Exam 12: Recursion

For the questions below, use the following recursive method. public int question1_2(int x, int y) { if (x == y) return 0; else return question1_2(x-1, y) + 1; } -The following method should return True if the int parameter is even and either positive or 0, and false otherwise. Which set of code should you use to replace ... so that the method works appropriately? Public boolean question3(int x) { ... }

The recursive method to solve the Towers of Hanoi is usable only if the parameter for the number of disks is 7 or smaller.

Demonstrate how factorial(4) is computed given the following recursive method for factorial: public int factorial(int n) { if (n > 1) return factorial(n - 1) * n; else return 1; }

Write a recursive method called numSegments(int order) that yields the number of line segments in a Koch snowflake of order "order."

Rewrite the following iterative method as a recursive method that returns the same String. public String listOfNumbers( ) { String s = ""; for (j = 1; j<10; j++) s += j; return s; }

For the questions below, assume that int[ ] a = {6, 2, 4, 6, 2, 1, 6, 2, 5} and consider the two recursive methods below foo and bar. public int foo(int[ ] a, int b, int j) { if (j < a.length) if (a[j] != b) return foo (a, b, j+1); else return foo (a, b, j+1) + 1; else return 0; } public int bar(int[ ] a, int j) { if (j < a.length) return a[I] + bar(a, j+1); else return 0; } -What is the result of calling foo(a, 2, 0);?

Recursion is a popular programming tool but beginning programmers tend to shy away from it. Why do you suppose this is True?

Explain what a "base case" is in a recursive method.

A Koch snowflake of order = 1 can be drawn without recursion.

For the questions below, recall the Towers of Hanoi recursive solution. -If there are 2 disks to move from one Tower to another, how many disk movements would it take to solve the problem using the recursive solution?

For the questions below, refer to the following recursive factorial method. public int factorial(int x) { if (x > 1) return x * factorial (x - 1); else return 1; } -What is returned if factorial(3) is called?

What does the following recursive method determine? Public boolean question16(int[ ]a, int[ ] b, int j) { If (j = = a.length) return false; Else if (j = = b.length) return True; Else return question16(a, b, j+1); }

It always is possible to replace a recursion by an iteration and vice versa.

For the Towers of Hanoi problem, show how many moves it will take to solve the problem with 5 disks, 6 disks, 7 disks, 8 disks, 9 disks, and 10 disks.

What is wrong with the following recursive sum method? The method is supposed to sum up the values between 1 and x (for instance, sum(5) should be 5 + 4 + 3 + 2 + 1 = 15). Public int sum(int x) { If (x = = 0) return 0; Else return sum(x - 1) + x; }

Why is the following method one which has infinite recursion? Public int infiniteRecursion(int n) { If (n > 0) return infiniteRecursion(n) + 1; Else return 0; }

For the questions below, use the following recursive method. public int question1_2(int x, int y) { if (x == y) return 0; else return question1_2(x-1, y) + 1; } -Calling this method will result in infinite recursion if which condition below is initially True?

For the questions below, recall the Towers of Hanoi recursive solution. -Which of the following methods would properly compute the value of x % y (x mod y) recursively, assuming that x and y not negative numbers?

For the questions below, consider the following representation of grid and the maze code from Chapter 11. Grid: 1 1 1 1 1 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 1 0 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 1 1 Code: public boolean traverse(int row, int column) { if (valid(row, column)) { boolean done = false; grid[row][column] = TRIED; if (row == grid.length - 1 && column == grid[0].length - 1) done = True; else { done = traverse(row + 1, column); if (!done) done = traverse(row, column + 1); if (!done) done = traverse(row - 1, column); if (!done) done = traverse(row, column - 1); } if (done) grid[row][column] = PATH; } return done; } Assume valid returns True if row and column are >= 0 and <= the grid's row length or column length and the entry at this position = = 1. And assume TRIED = 3 and PATH = 7 -Which of the following grids would be the result after traverse has completed all of its recursive calls?

For the questions below, assume that int[ ] a = {6, 2, 4, 6, 2, 1, 6, 2, 5} and consider the two recursive methods below foo and bar. public int foo(int[ ] a, int b, int j) { if (j < a.length) if (a[j] != b) return foo (a, b, j+1); else return foo (a, b, j+1) + 1; else return 0; } public int bar(int[ ] a, int j) { if (j < a.length) return a[I] + bar(a, j+1); else return 0; } -What is the result of calling foo(a, 2, 9);?