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Let (a1,. . , a12) be a valid UPC. Show that the error in transposing the...
Let (di, d2,... .dk) (w1, w2,..., wx)-0 (mod n) be an error detection scheme for the...
Let (di, d2,... .dk) (w1, w2,..., wx)-0 (mod n) be an error detection scheme for the k-digit identification number did2 . . .dk, where 0 〈 di 〈 n. Prove that all transposition errors of two digits di and dj are detected if and only if gcd(ui-y,n) = 1 for i and j between 1 and k
Let {dn}n≥0 denote the number of integer solutions a1 +a2 +a3 +a4 = n where 0 ≤ ai ≤ 5 for each i...
Let {dn}n≥0 denote the number of integer solutions a1 +a2 +a3 +a4 = n where 0 ≤ ai ≤ 5 for each i = 1, 2, 3, 4. Write the ordinary generating function for {cn}n≥0. Please express the ordinary generating function as a rational function p(x) /q(x) where both p(x) and q(x) are polynomials in the variable x.
Someone help please Let A be an array of 5 integers, whose contents are as follows:...
Someone help please Let A be an array of 5 integers, whose contents are as follows: 3, 2, 1, 5, 4 We will apply quick sort to sort this array. Show all of the element-wise comparisons made by the algorithm in the correct order. Here an element-wise comparison means the comparison of one element of the array with another element of the array or the key set in a particular step of the algorithm. Since the algorithm may move the...
Exercise 7 (2 points) Recall the binomial coefficient for integer parameters 0 Sk< n. Prove that...
Exercise 7 (2 points) Recall the binomial coefficient for integer parameters 0 Sk< n. Prove that Exercise 8 (2 points) Prove the following: if z is an integer with at most three decimal digits aia2a3, then x is divisible by 3 if and only if aut a2 +a3 is divisible by 3. Exercise 9 (3 points) A square number is an integer that is the square of another integer. Let x and y be two integers, each of which can...
The input consists of n numbers a1, a2, . . . , an and a target...
The input consists of n numbers a1, a2, . . . , an and a target value t. The goal is to determine in how many possible ways can we add up two of these numbers to get t. Formally, your program needs to find the number of pairs of indices i, j, i < j such that ai+aj = t. For example, for 2, 7, 3, 1, 5, 6 and t = 7, we can get t in two...
3. A sequence is a map a N°R, typically written (an) = (ao, a1, a2, a3, a4,) As an example, the sequence (an) = 1/(...
3. A sequence is a map a N°R, typically written (an) = (ao, a1, a2, a3, a4,) As an example, the sequence (an) = 1/(n2 +1) begins (1, 1/2, 1/5, 1/10, 1/17,..) Here is a useful fact relating sequences and continuity: A function f(x) is continuous at x c if and only if for every sequence (an) that converges to c, written anc, then f(x,) f(c). Alternatively, if you and f(yn)L" with L' L", then f is not continuous at...
Q3 14 Points Consider the vector space P2(R). Let T1, T2, T3 be 3 distinct real...
Q3 14 Points Consider the vector space P2(R). Let T1, T2, T3 be 3 distinct real numbers and 21, 22, az be three strictly positive real numbers. Define (p(x), q(x)) = Li_1 Qip(ri)q(ri) Q3.1 5 Points Show that this P2 (R) together with (-:-) is an inner product space. Please select file(s) Select file(s) Save Answer Q3.2 2 Points Give a counter example that (-, - ) is not an inner product when T1, 12, 13 are still distinct real...
Question 1: Complexity Take a look at the following algorithm written in pseudocode: procedure mystery(a1, a2,...
Question 1: Complexity Take a look at the following algorithm written in pseudocode: procedure mystery(a1, a2, …, an: integer) i := 1 while (i < n and ai ≤ ai+1) i := i + 1 if i == n then print “Yes!” else print “No!” What property of the input sequence {an} does this algorithm test? What is the computational complexity of this algorithm, i.e., the number of comparisons being computed as a function of the input size n? Provide...
Question 4 (10 marks) When analysing the complexity of algorithms, there are three main approaches: worst case, best ca...
Question 4 (10 marks) When analysing the complexity of algorithms, there are three main approaches: worst case, best case and average case. As an example, consider measuring the complexity of list-merging by counting the number of comparisons used As a test example, assume the following A1: There are two ordered lists, each of length 4, say A2: Neither list contains repeats, so a! < a2 < аз < a4 and bl <b2 < b3 < b4 A3: The lists are...
Please I need help with this c++ code. please show all steps , write comments and...
Please I need help with this c++ code. please show all
steps , write comments and show sample runs. Thank you.
1. The Federal Bureau of Investigation (FBI) has recently changed its Universal Control Numbers (UCN) for identifying individuals who are in the FBI's fingerprint database to an eight-digit base 27 value with a ninth check digit. The digits used are: 0123456789ACDE FHJKLMNPRTVWX Some letters are not used because of possible confusion with other digits: B->8, G->C, I- >1, 0->0,...
Let (di, d2,... .dk) (w1, w2,..., wx)-0 (mod n) be an error detection scheme for the k-digit identification number did2 . . .dk, where 0 〈 di 〈 n. Prove that all transposition errors of two digits di and dj are detected if and only if gcd(ui-y,n) = 1 for i and j between 1 and k
Exercise 7 (2 points) Recall the binomial coefficient for integer parameters 0 Sk< n. Prove that Exercise 8 (2 points) Prove the following: if z is an integer with at most three decimal digits aia2a3, then x is divisible by 3 if and only if aut a2 +a3 is divisible by 3. Exercise 9 (3 points) A square number is an integer that is the square of another integer. Let x and y be two integers, each of which can...
3. A sequence is a map a N°R, typically written (an) = (ao, a1, a2, a3, a4,) As an example, the sequence (an) = 1/(n2 +1) begins (1, 1/2, 1/5, 1/10, 1/17,..) Here is a useful fact relating sequences and continuity: A function f(x) is continuous at x c if and only if for every sequence (an) that converges to c, written anc, then f(x,) f(c). Alternatively, if you and f(yn)L" with L' L", then f is not continuous at...
Q3 14 Points Consider the vector space P2(R). Let T1, T2, T3 be 3 distinct real numbers and 21, 22, az be three strictly positive real numbers. Define (p(x), q(x)) = Li_1 Qip(ri)q(ri) Q3.1 5 Points Show that this P2 (R) together with (-:-) is an inner product space. Please select file(s) Select file(s) Save Answer Q3.2 2 Points Give a counter example that (-, - ) is not an inner product when T1, 12, 13 are still distinct real...
Question 4 (10 marks) When analysing the complexity of algorithms, there are three main approaches: worst case, best case and average case. As an example, consider measuring the complexity of list-merging by counting the number of comparisons used As a test example, assume the following A1: There are two ordered lists, each of length 4, say A2: Neither list contains repeats, so a! < a2 < аз < a4 and bl <b2 < b3 < b4 A3: The lists are...
Please I need help with this c++ code. please show all
steps , write comments and show sample runs. Thank you.
1. The Federal Bureau of Investigation (FBI) has recently changed its Universal Control Numbers (UCN) for identifying individuals who are in the FBI's fingerprint database to an eight-digit base 27 value with a ninth check digit. The digits used are: 0123456789ACDE FHJKLMNPRTVWX Some letters are not used because of possible confusion with other digits: B->8, G->C, I- >1, 0->0,...
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