### **What is the purpose of `howMany` and `target`? Why...

What is the purpose of howMany and target? Why is lastadded initialized to zero?

• Purpose of howMany:
  This specifies how many numbers must be selected from the set. For example, if howMany = 3, the configuration is looking for exactly three numbers.

• Purpose of target:
  This specifies the sum that the selected numbers should add up to. For example, if target = 15, the program attempts to find combinations of numbers whose sum equals 15.

• Why is lastadded initialized to zero?
  lastadded keeps track of the most recently added number in the solution process. It is initialized to zero because, in the initial configuration, no numbers have been added yet, so the starting point (or "last added number") is logically zero.

Why do we use copy constructors, and how do we write one in general?

• Why copy constructors are used:
  Copy constructors are used to create a new object by copying properties from an existing object. In this case, the second constructor creates a new configuration by copying the existing one and adding a new number (newNum) to the nums set. This is essential in algorithms like backtracking or search, where you explore one branch of solutions without modifying the original configuration.

• General example of a copy constructor:

  public class MyClass {
      private int value;
  
      // Standard constructor
      public MyClass(int value) {
          this.value = value;
      }
  
      // Copy constructor
      public MyClass(MyClass original) {
          this.value = original.value;
      }
  }
  

  In the context of the provided code, the second constructor in FindSumConfig takes an existing configuration (conf) and makes a new configuration by copying all the values and adding a new number to the nums set (nums.add(newNum)).

Why does it have a for loop in the isGoal method?

• The for loop in isGoal iterates through all numbers in the nums set to calculate their sum. For the nums set to meet the goal, both of the following conditions must be satisfied:
  1. The set contains the exact number of elements (nums.size() == howMany).
  2. The sum of all numbers in the set matches the specified target.
  The for loop calculates the sum of numbers in the set to validate the second condition.

What does "search" mean?

• Search in this context refers to exploring all possible configurations (or combinations of numbers) to reach the desired result (achieving the target sum with the specified number of elements).
  The getNeighbors method generates potential "next steps" in this search by creating new configurations with additional numbers. This typically aligns with algorithms like backtracking or depth-first search.

What does a config generally result in?

• A configuration typically leads to one of the following results:
  1. A valid goal state (a configuration where the isGoal method returns true, meaning it satisfies the problem's requirements).
  2. An intermediate state, which might lead to a valid state (a configuration that is not yet a goal but is still valid based on the isValid method).
  3. An invalid state, which is discarded because it can no longer lead to a solution.

What is the purpose of a configuration (config)?

• The purpose of a configuration is to represent a state in the problem-solving process. It encapsulates the current state of the numbers selected so far (nums), ensures the constraints (howMany and target) are respected, and provides methods to:

  1. Check if the current state is the goal (isGoal).
  2. Verify if the state can lead to a solution (isValid).
  3. Generate potential next states to explore (getNeighbors).

  By using configurations, the program can systematically and efficiently explore all possibilities in a structured manner (e.g., through backtracking or search algorithms).