Given a positive number n, say n = 36489, we are interested in numbers obtained by...
Given a positive number n, say n = 36489, we are interested in numbers obtained by sorting digits in n; in this example, number 98643 and 34689. Write a Python function for this purpose.
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Given a positive number n, say n = 36489, we are interested in
numbers obtained by...
[10 marks] Assume that we have two decimal positive numbers A and B. Both numbers have n digits. ...
[10 marks] Assume that we have two decimal positive numbers A and B. Both numbers have n digits. We want to know what is the minimum number of swaps that we need in order to get from number A to B, where in each swap we choose two digits of a number and simply swap them For simplicity, we assume that A and B do not have the digit 0 in them, and that A and B have the set...
Let's say you are given a sequence of distinct positive numbers. We want to find a...
Let's say you are given a sequence of distinct positive numbers. We want to find a subsequence with the maximum possible sum, with the restriction that we are not allowed to take three consecutive elements from the original sequence. For example, for input 1, 6, 5, 2, 7, 9, 3, 4, the subsequence with the maximum possible sum is 6, 5, 7, 9, 4 (we have two pairs of consecutive elements 6, 5 and 7, 9 but not three consecutive...
We write R+ for the set of positive real numbers. For any positive real number e,...
We write R+ for the set of positive real numbers. For any positive real number e, we write (-6, 6) = {x a real number : -e < x <e}. Prove that the intersection of all such intervals is the set containing zero, n (-e, e) = {0} EER+
We write R+ for the set of positive real numbers. For any positive real number e,...
We write R+ for the set of positive real numbers. For any positive real number e, we write (-6, 6) = {x a real number : -e < x <e}. Prove that the intersection of all such intervals is the set containing zero, n (-e, e) = {0} EER+
Problem 2. Let n be a positive integer. We sample n numbers ai,...,an from the set...
Problem 2. Let n be a positive integer. We sample n numbers ai,...,an from the set 1, 2,...,n} uniformly at random, with replacement. Say that the picks i and j with i < j are a match if a -aj. What is the expected total number of matches? Hint: Use indicators. Wİ
Let n be a positive integer. We sample n numbers a1, a2,..., an from the set...
Let n be a positive integer. We sample n numbers a1, a2,..., an from the set {1,...,n} uniformly at random, with replacement. We say that picks i and j with are a match if ai = aj, i < j. What is the expected total number of matches? Use indicators.
IN PYTHON: Write a function that takes, as an argument, a positive integer n, and returns...
IN PYTHON: Write a function that takes, as an argument, a positive integer n, and returns a LIST consisting of all of the digits of n (as integers) in the same order. Name this function intToList(n). For example, intToList(123) should return the list [1,2,3].
A triangle is expressed by tuples of three positive numbers, which are the length of sides...
A triangle is expressed by tuples of three positive numbers, which are the length of sides of the triangle. Two triangles a1 and a2 are similar if a2 can be generated by rotating and reflecting triangle a1. For example, t1 = (7, 10, 13) is similar to t2 = (7, 13, 10) since a2 can be obtained by rotating and reflecting t1. (7, 10, 13) rotate −−−→ (10, 13, 7) reflect −−−−→ (7, 13, 10) On the other hand, t1...
Using python Write a Python function called sgm that requests a positive integer n and returns...
Using python Write a Python function called sgm that requests a positive integer n and returns the series geometric mean of the numbers 1,2,3, . . . n. For example sgm(5) = (5 x 4 x 3 x 2 x 1)1/5 = (120) 1/5 = 2.605 . Write the program so that a user is requested for a positive integer and program prints the series geometric mean of the integer. Example execution: Enter number: 5 series geometric mean of 5...
Suppose we are given a line segment of length 1. We say that a real number x is constructible if ...
Suppose we are given a line segment of length 1. We say that a real number x is constructible if we can construct, with unmarked straightedge and compass, a line segment of length (So for example, -3 is constructible since we can construct a line segment of length 3 by joining three segments of length 1 along the same line.) Prove that the set G of constructible numbers is a field. (Constructible numbers are real numbers, so you don't need...
[10 marks] Assume that we have two decimal positive numbers A and B. Both numbers have n digits. We want to know what is the minimum number of swaps that we need in order to get from number A to B, where in each swap we choose two digits of a number and simply swap them For simplicity, we assume that A and B do not have the digit 0 in them, and that A and B have the set...
We write R+ for the set of positive real numbers. For any positive real number e, we write (-6, 6) = {x a real number : -e < x <e}. Prove that the intersection of all such intervals is the set containing zero, n (-e, e) = {0} EER+
We write R+ for the set of positive real numbers. For any positive real number e, we write (-6, 6) = {x a real number : -e < x <e}. Prove that the intersection of all such intervals is the set containing zero, n (-e, e) = {0} EER+
Problem 2. Let n be a positive integer. We sample n numbers ai,...,an from the set 1, 2,...,n} uniformly at random, with replacement. Say that the picks i and j with i < j are a match if a -aj. What is the expected total number of matches? Hint: Use indicators. Wİ
Suppose we are given a line segment of length 1. We say that a real number x is constructible if we can construct, with unmarked straightedge and compass, a line segment of length (So for example, -3 is constructible since we can construct a line segment of length 3 by joining three segments of length 1 along the same line.) Prove that the set G of constructible numbers is a field. (Constructible numbers are real numbers, so you don't need...
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