What is the order of growth of the running time for your implementation of function edit_distance in the best case and in the worst case? Express your answers using Big- notation. and what is the order of growth of the running time for your implementation of function align in the best case and in the worst case? Express your answers using Big-O notation and provide a tight bound.

#include #include using namespace std; int m; int n; int d[5001][5001]; int edit_distance (string A, string B) { m = A.length(); n = B.length(); for (int i = m; i >= 0; i--) { for (int j = n; j >= 0; j--) { if (i == m) d[i][j] = 2 * (n - j);

else if (j == n) d[i][j] = 2 * (m - i);

else if (A[i] == B[j]) { d[i][j] = d[i + 1][j + 1]; }

else d[i][j] = min(2 + d[i][j + 1], min(2 + d[i + 1][j], 1 + d[i + 1][j + 1]));

} }

return d[0][0];

}

void align (string A, string B) { edit_distance(A, B);

int i = 0; int j = 0; string first = ""; string second = "";

while (1) { if (i == m && j == n) break;

if(j == n) { for(int k =i;k

if(i == m) { for(int k =j;k

first = first + A[i]; second = second + '-'; i = i + 1; continue; } if (d[i][j + 1] + 2 == d[i][j]) { first = first + '-'; second = second + B[j]; j = j + 1; continue; }

if (d[i + 1][j + 1] == d[i][j] || d[i + 1][j + 1] + 1 == d[i][j]) { first = first + A[i]; second = second + B[j]; i = i + 1; j = j + 1; } } cout << first << endl; cout << second << endl;

}