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Burka [1]
3 years ago
6

Suppose that the splits at every level of quicksort are in the proportion 1 − α to α where 0 < α ≤ 1/2 is a constant. Show th

at the minimum depth of a leaf in the recursion tree is approximately
Computers and Technology
1 answer:
Lady_Fox [76]3 years ago
4 0

Answer:

Explanation:

The minimum depth occurs for the path that always takes the smaller portion of the

split, i.e., the nodes that takes α proportion of work from the parent node. The first

node in the path(after the root) gets α proportion of the work(the size of data

processed by this node is αn), the second one get (2)

so on. The recursion bottoms

out when the size of data becomes 1. Assume the recursion ends at level h, we have

(ℎ) = 1

h = log 1/ = lg(1/)/ lg = − lg / lg

Maximum depth m is similar with minimum depth

(1 − )() = 1

m = log1− 1/ = lg(1/)/ lg(1 − ) = − lg / lg(1 − )

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Question: 4/8
Gemiola [76]

The generated test cases for the function assuming another developer coded the function is given below in a C++ program.

<h3>THE CODE</h3>

#include <iostream>  

#include <iomanip>

#include <string>

using namespace std;

// define the data type "triangletype" with {values}

enum triangleType { scalene, isosceles, equilateral, noTriangle };

// Prototype function which returns the position of triangleType{value}

// Example: Scalene = 0, isosceles = 1, etc. These are zero indexed.

triangleType triangleShape(double a, double b, double c);

// Prototype function which takes the integer value of the

// triangle type and outputs the name of triangle

string shapeAnswer(int value);

int main() {

   double inputA;

   double inputB;

   double inputC;

   cout << "To determine whether a triangle is either:" << endl;

   cout << setw(50) << " - Scalene" << endl; // Unequal in length

   cout << setw(52) << " - Isosceles" << endl; // Two sides equal length

   cout << setw(54) << " - Equilateral" << endl; // All sides equal

   cout << setw(57) << " - Not a triangle" << endl;

   cout << "Enter side A: ";

   cin >> inputA;

   cout << "Enter side B: ";

   cin >> inputB;

  cout << "Enter side C: ";

   cin >> inputC;

   cout << "The triangle is " << shapeAnswer(triangleShape(inputA, inputB, inputC)) << endl;

}

triangleType triangleShape(double a, double b, double c) {

   triangleType answer;

   if ( c >= (a + b) || b >= (a + c) || a >= (b + c) ) {

       answer = noTriangle;

   }

   else if (a == b && b == c) {

       answer = equilateral;

   }

   // Test the 3 options for Isosceles equality

   else if ( (a == b) && (a != c) || (b == c) && (b != a) || (a == c) && (a != b) ) {

       answer = isosceles;

   }

   else {

       answer = scalene;

   }

   return answer;

}

string shapeAnswer(int value) {

   string answer;

  switch (value) {

   case 0:

       answer = "Scalene";

       break;

   case 1:

       answer = "Isosceles";

       break;

   case 2:

       answer = "Equilateral";

       break;

   case 3:

       answer = "Not a triangle";

       break;

   default:

       break;

   }

   return answer;

}

Read more about C++ programs here:

brainly.com/question/20339175

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