In this article, we will look at one of the famous problems in Java coding tests, the “I Will Become the Apartment Manager” problem.
This problem serves as a good example to learn the basics of dynamic programming, and I will detail the process of solving the given problem through an efficient algorithm.
Problem Description
The goal of the “I Will Become the Apartment Manager” problem is as follows.
Problem:
Assume there are N floors and K apartments. Write an algorithm to calculate the number of people living in apartment N on the Kth floor.
Each apartment has a problem to find the number of people living in apartment N on the Kth floor. There is 1 person on the ground floor, and the number of people in apartment N on each floor is the sum of the number of people in all apartments on the floor below. Therefore,
- 1st floor apartment 1 = 1
- 1st floor apartment 2 = 1
- 2nd floor apartment 1 = 1
- 2nd floor apartment 2 = 1 + 1 = 2
- 3rd floor apartment 1 = 1
- 3rd floor apartment 2 = 1 + 2 = 3
This pattern emerges.
For the given K and N, please create a function that calculates the number of people living in that apartment.
Input and Output Format
Input: The first line gives the number of test cases T (1 ≤ T ≤ 14).
Each test case consists of two integers K and N (0 ≤ K ≤ 14, 1 ≤ N ≤ 14).
Output: For each test case, print the number of people living in apartment N on the Kth floor.
Problem Solving Process
Step 1: Understanding the Problem
The essence of the problem is to understand the pattern of the number of people from the ground floor to the Kth floor, and based on this pattern, to find the number of people in apartment N.
As I understand, the apartment problem can apply the rules of dynamic programming.
In other words, the value of apartment N on each floor can be defined as the sum of the values in apartments N and (N-1) on the previous floor.
Step 2: Designing the Dynamic Programming Table
To solve this problem, we will declare a 2D array to calculate the number of people in Kth floor apartment N.
We will proceed by filling in the array with the number of people at each position.
// Example Java code
int[][] dp = new int[15][15]; // Declare a 15 x 15 array
for (int i = 0; i < 15; i++) {
dp[i][1] = 1; // Initialize all apartments on the ground floor
dp[0][i] = i; // Set the number of people on the ground floor
}
for (int i = 1; i < 15; i++) {
for (int j = 2; j < 15; j++) {
dp[i][j] = dp[i - 1][j] + dp[i][j - 1]; // Dynamic programming recurrence relation
}
}
Step 3: Final Calculation
Based on the above rules, we can calculate the value for Kth floor apartment N. For each test case, we simply need to print the value of dp[K][N].
Step 4: Code Implementation
import java.util.Scanner;
public class Main {
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int T = sc.nextInt(); // Number of test cases
int[][] dp = new int[15][15]; // 15x15 array
// Initialize the DP array
for (int i = 0; i < 15; i++) {
dp[i][1] = 1; // Initialize all apartments on the ground floor
dp[0][i] = i; // Set the number of people on the ground floor
}
// Fill the DP table
for (int i = 1; i < 15; i++) {
for (int j = 2; j < 15; j++) {
dp[i][j] = dp[i - 1][j] + dp[i][j - 1]; // Recurrence relation
}
}
// Process each test case
for (int t = 0; t < T; t++) {
int K = sc.nextInt(); // Floor number
int N = sc.nextInt(); // Apartment number
System.out.println(dp[K][N]); // Print the result
}
sc.close();
}
}
Conclusion
I hope that through this lesson, you have gained a basic understanding of dynamic programming related to solving the “I Will Become the Apartment Manager” problem.
This problem serves as a good example to learn important principles in algorithm design and implementation.
By applying such patterns to various problems, you can solve more complex issues relatively easily.
Practice with more types of problems!