
                low = mid + 1;
            }
            else {
                high = mid;
            }
        }
        return low;
    }
};