Requirements: Your big-Oh bound must be as TIGHT as possible, e.g., if 0(n) is the correct answer, then 0(n^2) will NOT be given marks because it is not tight enough. Your big-Oh bound must be SIMPLIFIED, e.g., answers such as 0(n-1) or 0(3n) will NOT ben given marks because they are not simplified enough. Please write your answer for each question on the appropriate TODO line.

Requirements: Your big-Oh bound must be as TIGHT as possible, e.g., if 0(n) is the correct answer, then 0(n^2) will NOT be given marks because it is not tight enough. Your big-Oh bound must be SIMPLIFIED, e.g., answers such as 0(n-1) or 0(3n) will NOT ben given marks because they are not simplified enough. Please write your answer for each question on the appropriate TODO line.

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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Consider the LCS problem discussed in class. Suppose we only want to compute the length of the LCS of x[1..m] and y[1..n] (i.e. we do not care about the actual subsequence itself). This means we do not need to “traceback” to find the LCS. In this setting, show how the algorithm can be altered so that it only needs min(m,n) + O(1) space rather than m · n space (note that it must be min(m,n) and not O(min(m, n))).
What is big-O estimate of function f(x) = log(x^2 +1) + log(x^3 +1). Be sure to specify the values of the witnesses C and k. Show your work.
Running Time Analysis: Give the tightest possible upper bound for the worst case running time for each of the following in terms of N. You MUST choose your answer from the following (not given in any particular order), each of which could be reused (could be the answer for more than one of a) – f)): O(N2), O(N3 log N), O(N log N), O(N), O(N2 log N), O(N5), O(2N), O(N3), O(log N), O(1), O(N4), O(NN), O(N6)
2. Prove from the definition that 2n2 + 100n log n + 1000 = O(n2) 3. For what values of n is 50 n lg n greater than 0.5 n2? Why do we say that 0.5 n2 is asymptotically larger, if 50 n lg n is larger for many values? (Hint: you may need to graph the functions or play around with your calculator.)
assess the complexity of two_peak terms of n (in theory - hand calculation) def findMax(arr,mid,max): max_index = 0 for i in range(4): if (max < arr[i][mid]): max = arr[i][mid] max_index = i return max,max_index def findPeakRec(arr,mid): max = 0 max, max_index = findMax(arr, mid, max) if (mid == 0 or mid == 4 - 1): return max if (max >= arr[max_index][mid - 1] and max >= arr[max_index][mid + 1]): return max if (max < arr[max_index][mid - 1]): return findPeakRec(arr, mid - ceil(mid / 2.0)) if (max < arr[max_index][mid+1]): return findPeakRec(arr,mid + ceil(mid / 2.0)) def two_peak(arr): return findPeakRec(arr, 4 // 2)
Question: How many times is the function 'YellowJackets' called in the functions below? Give an exact bound and a tight asymptotic bound in Big-O notation. Show your work (summations and closed forms), but no formal proof is necessary. a) function A(n) for i = 0, i <= n, i = i + 1 do for j = i, j <= n^2, j = j + 1 do YellowJackets() end for end for end function b) function B(n) for i = 0, i <= n, i = i + 1 do for j = 0, j <= n, j = j + 2 do YellowJackets() end for end for for k = 0, k < n, k = k + 1 do YellowJackets() end for end function c) function C(n) for i = 1, i <= n, i = i + 1 do for j = 1, j <= n, j = j ∗ 2 do YellowJackets() end for end for end function d) function D(n) i = 1 while i < n^4 do i = i + 2 for j = i, j…
Compute the gradient with respect to all parameters of f(w0 + w1a1 + w2a2) when w0 = 3, w1 = −2, a1 = 2, w2 = −1, a2 = 4, and β = 0.25 using backpropagation
No need for coding (Subject is Python) Give the tilde approximations and explain for the following quantities. d) ?^2+1+(1/2^?) e) log(?^3+1/???(?^2) f) 20?^3−15?^2+? g) log(4?)/???(2?)
Correct answer will be upvoted else downvoted. Computer science. way from block u to obstruct v is a grouping u=x0→x1→x2→⋯→xk=v, where there is a street from block xi−1 to hinder xi for each 1≤i≤k. The length of a way is the amount of lengths over all streets in the way. Two ways x0→x1→⋯→xk and y0→y1→⋯→yl are unique, if k≠l or xi≠yi for some 0≤i≤min{k,l}. Subsequent to moving to another city, Homer just recalls the two exceptional numbers L and R yet fails to remember the numbers n and m of squares and streets, separately, and how squares are associated by streets. Be that as it may, he accepts the number of squares ought to be no bigger than 32 (in light of the fact that the city was little). As the dearest companion of Homer, if it's not too much trouble, let him know whether it is feasible to see as a (L,R)- constant city or not. Input The single line contains two integers L and R (1≤L≤R≤106). Output In case it is difficult to track down a (L,R)- consistent city…
Question: Factor 262063, 9420457, and 181937053 using the POLLARD RHO ALGORITHM, if the function f is defined to be f(x) = x 2 + 1. How many iterations are needed to factor each of these three integers? Using various choices for the bound, B, attempt to factor 262063 and 9420457 using the p − 1 method. How big does B have to be in each case to be successful?Factor 262063, 9420457, and 181937053 using the POLLARD RHO ALGORITHM, if the function f is defined to be f(x) = x 2 + 1. How many iterations are needed to factor each of these three integers? Using various choices for the bound, B, attempt to factor 262063 and 9420457 using the p − 1 method. How big does B have to be in each case to be successful?
f(n) = n3 - (n2 log2 n) + 2n f(n) ∈ O(n3) by giving the constants (c, n0) and arguing that your constants hold as n goes to infinity by either "chaining up", "chaining down", carefully treating the inequality as an equality and doing some algebra, or even weak induction. Also, what is the minimum value for c (in the definition of O() ) forj this problem and is it an exclusive or inclusive minimum/bound.
Use a computer to plot formula 2.22 directly, as follows. Define z = qA/q, so that (l-z) = qB/q. Then, aside from an overall constant that we'll ignore, the multiplicity function is [4z(1-z)]N, where z ranges from 0 to 1 and the factor of 4 ensures that the height of the peak is equal to 1 for any N. Plot this function for N = 1, 10, 100, 1000, and 10,000. Observe how the width of the peak decreases as N increases.