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lawyer [7]
3 years ago
10

Using Sequential Search on an array of size n, the search key is definitely present in the array. The probability of matching th

e key to the nth item in the array is 1/3, and the probability of matching the key to the (n-1)st item is 1/2. The probabilities of matching each of the remaining items are all equal. What is the average case complexity function for Sequential Search under these conditions?
Computers and Technology
1 answer:
MissTica3 years ago
7 0

Answer:

(11n-5) / 12 is correct answer.

Explanation:

The Probability that key will match to nth term = 1/2

The Probability that key will match to n-1th term = 1/3

As all other probabilities are equal

The Total Probability that key matches to any of 1 to n-2 index = 1 - 1/2 - 1/3 = 1/6

The Probability that key matches to any of 1 to n-2 index = (1/6) / n-2 = (1/6)* (n-2))

Let P(i) = Probability that key matches to ith index.

The Average time complexity = 22 i=1 P(i) * i

The Average time complexity = 1/(6(n-2) * ( sum of 1 to n-2 ) + (n-1) / 3 + n/2

The Average time complexity = 1/(6(n-2) * ( n-2)*(n-1) / 2 + ( n-1) / 3 + n/2

The Average time complexity = 1/6 * (n-1)/2 + (n-1)/3 + n/2

The Average time complexity = (n-1)/12 + (n-1)/3 + n/2

The Average time complexity = (n-1 + 4 * n - 4 * 1 +6 * n)/12

The Average time complexity = 11n-5 / 12

so (11n-5) / 12 is correct answer.

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<h3>THE CODE</h3>

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#include <iomanip>

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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;

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

   cout << "Enter side A: ";

   cin >> inputA;

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   cin >> inputB;

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   cin >> inputC;

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

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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) {

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   }

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   }

   return answer;

}

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   string answer;

  switch (value) {

   case 0:

       answer = "Scalene";

       break;

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       break;

   case 2:

       answer = "Equilateral";

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   case 3:

       answer = "Not a triangle";

       break;

   default:

       break;

   }

   return answer;

}

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