Consider the following function. Determine (1) which values of i and j the function will use, and then (2) what the output will be ef change(i = 1,j - 1): i - i + j j = j + 1 %3D print(i, j) hange(j = 2, i = 1)
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- I need help with this question of Data Structures and Algorithmns with explanation 1 True of False a) For two functions f(n) and g(n) if f(n) =O(g(n)) then g(n) = Ω(f(n)) (True or False) b) For two positive functions g and h if f(n) =O(g(n)) then g(n) = O(h(n)) , then f(n)= O(h(n)) (True or False) c) If g1(n) = O(f(n)) and g2(n) = O(f(n)), then g1 + g2 = O(f(n)) (True or False)Implement a C function, named triangle, that outputs Pascal’s triangle. In general, the Pascal’s triangle can be represented as: 0C0 1C1 1C0 2C2 2C1 2C0 3C3 3C2 3C1 3C0 4C4 4C3 4C2 4C1 4C0. . .where nCr represents how many ways there are to choose r from n, not counting duplicates. The formula used to calculate nCr can be written as:nCr = n!/r!(n −r)!where n! is the factorial of n. The function triangle:• is called by value where exactly one parameter (the number of rows of Pascal’s triangle)is passed to it.• returns void (i.e., no value).• prints out Pascal’s triangle to the standard output.• Employs two other functions, namely:– int choose(int n, int r);That chooses r from n– int factorial(int n);That calculates the factorial of n.Note: You are allowed — in fact, encouraged — to design and use any other functions as needed. Note:• The number of the rows is limited to integers between 0 and 13 inclusive.• If 0 is entered…Which functions are one-to-one? Which functions are onto? Describe the inversefunction for any bijective function.(a) f : Z → N where f is defined by f (x) = x4 + 1(b) f : N → N where f is defined by f (x) = { x/2 if x is even, x + 1 if x is odd}(c) f : N → N where f is defined by f (x) = { x + 1 if x is even, x − 1 if x is odd}
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- Simplify the complement of the following function: F(A,B,C,D)=(0,2,4,5,8,9,10,11) Your answer: F=((A'B'D)' (BC)'(AB)')' F=((A'BD)'(BC)'(AB)')' F=((A'B'D)'(B'C)'(AB)') F=((A'B'D')' (BC)'(AB)')Consider the function, f(n), defined by the following code int f(int n) { int r = 0; if ( n % 2 == 0 ) return 1; // when n is even while ( n > 1 ) { n = n – 3; r++; } return r; } From the definitions of big-Theta and little-oh: Prove or disprove that f(n) is Θ ( n ) 2. Prove or disprove that f(n) is o ( n^2 ) ( note: function f(n) as defined by the code, that is, the return value, and is not asking about the runtime of the code.)Define a function calc_pyramid_volume() with parameters base_length, base_width, and pyramid_height, that returns the volume of a pyramid with a rectangular base. calc_pyramid_volume() calls the given calc_base_area() function in the calculation.Relevant geometry equations:Volume = base area x height x 1/3(Watch out for integer division).Sample output with inputs: 4.5 2.1 3.0 Volume for 4.5, 2.1, 3.0 is: 9.45 def calc_base_area(base_length, base_width): return base_length * base_width ''' Your solution goes here ''' length = float(input())width = float(input())height = float(input())print('Volume for', length, width, height, "is:", calc_pyramid_volume(length, width, height))
- Consider the following function someFunc::Integer -> Integer -> Integer -> Integer someFunc x y z = x *(y + z) Prove that someFunc a b c = sumFunc a c bWrite a function that makes the base conversion. It takes two integers n and b as input (n >= 0 andb > 1, both in base 10) and expresses n in base b. For example, the decimal expansion of 345 inbase 10 is 345 = 3 × 102 + 4 × 101 + 5 × 100.Sample input: n = 12, b =2. Sample output: 1100Explanation: (12)10 = (1100)2How 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.