1. Analyze and write the time complexity of the given program: int j = 2 while (j < n) { int k = j while (k < n) { Sum += a[k]*b[k] k += } j = j*sqrt(5) } 1/3 n* log n 2. Explain your analysis
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- 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.The language must be in python. Just do numbers 5-7 Neural Network Units Implement a single sigmoid neural network unit with weights of [-1.2, -1.1, 3.3, -2.1] Calculate the outputs for two training examples:Example 1: [0.9, 10.0, 3.1, 1]Example 2: [0.9, 2.1, 3.7, 1] Note that you don't have to explicitly include a threshold or bias since the examples include a last element of 1 which means that the last weight effectively operates as a threshold. Assuming that a sigmoid unit response >0.5 denotes a positive class and <0.5 is negative class, is example 1 positive or negative? is example 2 positive or negative? Create a single ReLU unit and provide the outputs for those examples. Calculate the derivative of the sigmoid with respect to net input for both examples Calculate the derivative of the ReLU with respect to net input for both examplesa) Consider a recursive function to return the Number of Binary Digits in the Binary Representation of a Positive Decimal Integer (n) using a recursive algorithm. int Process (int n) { if (n == 1) return 1; else return (Extra() + Process (n/4) + Process (n/4)); } Given that Extra(n) is a function of O(n)1) Find T(n) = number of arithmetic operations. 2) Calculate the complexity of this algorithm using Back Substitution.
- Check these two codes and then answer these questions please: 1) Empirically, show the performance curve of the algorithm using time measurements 2) Using the basics of the theoretical analysis, write the complexity of its worst-casetime. 1. Approach: Non recursive: //include necessary header files#include <iostream>using namespace std;//main functionint main(){ int days,buy_on_this_day ,sell_on_this_day; //get number of days as input from user cout<<"Enter number of days: "; cin>>days; int stock_price[days]; for(int i=0;i<days;i++) { cout<<"Enter stock_price"; cin>>stock_price[i]; } int i=0; for(int i=0;i<days-1;i++) { //comparing current price with next day price and finding the minima while(i<days-1 && stock_price[i+1]<=stock_price[i]) i++; if(i==days-1) break; buy_on_this_day =i++; while(i<days && stock_price[i]>=…Computer Science Find the correct asymptotic complexity of an algorithm with runtime T(n) and step-by-step workings where T(x) = O(n) + T((2*x)/8) Assume x and n are the same. If it is different, how will the working be like?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.…
- Generate a graph of performance improvement for code below. Tip: Figure 5.17 in the textbook provides an example of a graph depicting performance improvements associated with loop unrolling. code: //normal code int main() { int n, sum=0; n=50; int a[50]; { for(int i=0; i<n; i++) { sum= sum +a[i]; } printf("sum is %d", sum); return 0; } //with unrolling int main() { int n, sum=0; n=50; int a[50] for(int i=0; i<n; i+=10) { scanf("%d", &a[i]); } sum= sum + a[0]; sum= sum + a[1]; sum= sum + a[2]; sum= sum + a[3]; sum= sum + a[4]; sum= sum + a[5]; sum= sum + a[6]; sum= sum + a[7]; sum= sum + a[8]; sum= sum + a[9]; printf("sum is %d", sum); return 0; }Any clearly defined computational process that receives a value or set of values as input and produces a value or set of values is known as an algorithm. Is it feasible to compare and contrast two different methods that address the same issue? Provide a brief explanation of the optimisation metrics or algorithm.Compute time complexity of the given programs. The complexity computation should be for the complete program. Map it on its relevant standard function. Clear computation required. void swap(int *xp, int *yp) { int temp = *xp; *xp = *yp; *yp = temp; } // A function to implement bubble sort void bubbleSort(int arr[], int n) { int i, j; for (i = 0; i < n-1; i++) // Last i elements are already in place for (j = 0; j < n-i-1; j++) if (arr[j] > arr[j+1]) swap(&arr[j], &arr[j+1]); } /* Function to print an array */ void printArray(int arr[], int size) { int i; for (i = 0; i < size; i++) cout << arr[i] << " "; cout << endl; }
- 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 are the TA for the FCP course in environment engineering. You are given the midsem and endsem marks for the N Students in the course. A student P is said to dominate a student Q, if the midsem and endsem marks of P are both greater than the respective midsem and endsem marks of Q. Design an efficient algorithm for finding all the students that are not dominated by any other student in the class. Analyse the time complexity as wellInformation 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/memoization. Make sure ALL test cases return expected outputs. Sample Input 04 412340123 Sample Output 013715 Explanation 0You are given the sequence 1,2,3,4.F0 = A0 = 1F1 = A1 + F0 = 2 + 1 = 3F2 = A2 + F1 + F0 = 3 + 3 + 1 = 7F3 = A3 + F2 + F1 + F0 = 4 + 7 + 3 + 1 = 15 The actual code def solve(k,a): MOD = 1000000007 # compute and return answer here q, n = list(map(int,input().rstrip().split(" ")))a = [int(input().rstrip()) for i in range(n)]outs = []for i in range(q): k = int(input().rstrip()) outs.append(solve(k,a))print("{}".format("\n".join(list(map(str,outs)))))