This is three formulas for the same question:

Perform an experimental analysis to determine the largest value of n for each of the three algorithms given in the chapter 4 for solving the element uniqueness problem such that the given algorithm runs in one minute or less. Provide answer in C++

bool isUniqueLoop(const vector<int>& arr, int start, int end) {

if (start >= end) return true;

for (int i = start; i < end; i++)

for (int j = i+1; j <= end; j++)

if (arr{i} == arr{j} return false;

return true;

}

bool isUnique(const vector& arr, int start, int end) {

if (start >= end) return true;

if (!isUnique(arr, start, end1))

return false;

if (!isUnique(arr, start+1, end))

return false;

return (arr[start] != arr[end]);

}

bool isUniqueSort(const vector<int>& arr, int start, int end) {

if (start >= end) return true;

vector<int> buf(arr); // duplicate copy of arr

sort(buf.begin()+start, buf.begin()+end); // sort the subarray

for (int i = start; i < end; i++) // check for duplicates

if (buf{i} == buf{i+1}) return false;

return true;

}