) In sage, reducing an integer a modulo m is achieved with the expression a % m. The following sage code implements the fast power algorithm, but a few blanks are missing Fill in the blanks. def fast_power (a, k, m) : """for non-negative integers k, computes a^k modulo m""" if (k 0): == return if ((k % 2) == 1): # k is odd # recursively compute y = a^{k-1} (mod m) y = fast_power (a, k-1, m) return % m else: # k is even # recursively compute y y = fast_power(a, k/2, m) a^{k/2} (mod m) return % m

) In sage, reducing an integer a modulo m is achieved with the expression a % m. The following sage code implements the fast power algorithm, but a few blanks are missing Fill in the blanks. def fast_power (a, k, m) : """for non-negative integers k, computes a^k modulo m""" if (k 0): == return if ((k % 2) == 1): # k is odd # recursively compute y = a^{k-1} (mod m) y = fast_power (a, k-1, m) return % m else: # k is even # recursively compute y y = fast_power(a, k/2, m) a^{k/2} (mod m) return % m

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Assume that you were given N cents (N is an integer) and you were asked to break up the N cents into coins consisting of 1 cent, 2 cents and 5 cents. Write a dynamicprogramming based recursive algorithm, which returns the smallest (optimal) number of coins needed to solve this problem. For example, if your algorithm is called A, and N = 13, then A(N) = A(13) returns 4, since 5+5+2+1 = 13 used the smallest (optimal) number of coins. In contrast, 5+5+1+1+1 is not an optimal answer.
Suppose that your implementation of a particular algorithm appears in C++ as for (int pass = 1; pass <= n; pass++) { for (int index = 0; index < n; index++) { for (int count = 1; count < 10; count++) { ... } // end for } // end for } // end for The previous code shows only the repetition in the algorithm, not the computations that occur within the loops. These computations, however, are independent of n. What is the Big O of the algorithm?
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Computer Science you are given a string X of length n and another string Y of length m ≤n. Say,the indexes p1, p2, p3, p4 and q1, q2, q3, q4 form two sub-sequences, i.e., 0 ≤ p1 < p2 < p3 < p4 < nand 0 ≤q1 < q2 < q3 < q4 < n; then, they are non-overlapping if p4 < q1.The task is to count the maximum number of non-overlapping sub-sequences of X that are thesame as Y . Thus, if X = GAXTYAWBGTAUGBTABGRGTAXB and Y = GTAB, then the answer is3 as shown by the red fonts. We cannot select the underlined GTAB as it overlaps with a red GTAB(i.e., among overlapping sub-sequences, you can select only one of them).Describe an O(m + n) time algorithm to obtain the count. Write a pseudo-code.
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The solution must be submitted in the Coral programming language. A program that reads a list of 10 integers, and outputs those integers in reverse. For coding simplicity, follow each output integer by a space, including the last one. Then, output a newline. Ex: If the input is 2 4 6 8 10 12 14 16 18 20, the output is: 20 18 16 14 12 10 8 6 4 2 To achieve the above, first read the integers into an array. Then output the array in reverse.
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