Introduction

In this blog post, we will explore how to solve the LeetCode problem "2017" 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 a 0-indexed 2D array grid of size 2 x n, where grid[r][c] represents the number of points at position (r, c) on the matrix. Two robots are playing a game on this matrix. Both robots initially start at (0, 0) and want to reach (1, n-1). Each robot may only move to the right ((r, c) to (r, c + 1)) or down ((r, c) to (r + 1, c)). At the start of the game, the first robot moves from (0, 0) to (1, n-1), collecting all the points from the cells on its path. For all cells (r, c) traversed on the path, grid[r][c] is set to 0. Then, the second robot moves from (0, 0) to (1, n-1), collecting the points on its path. Note that their paths may intersect with one another. The first robot wants to minimize the number of points collected by the second robot. In contrast, the second robot wants to maximize the number of points it collects. If both robots play optimally, return the number of points collected by the second robot. Example 1: Input: grid = [[2,5,4],[1,5,1]] Output: 4 Explanation: The optimal path taken by the first robot is shown in red, and the optimal path taken by the second robot is shown in blue. The cells visited by the first robot are set to 0. The second robot will collect 0 + 0 + 4 + 0 = 4 points. Example 2: Input: grid = [[3,3,1],[8,5,2]] Output: 4 Explanation: The optimal path taken by the first robot is shown in red, and the optimal path taken by the second robot is shown in blue. The cells visited by the first robot are set to 0. The second robot will collect 0 + 3 + 1 + 0 = 4 points. Example 3: Input: grid = [[1,3,1,15],[1,3,3,1]] Output: 7 Explanation: The optimal path taken by the first robot is shown in red, and the optimal path taken by the second robot is shown in blue. The cells visited by the first robot are set to 0. The second robot will collect 0 + 1 + 3 + 3 + 0 = 7 points. Constraints: grid.length == 2 n == grid[r].length 1 <= n <= 5 * 104 1 <= grid[r][c] <= 105

Explanation

Here's the breakdown of the solution:

• Dynamic Programming/Prefix and Suffix Sums: The problem can be efficiently solved using prefix and suffix sums. The first robot wants to minimize the maximum possible score of the second robot. The key idea is to iterate through all possible "split points" where the first robot switches from row 0 to row 1.
• Calculate Maximum Score for Each Split Point: For each split point (column i), calculate the maximum score the second robot can achieve if the first robot switches at that column. This involves calculating the sum of the remaining elements in the first row to the right of column i and the sum of the elements in the second row to the left of column i. The maximum of these two sums represents the maximum score the second robot can achieve.

• Minimize the Maximum Score: The first robot will choose the split point that minimizes the maximum score the second robot can achieve.

• Time Complexity: O(n), where n is the number of columns in the grid.

• Space Complexity: O(1). The solution uses a constant amount of extra space.

Code

    def gridGame(grid):
    n = len(grid[0])

    top_suffix = [0] * n
    bottom_prefix = [0] * n

    top_suffix[n-1] = grid[0][n-1]
    for i in range(n-2, -1, -1):
        top_suffix[i] = top_suffix[i+1] + grid[0][i]

    bottom_prefix[0] = 0
    for i in range(1, n):
        bottom_prefix[i] = bottom_prefix[i-1] + grid[1][i-1]

    ans = float('inf')
    for i in range(n):
        ans = min(ans, max(bottom_prefix[i], top_suffix[i]))

    return ans