urgent please Given code:for i in range(n):aFn(i)for j in range(n):for k in range(j+1):bFn()a) Suppose both functions aFn(i) and bFn() require only one unit of time to be executed.Find the complexity T(n) of the Python code segment above, where n is the size of the inputdata. No explanation required.b) Suppose function aFn(i) requires i units of time to be executed and bFn()requires only oneunit of time. Find the complexity T(n) of the Python code segment above, where n is thesize of the input data. No explanation required.c) Given complexity function f(n)=An^+Bn+n^B+B where A and B are positive integerconstants, use the definition of Big-O to prove f(n)=0(n^B). Clearly show the steps ofyour proof. (* Use definition, not properties of Big-O.)

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Suppose both functions aFn(i) and bFn() require only one unit of time to be executed. Find the complexity T(n) of the Python code segment above, where n is the size of the input data. No explanation required.

Suppose both functions aFn(i) and bFn() require only one unit of time to be executed. Find the complexity T(n) of the Python code segment above, where n is the size of the input data. No explanation required.

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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The binomial coefficient C(N,k) can be defined recursively as follows: C(N,0) = 1, C(N,N) = 1, and for 0 < k < N, C(N,k) = C(N-1,k) + C(N - 1,k - 1). Write a function and give an analysis of the running time to compute the binomial coefficients as follows: A. The function is written using dynamic programming.
Please answer this, thanks! a. give the running time (Big-Oh) and the space complexity. b. implement the code in the language of your choice and give the running time for three values of N (N must be >; 5). c. Compare your analysis with the actual running times. (1) sum = 0;for( i = 0; i < n; ++i )++sum;
For each of the following three program fragments:a. Give an analysis of the running time (Big-Oh will do).b. Implement the code in the language of your choice, and give the running time for several values of N (100, 500, 1000, 5000).c. Compare your analysis with the actual running times. (1) sum = 0; for( i = 0; i < n; ++i )++sum; (2) sum = 0; for( i = 0; i < n; ++i ) for( j = 0; j < n * n; ++j ) ++sum;(3) sum = 0; for( i = 0; i < n; ++i ) for( j = 0; j < i * i; ++j ) for( k = 0; k < j; ++k ) ++sum;
Big-O Complexity Remember, Big-O time complexity gives us an idea of the growth rate of a function. In other words, for a large input size N, as N increases, in what order of magnitude is the volume of statements executed expected to increase? A) Rearrange the following functions in increasing order of their Big-O Complexity B) Also Find the time if n=5: 4n2 log3 n 20n n2.5 n0.00000001 log n! nn 2n 2n+1 22n 3n n log n 100 n2/3 log [(log n)2 ] N! (n−1)!
Let recursive algorithm F be defined as follows: F(int n):if n=1 then return 1else return F(n-1)*n (a) i. Assuming x is a positive integer, what mathematical expression is returned by F(x)?ii. Repeat (i) but assume the line “return 1” is replaced by “return 0”? (b) Which of the following replacements for the last line will yield a function guaranteed to terminate for all valid inputs? i. return F(n-2)+2ii. return F( )*2iii. return F( )*2
Information is present in the screenshot and below. Based on that need help in solving the code for this problem in python. The time complexity has to be as less as possible (nlogn or n at best, no n2) and runtime should be under 1 second. Apply dynamic programming. Do not use recursion. Make sure ALL test cases return expected outputs. Output FormatFor each query, output one line containing an integer Dn. The number must be output mod (109 + 7). Sample Input 0:501234 Sample Output 0:10129 Edge Case: (to test against runtime and timeout error)300000 (number of queries)300000300000300000300000...and so on until there are 300,000 of them The actual code: def solve(n): MOD = 1000000007 # compute and return answer here q = int(input().rstrip()) outs = [] for i in range(q): n = int(input().rstrip()) outs.append(solve(n)) print("{}".format("\n".join(list(map(str,outs)))))
Information is present in the screenshot and below. Based on that need help in solving the code for this problem in python. The time complexity has to be as less as possible (nlogn or n at best, no n^2). Apply dynamic programming. Do not use recursion. Make sure ALL test cases return expected outputs. Output FormatOutput a single line containing the fastest time to get to square N from square 1. Sample Input 05 2 1 4 13 Sample Output 06 Explanation 0The optimal answer is to: RUN to square 2 (+2 seconds). Sonic now has 1 energy. DASH to square 3 (+1 second). Sonic now has 0 energy. RUN to square 4 (+2 seconds). Sonic now has 1 energy. DASH to square 5 (+1 second). Sonic now has 0 energy. Total time is 6 seconds. Sample Input 15 4 2 10 0 Sample Output 112 Explanation 1The optimal answer is to: RUN to square 2 (+4 seconds). Sonic now has 1 energy. RUN to square 3 (+4 seconds). Sonic now has 2 energy. DASH to square 4 (+2 seconds). Sonic now has 1 energy.…
There are two algorithms called alg1 and alg2 for a problem of size n. alg1 runs in n2 microseconds and alg2 runs in 100n log n microseconds. alg1 can be implemented using 4 hours of programmer time and needs 2 minutes of cpu time. on the other hand, alg2 requires 15 hours of programmer time and 6 minutes of cpu time. if programmers are paid 20 dollars per hour and cpu time costs 50 dollars per minute, how many times must a problem instance of size 500 be solved using alg2 in order to justify its development cost?
implement a function using recursive implementation, for finding the n'th Fibonacci number using the MIPS assembly language.Let P be the Fibonacci function:P(0) = 0P(1) = 1For n > 1 P(n) = P(n-1) + P(n-2)Example Output of Execution:Enter the sequence number: 6P(6) = 8
The binomial coefficient C(N,k) can be defined recursively as follows: C(N,0) = 1, C(N,N) = 1, and for 0 < k < N, C(N,k) = C(N-1,k) + C(N - 1,k - 1). Write a function and give an analysis of the running time to compute the binomial coefficients as follows: A. The function is written recursively.
Construct a memoized algorithm for this algorithm and and derive its time complexity: 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. You do not need to prove the complexity bound formally, just derive it by analyzing each component in your algorithm.
Please answer this, thanks! 1. give the analysis of the running time (Big-Oh will do) and the space complexity. b. please implement the code in the language of your choice and give the running time for three values of N (N must be > 5). c. Compare your analysis with the actual running times. (3) sum = 0;for( i = 0; i < n; ++i )for( j = 0; j < i * i; ++j )for( k = 0; k < j; ++k ) ++sum;