Description

Instructions
The goal of this homework is to practice what we covered in Lecture 2 and 3. Please review both lectures in order to have the context to solve these problems.
Submitting This Assignment
iCollege
In order to complete the coding portions of this assignment, you must make commits of your code. We will take the latest commit as your “final submission”.
Grading and Corrections
Java Language API
Focus on Algorithms’ details, not Java Language. Runnable, correctness, efficiency.
(well organized, easy to read, not in a mass)
Showing Your Work
1. You should add comments that explain the key ideas behind your approach.
Q1: Find Missing Number (2 points)
Convert the following pseudocode algorithm into Java. You’ll find example tests within the main method to ensure you’re headed in the right direction. Make sure you understand each example.
algorithm findMissing
Input: integer array A of length N where each element is distinct and in the range [0, N]
Output: integer x where x is in the range [0, N], but not in A
s = the sum of all numbers in A return (N(N+1))/2 – s
Q2: TwoSum (Fast) (3 points)
Convert the following code into Pseudocode and put it in twosum.txt. Hint: for some loops, you should describe what it does in English. There are no tests for this problem, so be sure to double check and test your translation manually, similar to how we did in lecture.
public static int[] twoSumFast(int[] arr, int target) {
HashSet<Integer> seen = new HashSet<>(); for (int j = 0; j < arr.length; j++) {
int otherAddend = target – arr[j]; if (seen.contains(otherAddend)) { for (int i = 0; i < arr.length; i++) {
if (arr[i] == otherAddend) {
return new int[] {i, j};
}
}
} else { seen.add(arr[j]);
} } return new int[] {-1, -1};
}
Q3: countFives (2 points)
Write countFives, which takes in an integer and returns the number of times 5 appears as a digit within the number. Examples:
countFives(123467890) // should output 0 countFives(555555) // should output 6 countFives(15354) // should output 2
In order to receive full credit for this problem, you must use recursion. I.e. using =, for, while, etc. is prohibited.
Hint: recall the % and / operators:
123 % 10 // evaluates to 3
123 / 10 // evaluates to 12
Q4: pickTrees (3 points)
You build homes out of wood and you need material from a nearby forest. However, you want to avoid deforestation, so you decide for each tree you cut down, you’ll leave its neighbors alone, giving the forest time to recover. However, you still need as much wood as possible, so you have to be careful about which trees you pick to cut down.
Write pickTrees, which takes in an array of N trees arr where arr[i] represents how much wood you can harvest by cutting down tree i. It should return the max amount of wood you can harvest while following the rule of skipping neighbors:
// Pick tree 0, tree 2, and tree 4 => 1 + 3 + 5 = 9 wood total int testResult5 = pickTrees(new int[] {1, 2, 3, 4, 5}); System.out.println(testResult5); // should output 9
// Pick tree 1 and tree 3 => 3 + 3 = 6 wood total int testResult6 = pickTrees(new int[] {1, 3, 4, 3}); System.out.println(testResult6); // should output 6
// Pick tree 0 and tree 3 => 5 + 9 = 14 wood total int testResult7 = pickTrees(new int[] {5, 1, 4, 9}); System.out.println(testResult7); // should output 14
In order to receive full credit for this problem, you must use recursion. I.e. using =, for, while, etc. is prohibited.