Determine the time complexity function of the program
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Determine the time complexity function of the program snippet below, the proof must be in detail step by step until you get the time complexity function.
int f1(int n) {
if (n <= 1) return n;
return 2 * f1(n/2);
}
int f2(int n) {
if (n <= 1) return n;
return f2(n/2) + f2(n/2);
}
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- Compute for the time complexity (in milliseconds) of each letter of the given program segment below, then get the total time complexity. int main( ) { int a, b, c, d; for (a=0;a<10;a++) for (b=0;b<10;b++) for (c=0;c<10;c++) for (d=0;d<10;d++) { If ((a==0)&&(b==0)&&(c==0)&&(d==0)) { a=1, b=2,c=3,d=4; } cout<<a<<b<<c<<d; } }Determine the time complexity function of the program snippet below, int f1(int n) {if (n <= 1) return n;return 2 * f1(n/2);} please the answer must be in detail step by step until you get the time complexity function.What is the worse-case complexity scenario for the following snippets of code? Please show the breakdown of your calculations.Two loops in a row: A nested loop in which the number of times the inner loop executes depends on the value of the Outer loop index. For ( I = 0; I < N; i++) { For ( j = N; j > I; j- - ) { Sequence of statements } }
- 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. Sample Input 0:5 20011014 Sample Output 0:1 1 Explanation 0:The best way to jump from square 1 to square 5 is by jumping 4 squares. That requires only 1 jump.In fact, that is the only solution, thus the second output is 1. Sample Input 1:6 3010100123 Sample Output 1:2 2 Explanation 1The best sequence is to jump 2 squares to square 3 then 3 squares to end in square 6.This is one solution. The other solution is to jump from 1 -> 3 -> 5 -> 6. These are the only two solutions, therefore the second output is 2. Sample Input 2:7 2000110037 Sample Output 2:-1 0 Explanation 2:It is impossible to reach square 7 with the specified jump values. The actual…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.…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/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)))))
- Write a short introduction on algorithm complexity, followed by explaining why it is important, useful and/or exciting. Thanks!Looking at the following algorithm, please give an analysis of it in terms of time complexity using mathematics and put it in big O notation! Algorithm A: k := 0 For i = 1 to n: For j = (i + 1) to n: k = k + j + i Return kWhat is the difference between an algorithm and a heuristic, and how do these approaches differ in their effectiveness for solving complex computational problems?
- 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)))))Which assertion is false? CPU cycles are needed for time's complexity. Less memory is needed for space's complexity. Time complexity is measured by operations. An algorithm's worst-case scenario is the most operations.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. Apply dynamic programming and memoization. Do not use recursion. Make sure ALL test cases return expected outputs. Hint: Approach the problem with 2D Dynamic Programming. Output FormatOutput one line containing a single integer containing the answer as described in the problem statement. This number must be output mod 109 + 7. Sample Input 0:3 9357 Sample Output 0:5 Sample Input 1:3 23151615 Sample Output 1:4 Sample Input 2:3 6123 Sample Output 2:8 The actual code: def solve(n,c,ws): # compute and return answer here # place 2 nested for loops here MOD = 1000000007n, c = list(map(int,input().rstrip().split(" ")))ws = [int(input().rstrip()) for i in range(n)]print(solve(n,c,ws))