ALGORITHMS TO STUDY FOR THE MIDTERM
LINEAR SEARCH ALGORITHM
i = 0;
while((key != data[i]) && (i < n))
i++;
BINARY SEARCH ALGORITHM
Note: the array must be sorted first before using the binary search
first = 0;
last = n-1;
found = false;
while (first <= last) && (!found)
{
mid = (first + last)/2;
if (key == data[mid])
found = true;
if (key < data[mid])
last = mid-1;
if (key > data[mid])
first = mid+1;
}
Q1: Complete the table below by writing the number of times the algorithm will be executed.
Linear Search
Binary Search
Best case
1
1
Average case
n/2
log2n/2
Worst case
n
log2n
Note: n is the size of the array
Q2: When the size of the array is small, which algorithm is better to use (linear or binary)? Why?
Answer:
For small array size, linear search algorithm is better because in linear algorithm, there s no need to sort
the array and it will take few times of execution since it is small.
Q3: When the size of the array is big, which algorithm is better to use (linear or binary)? Why?
Answer:
For large array, binary Search algorithm is better to use because it will take few times of execution
compare to linear search.
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SORTING ALGORITHMS
BUBBLE SORT ALGORITHM
INSERTION SORT ALGORITHM
for (j = 0; j<n-1; j++)
for(i=1; i<N; i++)
{
temp = array[i];
j = i-1;
for (i=0; i<(n-1)-j ; i++)
if (array[i] > array[i+1])
while (temp < array[j] && j>=0)
{
array[j+1] = array[j];
j = j-1;
}
{ temp = array[i];
array[i] = array[i+1];
array[i+1] = temp;
}
array[j+1] = Temp;
}
Given the array below, answer the following questions:
4
10
1
8
5
Q1: If we are going t sort the array above using Bubble sort algorithm, how many comparisons will take
place? Answer: ___4+3+2+1 = 10____
How many swap will happen? Answer: ____5__ note that swapping contains 3 operations, hence, the
total number of operations is 5*3 = 15
Q2: If we are going to sort the array above using Insertion sort algorithm, how many comparisons will
take place? Answer: _1+2+3+4 = 10_
How many times this statement (array[j+1] = array[j];) will be executed number of insertions? Answer:
_____5___
Q3: Based on your answer in Q1 & Q2, which do you think is faster, Bubble algorithm or Insertion Sort
algorithm? Answer: ____________
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FIBONACCI NUMBERS
Below are two different C program of fibonacci numbers
# include <stdio.h>
# include <conio.h>
# include <stdio.h>
# include <conio.h>
main ()
{
// (1) creating an array, array name is fib, array size is 20
int fibonacci(int n);
main ()
{
int n; // number entered by the user
int fn; // stores the fibonacci number
int fib[20];
int n;
// (2) storing values to array based on THE FIBONACCI
ALGORITHM
// ask the user to enter number n
printf(" Enter a number n = ");
scanf("%d", &n);
for(n=0; n<20; n++)
{ if (n<2)
fib[n] = n;
else
fib[n] = fib [n-1] + fib [n-2];
}
// call the function fibonacci that contins the algorithm
fn = fibonacci(n);
// (4) printing the fibonacci number for the entered number
// (3) ask the user to enter number between 0 & 19
printf("\n The fibonacci number for %d is %d", n, fn);
getch();
return 0;
printf(" Enter a number between 0 and 19: ");
scanf("%d",&n);
}
// (4) printing the fibonacci number for the entered
number
// the FIBONACCI ALGORITHM
printf("\n The fibonacci number for %d is %d", n, fib[n]);
int fibonacci(int n)
{ if (n<2)
return n;
else
return (fibonacci(n-1) + fibonacci(n-2));
}
getch();
return 0;
}
Q1. Observe the differences of the two programs. Write all your observations below.
Answer:
Program 1
Used array
Limited numbers
Fibonacci numbers are stored in the array
The array is accessed to get the output
Program 2
Used functions
Any value of n
Fibonacci number are not pre-stored
The algorithm needs to be executed to get the
output.
Use more space
Use less space
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Q2: Compare the two algorithms in terms of space and time (e.g. which one uses more space?).
Answer:
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