Question

Find the complexity of the function used to find the kth smallest integer in an unordered array of integers:

int selectkth (int a [], int k, int n) {
int i, j, mini, tmp;
for (i = 0; i < k; i++) {
%3D mini i; %3! for (j i+1; j < n; j++)
if (alj]mini = j;
tmp = a[i];
a[i] = a [mini];
a [mini] = tmp;
}
return a [k-1];
}

Answer 1

The function selectkth to find the kth smallest integer in an unordered array of integers has a worst-case time complexity of O(k*n), where k is the order of the statistic and n is the size of the array.

Step-by-step explanation:

The complexity of the function selectkth to find the kth smallest integer in an unordered array of integers involves a selection algorithm. This function performs a partial sort by iterating through the array k times and finding the minimum element from the unsorted part of the array in each iteration. The inner loop runs from index i+1 to n (where n is the array size), and the outer loop runs k times. Therefore, in the worst case, the time complexity of this function is O(k*n), where k is the order of the statistic and n is the size of the array. However, since this function stops after the kth iteration, it does not fully sort the entire array, making it more efficient than a complete sort for small values of k.