Sync LeetCode submission Runtime - 95 ms (63.61%), Memory - 29.7 MB (48.20%)

Author: jimit105

2145-grid-game/README.md

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+<p>You are given a <strong>0-indexed</strong> 2D array <code>grid</code> of size <code>2 x n</code>, where <code>grid[r][c]</code> represents the number of points at position <code>(r, c)</code> on the matrix. Two robots are playing a game on this matrix.</p>
+
+<p>Both robots initially start at <code>(0, 0)</code> and want to reach <code>(1, n-1)</code>. Each robot may only move to the <strong>right</strong> (<code>(r, c)</code> to <code>(r, c + 1)</code>) or <strong>down </strong>(<code>(r, c)</code> to <code>(r + 1, c)</code>).</p>
+
+<p>At the start of the game, the <strong>first</strong> robot moves from <code>(0, 0)</code> to <code>(1, n-1)</code>, collecting all the points from the cells on its path. For all cells <code>(r, c)</code> traversed on the path, <code>grid[r][c]</code> is set to <code>0</code>. Then, the <strong>second</strong> robot moves from <code>(0, 0)</code> to <code>(1, n-1)</code>, collecting the points on its path. Note that their paths may intersect with one another.</p>
+
+<p>The <strong>first</strong> robot wants to <strong>minimize</strong> the number of points collected by the <strong>second</strong> robot. In contrast, the <strong>second </strong>robot wants to <strong>maximize</strong> the number of points it collects. If both robots play <strong>optimally</strong>, return <em>the <b>number of points</b> collected by the <strong>second</strong> robot.</em></p>
+
+<p>&nbsp;</p>
+<p><strong class="example">Example 1:</strong></p>
+<img alt="" src="https://assets.leetcode.com/uploads/2021/09/08/a1.png" style="width: 388px; height: 103px;" />
+<pre>
+<strong>Input:</strong> grid = [[2,5,4],[1,5,1]]
+<strong>Output:</strong> 4
+<strong>Explanation:</strong> 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.
+</pre>
+
+<p><strong class="example">Example 2:</strong></p>
+<img alt="" src="https://assets.leetcode.com/uploads/2021/09/08/a2.png" style="width: 384px; height: 105px;" />
+<pre>
+<strong>Input:</strong> grid = [[3,3,1],[8,5,2]]
+<strong>Output:</strong> 4
+<strong>Explanation:</strong> 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.
+</pre>
+
+<p><strong class="example">Example 3:</strong></p>
+<img alt="" src="https://assets.leetcode.com/uploads/2021/09/08/a3.png" style="width: 493px; height: 103px;" />
+<pre>
+<strong>Input:</strong> grid = [[1,3,1,15],[1,3,3,1]]
+<strong>Output:</strong> 7
+<strong>Explanation: </strong>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.
+</pre>
+
+<p>&nbsp;</p>
+<p><strong>Constraints:</strong></p>
+
+<ul>
+	<li><code>grid.length == 2</code></li>
+	<li><code>n == grid[r].length</code></li>
+	<li><code>1 &lt;= n &lt;= 5 * 10<sup>4</sup></code></li>
+	<li><code>1 &lt;= grid[r][c] &lt;= 10<sup>5</sup></code></li>
+</ul>

2145-grid-game/solution.py

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+# Approach 1: Prefix and Suffix Sum
+
+# Time: O(n)
+# Space: O(1)
+
+class Solution:
+    def gridGame(self, grid: List[List[int]]) -> int:
+        first_row_sum = sum(grid[0])
+        second_row_sum = 0
+        minimum_sum = float('inf')
+
+        for turn_index in range(len(grid[0])):
+            first_row_sum -= grid[0][turn_index]
+            # Find the minimum maximum value out of first_row_sum and second_row_sum.
+            minimum_sum = min(minimum_sum, max(first_row_sum, second_row_sum))
+            second_row_sum += grid[1][turn_index]
+
+        return minimum_sum
+
+