LeetCode 3235: Check if the Rectangle Corner Is Reachable Solution

Master LeetCode problem 3235 (Check if the Rectangle Corner Is Reachable), a hard challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

3235. Check if the Rectangle Corner Is Reachable

Hard

Array Math Depth-First Search Breadth-First Search Union Find Geometry

Problem Explanation

Explanation

To solve this problem, we need to determine if there exists a path from the bottom left corner to the top right corner of the rectangle that avoids touching or intersecting any circles, while touching only the two corners of the rectangle.

We can approach this problem by considering the four corners of the rectangle and checking if any of them are reachable. If at least one corner is reachable, then a valid path exists. We can use breadth-first search (BFS) to explore all possible paths from the bottom left corner to the top right corner while avoiding the circles.

Algorithm

Create a function isValidPath that takes the rectangle's dimensions and the list of circles as input.
Initialize a set to store visited points to avoid revisiting them.
Perform a BFS starting from the bottom left corner of the rectangle.
At each step, check if the current point is the top right corner of the rectangle. If it is, return true.
Check if the current point is inside any circle or outside the rectangle. If it is, skip to the next step.
Add adjacent points (up, right, down, left) to the queue if they are valid (inside the rectangle and not inside any circle).
Continue the BFS until all possible paths are explored.
If no valid path is found, return false.

Time Complexity

The time complexity of this algorithm is O(n), where n is the total number of points in the rectangle.

Space Complexity

The space complexity of this algorithm is O(n), where n is the total number of points in the rectangle.

Solution Code

import java.util.*;

class Solution {
    public boolean isValidPath(int xCorner, int yCorner, int[][] circles) {
        Set<String> visited = new HashSet<>();
        Queue<int[]> queue = new LinkedList<>();
        queue.offer(new int[]{0, 0});

        while (!queue.isEmpty()) {
            int[] curr = queue.poll();
            int x = curr[0];
            int y = curr[1];

            if (x == xCorner && y == yCorner) {
                return true;
            }

            if (x < 0 || y < 0 || x > xCorner || y > yCorner) {
                continue;
            }

            boolean insideCircle = false;
            for (int[] circle : circles) {
                int cx = circle[0];
                int cy = circle[1];
                int r = circle[2];
                if ((x - cx) * (x - cx) + (y - cy) * (y - cy) <= r * r) {
                    insideCircle = true;
                    break;
                }
            }

            if (insideCircle) {
                continue;
            }

            String key = x + "," + y;
            if (visited.contains(key)) {
                continue;
            }

            visited.add(key);

            queue.offer(new int[]{x + 1, y});
            queue.offer(new int[]{x - 1, y});
            queue.offer(new int[]{x, y + 1});
            queue.offer(new int[]{x, y - 1});
        }

        return false;
    }
}

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