Javascript Coding Test Course, I Will Become the Community Chairperson

Problem Definition

Today’s problem is “I Will Become the Residents’ Association President”. This problem involves calculating the number of people living in a specific unit on a given floor when information about the floor and unit number is provided.

The residents’ association president manages according to the following rules. Each unit has one household living in it, and there is always 1 person living in unit 1 of each floor. Then, the population of each unit is calculated as the sum of the population of the same unit on the floor below and the population of the unit immediately to the left on the floor below.

Problem Description

Input:
– The first input value is the number of test cases T (1 <= T <= 1000).
– Each test case consists of two integers K (0 <= K <= 14) and N (1 <= N <= 14).
– K represents the floor number, and N represents the unit number on that floor.

Output:
For each test case, you need to output the number of people in unit N on floor K.

Example Input and Output

Problem Solving Process

1. Understanding the Combination Function

The key to this problem is calculating the population using dynamic programming. Basically, you use the population of the units on the floor below to compute the current floor’s population. The calculation process is as follows.

Calculation Method

def count_people(K, N):
    if K == 0:
        return N
    if N == 1:
        return 1
    return count_people(K-1, N) + count_people(K, N-1)

2. Progressing Through Loops

Since recursive functions can make the code complex, we will use loops for efficient computation. First, we create a 2D array to store the populations of floor K in advance.

3. Implementation

function countPeople(T, cases) {
    const results = [];
    const dp = Array.from(Array(15), () => Array(15).fill(0));

    for (let i = 0; i <= 14; i++) {
        dp[0][i] = i;  // For the 0th floor, there are i people
    }
    
    for (let k = 1; k <= 14; k++) {
        dp[k][1] = 1;  // For unit 1, there is always 1 person
        for (let n = 2; n <= 14; n++) {
            dp[k][n] = dp[k-1][n] + dp[k][n-1];  // Sum of the number of people in the unit above and the unit on the left
        }
    }

    for (let i = 0; i < T; i++) {
        let k = cases[i][0];
        let n = cases[i][1];
        results.push(dp[k][n]);
    }
  
  return results;
}

const T = 2;
const cases = [[1, 3], [2, 3]];
console.log(countPeople(T, cases)); // Output: [3, 6]

Conclusion

The function we implemented efficiently calculates the number of people for each unit on the specified floor for T test cases. This problem is an excellent example demonstrating the basic concepts of dynamic programming. Proper use of dynamic programming can effectively solve similar types of problems.

Through this algorithm, you can strengthen various aspects of programming while preparing for coding tests. I hope this course enhances your understanding of JavaScript coding tests.