JavaScript Coding Test Course, Bridge Building

In this article, we will deal with the Bridge Building problem, which is one of the coding test problems using JavaScript. This problem utilizes the concept of combinations and has many applications. We will examine the problem definition, various approaches, and the solution process in great detail.

Problem Definition

Problem: There are two islands in a river. We want to build a bridge between the two islands. Given that we can build N bridges, we need to determine how many different ways we can construct these bridges. However, the bridges must not interfere with each other, and there are designated positions for the bridges on each island.

Example Input/Output

• Input: N = 3
• Output: 5 (the number of ways to build the bridges)

Problem Analysis

This problem serves as a foundation for understanding the properties of combinations. The positions of the bridges must be placed at fixed positions on the two islands, so the selection of bridges must not interfere with each other. We will refer to the two islands where the bridges will be placed as A and B. The positions for placing bridges on each island can be represented by indices starting from 0.

Approach

There are various approaches to solving combination problems. In the case of this problem, it is advisable to use the Dynamic Programming method. First, we will set basic situations as needed and develop more complex situations based on those.

Dynamic Programming Approach

To solve the bridge building problem using dynamic programming, we can set up the following recurrence relation:

count(N) = count(N-1) + count(N-2)

Here, count(N) represents the number of ways to place N bridges. The meaning of this equation is as follows:

• In the case of placing N-1 bridges, adding the last bridge (only one bridge is added).
• In the case of already placing N-2 bridges, adding two new bridges.

Algorithm Implementation

Now, based on the above recurrence relation, let’s implement the algorithm in JavaScript. Here is an example of the function:

function countWays(n) {
    if (n === 0) return 1; // Base case: not placing any bridges
    if (n === 1) return 1; // Base case: placing one bridge

    let dp = new Array(n + 1);
    dp[0] = 1;
    dp[1] = 1;

    for (let i = 2; i <= n; i++) {
        dp[i] = dp[i - 1] + dp[i - 2];
    }

    return dp[n];
}
    
let n = 3;
console.log(countWays(n)); // Result: 5
    

Code Explanation

The above function works through the following steps:

• If n is 0, it returns 1 to handle the base case.
• If n is 1, it also returns 1 to handle the case of placing only one bridge.
• Then, it initializes the array dp based on the number of bridges, and uses the recurrence relation to calculate the number of ways to place the bridges.

Time Complexity

The time complexity of this algorithm is O(N). This is because it calculates the result by traversing the array once. The space complexity is also O(N) since an array is used to store the number of ways depending on the number of bridges.

Conclusion

Through this tutorial, we have learned how to solve the bridge building problem using JavaScript. This problem greatly aids in understanding the concept of combinations and optimization approaches using dynamic programming. We hope to expand basic programming skills and develop the ability to utilize various algorithms through such problems. We look forward to solving more algorithm problems together in the future!