В4.Given a sequence of 5 keys < 53, 66, 32, 41, 88 > for searching task:a)Given the hash function H(k)(3.k) mod 7, insert the keys above according toits original order (from left to right) into a hash table of 7 slots. Indicate the cases ofcollision. Clearly show the steps and calculation with a table.b)In case of any collisions found above in a) part, determine the new slot for each collidedcase using Linear Probing to solve the collision problem. Clearly show your answer foreach identified case.No step of calculation required.(Answer with “NO collision found", in case there is no collisions found above)nityc)In case of any collisions found above in a) part, determine the new slot ONLY for the firstcollided case using Double-Hashing (with functions below) to solve the collision problem.Clearly show the steps of your calculation.di =H(k) = (3.k) mod 7(di-1 + ((5.k) mod 6) + 1) mod 7(Answer with "NO collision found", in case there is no collisions found above)%3Ddi =i > 2JT ВЗ.Given code:for i in range(n):aFn(i)for j in range(n):HTfor 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.HKUunity Cob) 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)=DAn^+Bn+nAB+B where A and B are positive integerRYRIGHconstants, use the definition of Big-O to prove f(n)=0(nAB). Clearly show the steps ofyour proof. (* Use definition, not properties of Big-O.)

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В4. Given a sequence of 5 keys < 53, 66, 32, 41, 88 > for searching task: a) Given the hash function H(k) (3.k) mod 7, insert the keys above according to its original order (from left to right) into a hash table of 7 slots. Indicate the cases of collision. Clearly show the steps and calculation with a table. COPY b) In case of any collisions found above in a) part, determine the new slot for each collided case using Linear Probing to solve the collision problem. Clearly show your answer for each identified case. No step of calculation required. H (Answer with “NO collision found", in case there is no collisions found above) c) In case of any collisions found above in a) part, determine the new slot ONLY for the first collided case using Double-Hashing (with functions below) to solve the collision problem. Clearly show the steps of your calculation. di = H(k) (3.k) mod 7 di = (di-1 + ((5•k) mod 6) + 1) mod 7 i 2 2 (Answer with “NO collision found", in case there is no collisions found above)

В4. Given a sequence of 5 keys < 53, 66, 32, 41, 88 > for searching task: a) Given the hash function H(k) (3.k) mod 7, insert the keys above according to its original order (from left to right) into a hash table of 7 slots. Indicate the cases of collision. Clearly show the steps and calculation with a table. COPY b) In case of any collisions found above in a) part, determine the new slot for each collided case using Linear Probing to solve the collision problem. Clearly show your answer for each identified case. No step of calculation required. H (Answer with “NO collision found", in case there is no collisions found above) c) In case of any collisions found above in a) part, determine the new slot ONLY for the first collided case using Double-Hashing (with functions below) to solve the collision problem. Clearly show the steps of your calculation. di = H(k) (3.k) mod 7 di = (di-1 + ((5•k) mod 6) + 1) mod 7 i 2 2 (Answer with “NO collision found", in case there is no collisions found above)

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.
Let, the time complexity of each of the following code snippets be T(n). Find out a tight bound for T(n) in Big-Theta () notation. p =0 for i=1;i<n;i=i*2 p++ for j=1;j<p;j=j*2 print(“hello”)
a) 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.
How can the following function be simplified so that it has a time complexity of O(n) or faster?For your information, the specifications of the functions are as follows: Using numbers ranging from 0 to 15 (inclusive), create all possible lists which sum up to K and have a length of N. Duplicated numbers are allowed as long as it fulfills the conditions above (this means [0,0,1], [0,1,0] and [1,0,0] are all correct outputs if K=1 and N=3). When instantiated with the list function, the list size of the function should be the number of all lists. For example, given K=23 and N=2, the expected list size is 8. The function must be able to accept N=10 and be finished before 9 seconds. Do not use itertools or external libraries.
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;
Please written by computer source Let x be a binary string. The minimal description of x, written d(x), is the shortest string ⟨M, w⟩ where TM M on input w halts with x on its tape. If several such strings exist, select the lexicographically first among them. The descriptive complexity, or Kolmogorov complexity, of x, written K(x), is K(x) = |d(x)|. Show that the function K(x) is not a computable function. HINTS: If K is a computable function, there is some TM which computes it. That TM can be used to find strings of large complexity. Try to design a program which outputs “complex” strings but which contradicts their supposed complexity, and even contradicting the supposed complexity of a single string suffices.
For each of the following two code fragments, give its asymptotic running time in the form T(n) = (f(n)) for an appropriate function f(n), and justify your answers. s = 0; for i=1 to n for j= i to n for k= i to j if (A[k] > A[i]+ A[j]) then s = s+1 return s
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.
Write a function that takes an unsigned integer andreturns the number of '1' bits it has(also known as the Hamming weight).For example, the 32-bit integer '11' has binaryrepresentation 00000000000000000000000000001011,so the function should return 3.T(n)- O(k) : k is the number of 1s present in binary representation.NOTE: this complexity is better than O(log n).e.g. for n = 00010100000000000000000000000000only 2 iterations are required..
Given: List L of pairs of characters String S Output: TRUE if S is a valid string, FALSE otherwise. A string is considered valid if each character in the string can be paired with another character in the string, where the pair belongs to the input list L. Furthermore, two pairs cannot cross each other. In other words, a pair most completely enclose another, or be completely separate. Design and implement an efficient dynamic programming solution to this problem. Examples: Input L: (a b) (b c) (c d) (a a) Input S: aaba Output: True (pairs shown color-coded: aaba, “aa” fully encloses “ab”) Input L: (a b) (b c) (c d) (a a) Input S: abcaad Output: True (pairs shown color-coded: abcaad, “ab” is separate from the other pairs) Input L: (a b) (b c) (c d) (a a) Input S: acbd Output: False (acbd is not valid because the pairs cross each other.) Input L: (a b) (b c) (c d) (a a) Input S: aaac Output: False Could you please provide python implementation to this?
Given: List L of pairs of characters String S Output: TRUE if S is a valid string, FALSE otherwise. A string is considered valid if each character in the string can be paired with another character in the string, where the pair belongs to the input list L. Furthermore, two pairs cannot cross each other. In other words, a pair most completely enclose another, or be completely separate. Design and implement an efficient dynamic programming solution to this problem. Examples: Input L: (a b) (b c) (c d) (a a) Input S: aaba Output: True (pairs shown color-coded: aaba, “aa” fully encloses “ab”) Input L: (a b) (b c) (c d) (a a) Input S: abcaad Output: True (pairs shown color-coded: abcaad, “ab” is separate from the other pairs) Input L: (a b) (b c) (c d) (a a) Input S: acbd Output: False (acbd is not valid because the pairs cross each other.) Input L: (a b) (b c) (c d) (a a) Input S: aaac Output: False
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 divide-and-conquer algorithm in the problem. Make sure all test cases return expected outputs. Hint: Apply bisection method/modules Output FormatOutput contains a line with two space-separated integers W_a and W_b.- W_a is the maximum matchups won by Hamiltonia- W_b is the maximum matchups won by Burrgadia. Sample Input 03 554402410 Sample Output 03 0 Sample Input 15 4833485183 Sample Output 12 2 Sample Input 27 81028121912601319851 Sample Output 27 0 The actual code """Solves a test case Parameters:a : int - number of leaders in Hamiltoniab : int - number of leaders in Burrgadias_i : array-like - rap proficiencies of Hamiltonia's leadersr_j : array-like - rap proficiencies of Burrgadia's leaders Returns:win_a : int - number of…