You are given a rows x cols matrix grid. Initially, you are located at the top-left corner (0,0) and, in each step, you can only move right or down in the matrix. Among all possible paths starting from the top-left corner (0,0) and ending in the bottom-right corner (rows 1, cols 1), 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 mod 10° +7. If the maximum product is negative, return -1. Note that the modulo is performed after getting the maximum product.
You are given a rows x cols matrix grid. Initially, you are located at the top-left corner (0,0) and, in each step, you can only move right or down in the matrix. Among all possible paths starting from the top-left corner (0,0) and ending in the bottom-right corner (rows 1, cols 1), 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 mod 10° +7. If the maximum product is negative, return -1. Note that the modulo is performed after getting the maximum product.
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Transcribed Image Text:Problem 1> Maximum Non-Negative Product in a Matrix
You are given a rows x cols matrix grid. Initially, you are located at the top-left corner (0,0)
and, in each step, you can only move right or down in the matrix.
Among all possible paths starting from the top-left corner (0,0) and ending in the bottom-right
corner (rows – 1, cols - 1), 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 mod 10° + 7. If the maximum product is negative,
return –1.
Note that the modulo is performed after getting the maximum product.
Example 1
Input:
-2
grid=
-3
-3
-3
-2
Output: -1
Explanation: It's not possible to get non-negative product in the path from (0, 0) to (2, 2), so
return -1.
Transcribed Image Text:Example 2
Input:
2 1
grid
3
1.
Output: 8
Explanation: Maximum non-negative product (in red) is 1.1.-2.-4-1= 8.
Example 3
Input:
ena -
3
grid
Output: 0
Explanation: Maximum non-negative product (in red) is 1.0.-4 = 0.
Example 4
Input:
1
grid
-2
0 1
1
-1
1.
1.
Output: 2
Explanation: Maximum non-negative product (in red) is 1.-2.1.-1-1.1 = 2.
You must solve this using both a bottom-up Dynamic Programming algorithm and a memoized
recursive algorithm.
(a) Pseudocode
• Define the subproblems for your DP solution for finding the maximum non-negative product
value.
• Give a recursive formulation, including the base cases, to solve this problem.
• What is the running time of your solution?
• Write a DP algorithm (give pseudocode) that outputs the maximum non-negative product
value.
• Write a memoized algorithm (give pseudocode) that outputs the maximum non-negative
product value.
(b) Source Code
• Write your solution in Python, C, C++, Java, or JavaScript.
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