Question

b) Design a presorting-based algorithm to find the smallest possible mean of k elements in an array of n elements. Algorithm SmallestKMean (AI1. .n], k) c)Consider the problem of searching for genes in DNA sequences using Boyer-Moore string matching algorithm. A DNA sequence is represented by a text on the alphabet (A, C, G, T), and the gene or gene segment is the pattern. Construct the bad-symbol shift table and good-suffix shift table for the following gene segment: TAATAA Apply Boyer-Moore algorithm to locate first occurrence of the above pattern in the following DNA sequence: TAATCAGGAAAGCGTAATAATAATA.

Answer 1

#include<iostream>

#include<cstdlib>

using namespace std;

int compare(const void* a, const void* b)

{

    const int* x = (int*) a;

    const int* y = (int*) b;

    if (*x > *y)

        return 1;

    else if (*x < *y)

        return -1;

    return 0;

}

double SmallestKMean(int A[], int n, int k)

{

//First need to sort the array

// Then find mean from first k smallest element in array

int total = 0;

qsort(A, n, sizeof(int),compare);

for(int i=0;i<k;i++){

total += A[i];

}

return total/k;

}

int main(int argc, char const *argv[])

{

int n=10, k =5;

int A[10] = {10,5,11,234,143,87,987,1,2,76};

cout << SmallestKMean(A,n,k);

return 0;

}

//output:

G smallestMean.cpp x 18 SmallestKMean(int A[], int int k) double n, //First need to sort the array f Then find mean from first k smallest element in array int total ; qsort (A, n, sizeof (int),compare); 21 23 25 26 for(int i-0;i<k;i++) total A[i]; return total/k; 30 int main(int argc, char const *argv[]) 31 32 int n=10, k =5; int A[10]110,5,11, 234,143,87,987,1,2, 763; cout <SmallestKMean(A, n, k); return 0; 34 35 38 PROBLEMS OUTPUT DEBUGCONSOLE TERMINAL surya@sitaram MINGH64 fe/APIStatus $ g++ smallestMean.cpp -o smallestMean surya@sitaram MINGH64 fe/APIStatus $ ./smallestMean. exe surya@sitaram MINGH64 fe/APIStatus

b)

#include <iostream>

#include<stdlib.h>

using namespace std;

# define NO_OF_CHARS 256

/*Algorithm

bad-Shift Table

Seq: T A A T C A G G A A A G C G T A A T A A T A A T A

Pat: T A A T A A

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 21 22 23

we start match from the last char of pattern and we find that index 4 is mismatch.

mismatching char is C is not in pattern So we will shift pattern past to index 5

Seq: T A A T C A G G A A A G C G T A A T A A T A A T A

Pat: T A A T A A

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 21 22 23

we start match from the last char of pattern and we find that index 11 is mismatch.

mismatching char is G is not in pattern So we will shift pattern past to index 10

Seq: T A A T C A G G A A A G C G T A A T A A T A A T A

Pat: T A A T A A

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 21 22 23

we start match from the last char of pattern and we find that index 13 is mismatch.

mismatching char is G is in pattern.

Now we will search for last occurence of G in pattern. which is not in Pattern

so we will move by last mismatch char which is at 13

Seq: T A A T C A G G A A A G C G T A A T A A T A A T A

Pat: T A A T A A

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 21 22 23

Now we got the pattern matched.

*/

void badCharHeuristic( string str, int size, int badchar[NO_OF_CHARS])

{

int i;

// Initialize all occurrences as -1

for (i = 0; i < NO_OF_CHARS; i++)

badchar[i] = -1;

// Fill the actual value of last occurrence of a character

for (i = 0; i < size; i++)

badchar[(int) str[i]] = i;

}

int findPattern( string txt, string pat)

{

int m = pat.size();

int n = txt.size();

int badchar[NO_OF_CHARS];

/* Fill the bad character array by calling

the preprocessing function badCharHeuristic()

for given pattern */

badCharHeuristic(pat, m, badchar);

int s = 0; // s is shift of the pattern with respect to text

while(s <= (n - m))

{

int j = m - 1;

/* Keep reducing index j of pattern while

characters of pattern and text are

matching at this shift s */

while(j >= 0 && pat[j] == txt[s + j])

j--;

/* If the pattern is present at current

shift, then index j will become -1 after

the above loop */

if (j < 0)

{

return s;

}

else

/* Shift the pattern so that the bad character

in text aligns with the last occurrence of

it in pattern. The max function is used to

make sure that we get a positive shift.

We may get a negative shift if the last

occurrence of bad character in pattern

is on the right side of the current

character. */

s += max(1, j - badchar[txt[s + j]]);

}

return -1;

}

/* Driver code */

int main()

{

string txt= "TAATCAGGAAAGCGTAATAATAATA";

string pat = "TAATAA";

cout << "First Pattern fount at index::" << findPattern(txt, pat);

return 0;

}

//output:

G smallestMean.cpp BoyerMoore.cpp x 73 /* If the pattern is present at current shift, then index j will become -1 after the above loop if (j0) 76 80 81 return S else 83 84 f* Shift the pattern so that the bad character in text aligns with the last occurrence of it in pattern. The max function is used to make sure that we get a positive shift. We may get a negative shift if the last occurrence of bad character in pattern is on the right side of the current character. f s += max( 1, j - badchar[txt[s + j]]); 86 87 89 90 91 92 93 94 95 return -1; PROBLEMS OUTPUT DEBUG CONSOLE TERMINAL surya@sitaram MINGH64 fe/APIStatus $ g++ BoyerMoore.cpp -o BoyerMoore surya@sitaram MINGH64 fe APIStatus $ ./BoyerMoore.exe First Pattern fount at index::14 surya@sitaram MINGH64 fe APIStatus