Problem Description
The bridge building problem is as follows. The given citizens want to build a bridge from ‘A’ to ‘B’.
This bridge will serve as a road connecting the two points ‘A’ and ‘B’ directly. Each citizen can choose several points to build the bridge,
and the distance between each point is predetermined. The problem is to find the length of the shortest bridge connecting the two points in the city.
Problem Input
– The first line contains the number of points n (1 ≤ n ≤ 1000).
– The second line contains an integer array positions representing the location of each point.
Problem Output
Output the minimum length required to build the bridge.
Example Input
5
1 2 4 5 10
Example Output
9
Solution Process
The first step to solving this problem is to sort the positions of the given points.
The first point in the sorted list represents the location of ‘A’, and the last point represents the location of ‘B’.
This way, it will be easy to calculate the total distance that needs to be traveled to build the bridge.
Step 1: Input and Sorting
function buildBridge(positions) {
// Sort the positions
positions.sort((a, b) => a - b);
return positions;
}
Step 2: Distance Calculation
The next step is to calculate the distance between the first and the last point.
This is the most important factor in determining the length of the bridge.
function calculateBridgeLength(positions) {
const firstPoint = positions[0];
const lastPoint = positions[positions.length - 1];
return lastPoint - firstPoint;
}
Step 3: Complete Function Implementation
Now, finally, we will integrate the two implemented steps to complete the function that calculates the total length needed to build the bridge.
function buildBridge(positions) {
// Sort the positions
positions.sort((a, b) => a - b);
// First and last points
const firstPoint = positions[0];
const lastPoint = positions[positions.length - 1];
// Calculate bridge length
return lastPoint - firstPoint;
}
// Example usage
const inputPositions = [1, 2, 4, 5, 10];
const bridgeLength = buildBridge(inputPositions);
console.log(bridgeLength); // 9
Conclusion
Through this lecture, we practiced how to approach the given problem.
By organizing basic arrays and calculating lengths, we were able to obtain the desired output from the provided input.
This methodology is very useful for solving other algorithmic problems.
Try out more challenging problems in the future!