Solve the questions on recursive function; 2)Consider the following recursive function, for which again, we can assume theparameters to be non-negative integers. This function computes the combinations ofk out of n objects using Pascal's triangle formula.int combinations (int k, int n){if (k>n)return 0;else if (n == k || k == 0)return 1;elsereturn combinations(k-1, n-1) + combinations(k, n-1);How many nodes does the runtime stack contain at the most for the function call above,not including the main?a)Draw the recursion tree for computing combinations (4, 7).b)c)How many repeated function calls can you observe in the tree? Give an example. Is thisan indication that the function is inefficient?

a) To draw the recursion tree for computing combinations(4, 7), we can start with the initial call…

Answered: 2) Consider the following recursive…

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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Your main task is to write a recursive function sierpinski() that plots a Sierpinski triangle of order n to standard drawing. Think recursively: sierpinski() should draw one filled equilateral triangle (pointed downwards) and then call itself recursively three times (with an appropriate stopping condition). It should draw 1 filled triangle for n = 1; 4 filled triangles for n = 2; and 13 filled triangles for n = 3; and so forth. Sierpinski.java When writing your program, exercise modular design by organizing it into four functions, as specified in the following API: public class Sierpinski { // Height of an equilateral triangle with the specified side length. public static double height(double length) // Draws a filled equilateral triangle with the specified side length // whose bottom vertex is (x, y). public static void filledTriangle(double x, double y, double length) // Draws a Sierpinski triangle of order n, such that the largest filled //…
Consider the following recursive function: if b = 0, if 6 > a > 0, a f(b, a) f (b, 2.(a mod b)) otherwise. f(a, b) = Estimate the number of recursive applications required to compute f(a, b).
The Polish mathematician Wacław Sierpiński described the pattern in 1915, but it has appeared in Italian art since the 13th century. Though the Sierpinski triangle looks complex, it can be generated with a short recursive function. Your main task is to write a recursive function sierpinski() that plots a Sierpinski triangle of order n to standard drawing. Think recursively: sierpinski() should draw one filled equilateral triangle (pointed downwards) and then call itself recursively three times (with an appropriate stopping condition). It should draw 1 filled triangle for n = 1; 4 filled triangles for n = 2; and 13 filled triangles for n = 3; and so forth. API specification. When writing your program, exercise modular design by organizing it into four functions, as specified in the following API: public class Sierpinski { // Height of an equilateral triangle whose sides are of the specified length. public static double height(double length) // Draws a filled equilateral…
For function addOdd(n) write the missing recursive call. This function should return the sum of all postive odd numbers less than or equal to n. Examples: addOdd(1) -> 1addOdd(2) -> 1addOdd(3) -> 4addOdd(7) -> 16 public int addOdd(int n) { if (n <= 0) { return 0; } if (n % 2 != 0) { // Odd value return <<Missing a Recursive call>> } else { // Even value return addOdd(n - 1); }}
Consider a recursive function, called f, that computes powers of 3 using only the + operator. Assume n > = 0. int f(int n) { if (n == 0) return 1; return f(n-1) + f(n-1) + f(n-1); } Give an optimized version of f, called g, where we save the result of the recursive call to a temporary variable t, then return t+t+t. i got int g(int n) { if (n == 0) return 1; int t = g(n - 1); return t+t+t; } so now Write a recurrence relation for T(n), the number addition operations performed by g(n) in terms of n.
Ackermann’s Function
Write an iterative function that determines the number of even elements in an array a of integers of size n. The function should return the number of elements that are even in array a of size n. Propose an appropriate prototype for your function and then write its code. Write a recursive function to solve the above problem. Propose an appropriate prototype for your function and then write its code.
The Lucas numbers are a series of numbers where the first two Lucas numbers (i.e., at indices 0 and 1) are 2 and 1 (respectively) and the kth Lucas number L_k (where k>1) is L_(k-1) + L_(k-2). Consider the following recursive definition for a function that is supposed to find the nth element of the Lucas numbers. Select the best option that identifies the line of code that prevents this function from running recursively and provides the correct code. Question options: line 5 should be return recursive_function(n-1) + recursive_function(n-2) line 3 should be return [2,1][n-1][n-2] line 3 should be return [2,1][n-1] line 2 should be if n <= 2: line 5 should be return recursive_function(n-1 + n-2) None of these options
The 4th problem mimics the situation where eagles flying in the sky can be spotted and counted.FindEagles: a recursive function that examines and counts the number of objects (eagles) in aphotograph. The data is in a two-dimensional grid of cells, each of which may be empty (value 0) orfilled (value 1 to 9). Maximum grid size is 50 x 50. The filled cells that are connected form an object(eagle). Two cells are connected if they are vertically, horizontally, or diagonally adjacent. Thefollowing figure shows 3 x 4 grids with 3 eagles. 0 0 1 21 0 0 01 0 3 1 FindEagle function takes as parameters the 2-D array and the x-y coordinates of a cell that is a part ofan eagle (non-zero value) and erases (change to 0) the image of an eagle. The function FindEagleshould return an integer value that counts how many cells has been counted as part of an eagle and havebeen erased. The following sample data has two pictures, the first one is 3 x 4, and the second one is 5 x 5 grids. Notethat your program…
Beeblebrox question help
8- Determine if each of the following recursive definition is a valid recursive definition of a function f from a set of non-negative integers. If f is well defined, find a formula for f(n) where n is non- negative and prove that your formula is valid. a. f(0) = 2,f(1) = 3, f(n) = f(n-1)-1 for n ≥ 2 b. f(0) = 1,f(1) = 2, f(n) = 2f (n-2) for n = 2
Exercise 1: The number of combinations CR represents the number of subsets of cardi- nal p of a set of cardinal n. It is defined by C = 1 if p = 0 or if p = n, and by C = C+ C in the general case. An interesting property to nxC calculate the combinations is: C : Write the recursive function to solve this problem.

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