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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.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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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: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.
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.
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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