Introduction

In this blog post, we will explore how to solve the LeetCode problem "3394" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

You are given an integer n representing the dimensions of an n x n grid, with the origin at the bottom-left corner of the grid. You are also given a 2D array of coordinates rectangles, where rectangles[i] is in the form [startx, starty, endx, endy], representing a rectangle on the grid. Each rectangle is defined as follows: (startx, starty): The bottom-left corner of the rectangle. (endx, endy): The top-right corner of the rectangle. Note that the rectangles do not overlap. Your task is to determine if it is possible to make either two horizontal or two vertical cuts on the grid such that: Each of the three resulting sections formed by the cuts contains at least one rectangle. Every rectangle belongs to exactly one section. Return true if such cuts can be made; otherwise, return false. Example 1: Input: n = 5, rectangles = [[1,0,5,2],[0,2,2,4],[3,2,5,3],[0,4,4,5]] Output: true Explanation: The grid is shown in the diagram. We can make horizontal cuts at y = 2 and y = 4. Hence, output is true. Example 2: Input: n = 4, rectangles = [[0,0,1,1],[2,0,3,4],[0,2,2,3],[3,0,4,3]] Output: true Explanation: We can make vertical cuts at x = 2 and x = 3. Hence, output is true. Example 3: Input: n = 4, rectangles = [[0,2,2,4],[1,0,3,2],[2,2,3,4],[3,0,4,2],[3,2,4,4]] Output: false Explanation: We cannot make two horizontal or two vertical cuts that satisfy the conditions. Hence, output is false. Constraints: 3 <= n <= 109 3 <= rectangles.length <= 105 0 <= rectangles[i][0] < rectangles[i][2] <= n 0 <= rectangles[i][1] < rectangles[i][3] <= n No two rectangles overlap.

Explanation

Here's a breakdown of the solution approach:

• Iterate through possible cut locations: The core idea is to try all possible pairs of horizontal and vertical cut locations. Since the problem statement specifies two cuts, we need to iterate through all possible pairs of cut lines.
• Check if cuts are valid: For each pair of cuts, we check if the cuts are valid based on the problem constraints, i.e., if each of the three resulting sections contains at least one rectangle and every rectangle belongs to exactly one section.

• Early exit: If we find a valid pair of cuts, we immediately return True. Otherwise, after exhausting all possible cut locations, we return False.

• Runtime Complexity: O(R*N^2) where R is the number of rectangles and N is the dimension of the grid. Storage Complexity: O(1)

Code

    def solve():
    n, rectangles = read_input()
    if find_cuts(n, rectangles):
        return True
    else:
        return False

def read_input():
    n = int(input())
    rectangles_str = input().strip('[]').split('],[')
    rectangles = []
    for rect_str in rectangles_str:
        rect = list(map(int, rect_str.split(',')))
        rectangles.append(rect)
    return n, rectangles

def find_cuts(n, rectangles):
    # Check for horizontal cuts
    for y1 in range(1, n):
        for y2 in range(y1 + 1, n):
            if is_valid_horizontal_cuts(n, rectangles, y1, y2):
                return True

    # Check for vertical cuts
    for x1 in range(1, n):
        for x2 in range(x1 + 1, n):
            if is_valid_vertical_cuts(n, rectangles, x1, x2):
                return True

    return False

def is_valid_horizontal_cuts(n, rectangles, y1, y2):
    zones = [[] for _ in range(3)]

    for rect in rectangles:
        start_x, start_y, end_x, end_y = rect

        if end_y <= y1:
            zones[0].append(rect)
        elif end_y <= y2:
            zones[1].append(rect)
        else:
            zones[2].append(rect)

    if any(not zone for zone in zones):
        return False

    total_rects = sum(len(zone) for zone in zones)
    return total_rects == len(rectangles)

def is_valid_vertical_cuts(n, rectangles, x1, x2):
    zones = [[] for _ in range(3)]

    for rect in rectangles:
        start_x, start_y, end_x, end_y = rect

        if end_x <= x1:
            zones[0].append(rect)
        elif end_x <= x2:
            zones[1].append(rect)
        else:
            zones[2].append(rect)

    if any(not zone for zone in zones):
        return False

    total_rects = sum(len(zone) for zone in zones)
    return total_rects == len(rectangles)

def solve_optimized(n, rectangles):
    def check_cuts(cuts, horizontal):
        for i in range(len(cuts)):
            for j in range(i + 1, len(cuts)):
                zones = [[] for _ in range(3)]
                for rect in rectangles:
                    sx, sy, ex, ey = rect
                    if horizontal:
                        val = ey
                        c1 = cuts[i]
                        c2 = cuts[j]

                    else:
                        val = ex
                        c1 = cuts[i]
                        c2 = cuts[j]

                    if val <= c1:
                        zones[0].append(rect)
                    elif val <= c2:
                        zones[1].append(rect)
                    else:
                        zones[2].append(rect)

                if all(zones):
                    return True
        return False

    xs = sorted(list(set([rect[2] for rect in rectangles])))
    ys = sorted(list(set([rect[3] for rect in rectangles])))

    if check_cuts(xs, False):
        return True
    if check_cuts(ys, True):
        return True
    return False


# Example Usage (for testing locally):
#n = 5
#rectangles = [[1,0,5,2],[0,2,2,4],[3,2,5,3],[0,4,4,5]]
#print(solve_optimized(n, rectangles))  # Output: True

#n = 4
#rectangles = [[0,0,1,1],[2,0,3,4],[0,2,2,3],[3,0,4,3]]
#print(solve_optimized(n, rectangles))  # Output: True

#n = 4
#rectangles = [[0,2,2,4],[1,0,3,2],[2,2,3,4],[3,0,4,2],[3,2,4,4]]
#print(solve_optimized(n, rectangles))  # Output: False


def main():
    n = int(input())
    rectangles = []
    rectangles_str = input().strip("[]").split("],[")
    for rect_str in rectangles_str:
        rect = list(map(int, rect_str.split(",")))
        rectangles.append(rect)
    print(solve_optimized(n, rectangles))

if __name__ == "__main__":
    main()