Programming Assignment 3 COSC 3320 Algorithms and Data Structures


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Programming Assignment 3
COSC 3320
Algorithms and Data Structures

Academic Honesty Policy
All submitted work should be your own. Copying or using other people’s work (including from the
Web) will result in −MAX points, where MAX is the maximum possible number of points for that
assignment. Repeat offenses will result in a failing grade for the course and will be reported to the
Chair. If you have any questions, please reach out to the professor and the TAs. The best way to
ask is on Piazza.
By submitting this assignment, you affirm that you have followed the Academic Honesty Policy.
The writeup portion of your submission must be typed. We prefer you use LATEX to type your
solutions — LATEX is the standard way to type works in mathematical sciences, like computer science, and
is highly recommended; for more information on using LATEX, please see this post on Piazza — but any
method of typing your solutions (e.g., MS Word, Google Docs, Markdown) is acceptable. Your writeup
must be in pdf format. The assignment can be submitted up to two days late for a penalty of
10% per day. A submission more than two days late will receive a zero.
Before you begin the assignment, create an account on LeetCode if you do not already have one.
Problem 1 I Maximum Non-Negative Product in a Matrix
You are given a rows × 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 109 + 7. If the maximum product is negative,
return −1.
Note that the modulo is performed after getting the maximum product.
Example 1
grid =

−1 −2 −3
−2 −3 −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
grid =

1 −2 1
1 −2 1
3 −4 1

Output: 8
Explanation: Maximum non-negative product (in red) is 1 · 1 · −2 · −4 · 1 = 8.
Example 3
grid =

1 3
0 −4

Output: 0
Explanation: Maximum non-negative product (in red) is 1 · 0 · −4 = 0.
Example 4
grid =

1 4 4 0
−2 0 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. Note that some solutions posted on LeetCodee may also be. In any case, a solution
that is largely copied from another source (e.g., verbatim or made to look different by simply changing
variable names) will be in violation of the Academic Honesty Policy.
The following must be submitted.
(a) Writeup (50 Points)
• Define the subproblems for your DP solution for finding the maximum non-negative product
• 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
• Write a memoized algorithm (give pseudocode) that outputs the maximum non-negative
product value.
(b) Source Code (50 Points)
• Write your solution in Python, C, C++, Java, or JavaScript.
• Your code should be well written and well commented.
• A comment with a link to your LeetCode profile (e.g.,
and a statement of whether or not your code was accepted by LeetCode. We will verify whether
your code is accepted.
• We must be able to directly copy and paste your code into LeetCode at the LeetCode problem
page. If your code does not compile on LeetCode, it will will receive zero points. Under
no circumstances will we attempt to modify any submission, so be sure the code you submit
• Submit two files – one with the bottom-up Dynamic Programming solution and one with the
recursive memoized solution.
Please submit these files individually. Do not submit as an archived file (zip file, tarball, etc.).
1 Pseudocode and Explanation
Algorithm 1 Max-Prod-DP
1: def Max-Prod-DP(grid):
Algorithm 2 Max-Prod-Rec
1: def Max-Prod-Rec(grid):
2 Analysis

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