Today’s problem is “Building a Bridge”. This problem is one of the frequently asked types in coding interviews, where the goal is to find the optimal solution based on the given information.<\/p>\n
Let’s assume a city needs a bridge with really high stairs. This bridge must be located between two beaches (left and right) and must meet specific requirements.<\/p>\n
Return the maximum height of the bridge. In other words, you need to output the minimum height at all areas where the bridge passes.<\/p>\n
\n n = 5\n height = [5, 3, 6, 2, 4]\n <\/pre>\nOutput Example<\/h4>\n
\n 3\n <\/pre>\nExplanation: The maximum height that can be swum to build the bridge is 3. This is because the second area from the left, Height[1], is 3.<\/p>\n
Problem Solving Process<\/h2>\n
Step 1: Understand the Problem<\/h3>\n
This problem requires finding the position of the highest bridge to be built. The height of the bridge is restricted by the heights of each regional area. Therefore, the height of the bridge is limited to the minimum of all the higher areas.<\/p>\n
Step 2: Design an Approach to the Problem<\/h3>\n
The approach to solving the problem is simply to find the minimum value of the array. The height of the bridge is determined by the lowest height at each section of the bridge. To achieve this, follow these steps:<\/p>\n
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- Find the minimum value in the given array.<\/li>\n
- Set the found minimum value as the maximum height of the bridge.<\/li>\n
- Return the result.<\/li>\n<\/ol>\n
Step 3: Write Java Code<\/h3>\n
Now, let’s solve the problem with Java code. We will write a simple program to find the optimal height of the bridge.<\/p>\n
\n import java.util.Arrays;\n\n public class BridgeBuilder {\n public static void main(String[] args) {\n int n = 5;\n int[] height = {5, 3, 6, 2, 4};\n int maxBridgeHeight = findMaxBridgeHeight(height);\n System.out.println(\"The maximum height of the bridge is: \" + maxBridgeHeight);\n }\n\n public static int findMaxBridgeHeight(int[] height) {\n \/\/ Find the minimum value in the height array\n return Arrays.stream(height).min().orElse(Integer.MAX_VALUE);\n }\n }\n <\/pre>\nStep 4: Explain the Code<\/h3>\n
The code above demonstrates a simple logic to calculate the maximum height of the bridge based on the heights of the given beaches.<\/p>\n
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- First, we import the
java.util.Arrays<\/code> package to easily handle the array.<\/li>\n- We create a method called
findMaxBridgeHeight<\/code> that returns the minimum value of the given height array.<\/li>\n- To find the minimum value, we used Java 8’s
Stream API<\/code> to create concise code.<\/li>\n<\/ul>\nStep 5: Analyze Time Complexity<\/h3>\n
The time complexity of this algorithm is O(n), because we need to check all the elements in the array to find the minimum value. This method is efficient and practical as long as the input size (n) does not become extremely large.<\/p>\n
Conclusion<\/h2>\n
The bridge-building problem can be understood simply as a process of finding the minimum value of an array. This approach is very useful for solving algorithmic problems and is commonly used when dealing with data such as arrays or lists. It teaches us techniques that can be applied to various problems.<\/p>\n
Additional Exercise Problems<\/h3>\n