maximum-non-negative-product-in-a-matrix

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Algorithms

You are given a <code>m x n</code> matrix <code>grid</code>. Initially, you are located at the top-left corner <code>(0, 0)</code>, and in each step, you can only move right or down in the matrix.

Among all possible paths starting from the top-left corner <code>(0, 0)</code> and ending in the bottom-right corner <code>(m - 1, n - 1)</code>, find the path with the maximum non-negative product. The product of a path is the product of all integers in the grid cells visited along the path.

Return the maximum non-negative product modulo <code>109 + 7</code>. If the maximum product is negative, return <code>-1</code>.

Notice that the modulo is performed after getting the maximum product.

&nbsp;
Example 1:
<img alt="" src="https://assets.leetcode.com/uploads/2021/12/23/product1.jpg" style="width: 244px; height: 245px;" />
<pre>
Input: grid = [[-1,-2,-3],[-2,-3,-3],[-3,-3,-2]]
Output: -1
Explanation: It is not possible to get non-negative product in the path from (0, 0) to (2, 2), so return -1.
</pre>

Example 2:
<img alt="" src="https://assets.leetcode.com/uploads/2021/12/23/product2.jpg" style="width: 244px; height: 245px;" />
<pre>
Input: grid = [[1,-2,1],[1,-2,1],[3,-4,1]]
Output: 8
Explanation: Maximum non-negative product is shown (1 * 1 * -2 * -4 * 1 = 8).
</pre>

Example 3:
<img alt="" src="https://assets.leetcode.com/uploads/2021/12/23/product3.jpg" style="width: 164px; height: 165px;" />
<pre>
Input: grid = [[1,3],[0,-4]]
Output: 0
Explanation: Maximum non-negative product is shown (1 * 0 * -4 = 0).
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>m == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 15</code></li>
	<li><code>-4 &lt;= grid[i][j] &lt;= 4</code></li>
</ul>

maxProductPath

Maximum Non Negative Product in a Matrix

Array

Dynamic Programming

Matrix

给你一个大小为 <code>m x n</code> 的矩阵 <code>grid</code> 。最初，你位于左上角 <code>(0, 0)</code> ，每一步，你可以在矩阵中 向右 或 向下 移动。

在从左上角 <code>(0, 0)</code> 开始到右下角 <code>(m - 1, n - 1)</code> 结束的所有路径中，找出具有 最大非负积 的路径。路径的积是沿路径访问的单元格中所有整数的乘积。

返回 最大非负积 对 <code>109&nbsp;+ 7</code> 取余 的结果。如果最大积为 负数 ，则返回 <code>-1</code> 。

注意，取余是在得到最大积之后执行的。

&nbsp;

示例 1：
<img alt="" src="https://assets.leetcode.com/uploads/2021/12/23/product1.jpg" style="width: 244px; height: 245px;" />
<pre>
输入：grid = [[-1,-2,-3],[-2,-3,-3],[-3,-3,-2]]
输出：-1
解释：从 (0, 0) 到 (2, 2) 的路径中无法得到非负积，所以返回 -1 。</pre>

示例 2：
<img alt="" src="https://assets.leetcode.com/uploads/2021/12/23/product2.jpg" style="width: 244px; height: 245px;" />
<pre>
输入：grid = [[1,-2,1],[1,-2,1],[3,-4,1]]
输出：8
解释：最大非负积对应的路径如图所示 (1 * 1 * -2 * -4 * 1 = 8)
</pre>

示例 3：
<img alt="" src="https://assets.leetcode.com/uploads/2021/12/23/product3.jpg" style="width: 164px; height: 165px;" />
<pre>
输入：grid = [[1,3],[0,-4]]
输出：0
解释：最大非负积对应的路径如图所示 (1 * 0 * -4 = 0)
</pre>

&nbsp;

提示：

<ul>
	<li><code>m == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 15</code></li>
	<li><code>-4 &lt;= grid[i][j] &lt;= 4</code></li>
</ul>