Problem 1 Greatest Sum Divisible by Three Given an array nuns of Integers, we need to find the maximun possible sum of elements of the array such that it is divisible by three. Hint: try splitting the array into three equvalence classes – the numbers whose remalnder are 0 mod 3, 1 mod 3, and 2 mod 3. Note that if a and b are integers, then (a mod 3 + b mod 3) mod 3 = (a + b) mod 3. In particular, if a mod 3=1 and b mod 3 = 2, then (a + b) mod 3 = 0. Example 1 3,6,5, 1, 8) Input: nuns Output: 18
Problem 1 Greatest Sum Divisible by Three Given an array nuns of Integers, we need to find the maximun possible sum of elements of the array such that it is divisible by three. Hint: try splitting the array into three equvalence classes – the numbers whose remalnder are 0 mod 3, 1 mod 3, and 2 mod 3. Note that if a and b are integers, then (a mod 3 + b mod 3) mod 3 = (a + b) mod 3. In particular, if a mod 3=1 and b mod 3 = 2, then (a + b) mod 3 = 0. Example 1 3,6,5, 1, 8) Input: nuns Output: 18
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![Explarnation: Pick numbers 3, 6, 1 and 8 their sum is 18 (maximum sum divisible by 3).
Example 2
Input: nuns = [4]
Output: 0
Explanation: Since 4 is not divisible by 3, do not plck any umber.
Example 3
Input: nuns = (1,2,3, 4, 4)
Output: 12
Explanatton: Pick numbers 1, 3, 4 and 4 their sum is 12 (maximun sum divisible by 3).
The following must be subrmitted.
(a) Writeup
• Explain your greedy algorithm.
• Provide pseudocode and prove Its correctness.
Determine and prove the runtime of your algorithmn.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F646a794d-e587-473e-a1b8-2a8879d17700%2F7fe38acd-113c-461d-ac99-2c360bf1fd35%2Fodkgnxg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Explarnation: Pick numbers 3, 6, 1 and 8 their sum is 18 (maximum sum divisible by 3).
Example 2
Input: nuns = [4]
Output: 0
Explanation: Since 4 is not divisible by 3, do not plck any umber.
Example 3
Input: nuns = (1,2,3, 4, 4)
Output: 12
Explanatton: Pick numbers 1, 3, 4 and 4 their sum is 12 (maximun sum divisible by 3).
The following must be subrmitted.
(a) Writeup
• Explain your greedy algorithm.
• Provide pseudocode and prove Its correctness.
Determine and prove the runtime of your algorithmn.
![Problem 1 Greatest Sum Divisible by Three
Given an array nuns of Integers, we need to find the maximun possible sum of elements of the
array such that it is divisible by three.
Hint: try splitting the array into three equlvalence classes – the numbers whose
remalnder are 0 mod 3, 1 mod 3, and 2 mod 3.
Note that if a and b are integers, then (a mod 3+5 mod 3) mod 3 = (a+ b) mod 3. In particular,
if a mod 3 = 1 and b mod 3 = 2, then (a +b) mod 3 = 0.
Example 1
(3,6,5, 1,8]
Input: nuns
Output: 18](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F646a794d-e587-473e-a1b8-2a8879d17700%2F7fe38acd-113c-461d-ac99-2c360bf1fd35%2Fg8mj8nl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 1 Greatest Sum Divisible by Three
Given an array nuns of Integers, we need to find the maximun possible sum of elements of the
array such that it is divisible by three.
Hint: try splitting the array into three equlvalence classes – the numbers whose
remalnder are 0 mod 3, 1 mod 3, and 2 mod 3.
Note that if a and b are integers, then (a mod 3+5 mod 3) mod 3 = (a+ b) mod 3. In particular,
if a mod 3 = 1 and b mod 3 = 2, then (a +b) mod 3 = 0.
Example 1
(3,6,5, 1,8]
Input: nuns
Output: 18
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