Step by Step solution about How to resolve the algorithm Quickselect algorithm step by step in the C++ programming language

Source Code Explanation

First Program

This program demonstrates the use of the std::nth_element() function to find the kth smallest element in an array.

• Header Files:

  • #include <algorithm>: Provides the std::nth_element() function.
  • #include <iostream>: For input/output.

• Inside the main() function:

  • A loop runs from 0 to 9, creating an array a of integers for each iteration.
  • The std::nth_element() function is used to find the ith smallest element in the array a.
  • The value of a[i] is then printed to the console.

Second Program

This program provides an implementation of the selection algorithm, which finds the kth smallest element in an array. It uses a randomized pivot selection to achieve O(n) average time complexity.

• Header Files:

  • #include <iterator>: For iterator operations.
  • #include <algorithm>: For sorting algorithms.
  • #include <functional>: For function objects.
  • #include <cstdlib>: For random number generation.
  • #include <ctime>: For time-based random seeding.
  • #include <iostream>: For input/output.

• select() Function Template:

  • This template function implements the selection algorithm. It takes an iterator range [begin, end) and the index n of the desired element.
  • It uses randomized pivot selection to reduce the average running time complexity to O(n).
  • The function returns an iterator pointing to the kth smallest element.

• Inside the main() function:

  • Random seed is set using std::srand().
  • A loop runs from 0 to 9, creating an array a of integers for each iteration.
  • The select() function is used to find the ith smallest element in the array a.
  • The value of the selected element is printed to the console.

#include <algorithm>
#include <iostream>

int main() {
  for (int i = 0; i < 10; i++) {
    int a[] = {9, 8, 7, 6, 5, 0, 1, 2, 3, 4};
    std::nth_element(a, a + i, a + sizeof(a)/sizeof(*a));
    std::cout << a[i];
    if (i < 9) std::cout << ", ";
  }
  std::cout << std::endl;

  return 0;
}


#include <iterator>
#include <algorithm>
#include <functional>
#include <cstdlib>
#include <ctime>
#include <iostream>

template <typename Iterator>
Iterator select(Iterator begin, Iterator end, int n) {
  typedef typename std::iterator_traits<Iterator>::value_type T;
  while (true) {
    Iterator pivotIt = begin + std::rand() % std::distance(begin, end);
    std::iter_swap(pivotIt, end-1);  // Move pivot to end
    pivotIt = std::partition(begin, end-1, std::bind2nd(std::less<T>(), *(end-1)));
    std::iter_swap(end-1, pivotIt);  // Move pivot to its final place
    if (n == pivotIt - begin) {
      return pivotIt;
    } else if (n < pivotIt - begin) {
      end = pivotIt;
    } else {
      n -= pivotIt+1 - begin;
      begin = pivotIt+1;
    }
  }
}

int main() {
  std::srand(std::time(NULL));
  for (int i = 0; i < 10; i++) {
    int a[] = {9, 8, 7, 6, 5, 0, 1, 2, 3, 4};
    std::cout << *select(a, a + sizeof(a)/sizeof(*a), i);
    if (i < 9) std::cout << ", ";
  }
  std::cout << std::endl;

  return 0;
}