Information is present in the screenshot and below. Based on that need help in solving the code for this problem in python. The time complexity has to be as less as possible. Apply dynamic programming and memoization. Do not use recursion. Make sure ALL test cases return expected outputs.Hint: Approach the problem with 2D Dynamic Programming.Output FormatOutput one line containing a single integer containing the answer as described in the problem statement. This number must be output mod 109 + 7.Sample Input 0:3 9357Sample Output 0:5Sample Input 1:3 23151615Sample Output 1:4Sample Input 2:3 6123Sample Output 2:8The actual code:def solve(n,c,ws): # compute and return answer here # place 2 nested for loops here MOD = 1000000007n, c = list(map(int,input().rstrip().split(" ")))ws = [int(input().rstrip()) for i in range(n)]print(solve(n,c,ws)) This problem is simple. You have N items numbered 1 to N. Each item has a weight Wį.But wait, you might be wondering why the items don't have values. Well, that's becausethis isn't your normal knapsack. This is an even more basic knapsack. There's no need toworry about values, because you will be given the capacity of your knapsack. Instead ofmaximizing a value, just count how many ways you can fill your knapsack withoutexceeding capacity.For example, if you have 3 items with weights 3, 5, and 7 and your knapsack has acapacity 9, there are 5 ways to fill the knapsack as follows:Empty knapsack●• 3• 5• 7• 3 + 5This number may be very large, so print it mod 10⁹ +7.Input FormatInput contains a single test case starting with a line containing two space-separatedintegers N and C, indicating the number of items and knapsack capacity respectively.N lines follow, the ith containing a single integer Wi, the weight of the ith line.Constraints1 ≤N, W; ≤ 2.10³i0≤ C≤2·10³

To solve this problem, we can use a dynamic programming approach. We can define a 2D array dp[i][j]…

Answered: This problem is simple. You have N…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Information is present in the screenshot and below. Based on that need help in solving the code for this problem in python. The time complexity has to be as less as possible. Apply dynamic programming and memoization. Do not use recursion. Make sure ALL test cases return expected outputs.

Hint: Approach the problem with 2D Dynamic Programming.

Output Format
Output one line containing a single integer containing the answer as described in the problem statement. This number must be output mod 10⁹+ 7.

Sample Input 0:
3 9
3
5
7

Sample Output 0:
5

Sample Input 1:
3 23
15
16
15

Sample Output 1:
4

Sample Input 2:
3 6
1
2
3

Sample Output 2:
8

The actual code:

def solve(n,c,ws):
# compute and return answer here

# place 2 nested for loops here

MOD = 1000000007
n, c = list(map(int,input().rstrip().split(" ")))
ws = [int(input().rstrip()) for i in range(n)]
print(solve(n,c,ws))

This problem is simple. You have N items numbered 1 to N. Each item has a weight Wį.
But wait, you might be wondering why the items don't have values. Well, that's because
this isn't your normal knapsack. This is an even more basic knapsack. There's no need to
worry about values, because you will be given the capacity of your knapsack. Instead of
maximizing a value, just count how many ways you can fill your knapsack without
exceeding capacity.
For example, if you have 3 items with weights 3, 5, and 7 and your knapsack has a
capacity 9, there are 5 ways to fill the knapsack as follows:
Empty knapsack
●
• 3
• 5
• 7
• 3 + 5
This number may be very large, so print it mod 10⁹ +7.
Input Format
Input contains a single test case starting with a line containing two space-separated
integers N and C, indicating the number of items and knapsack capacity respectively.
N lines follow, the ith containing a single integer Wi, the weight of the ith line.
Constraints
1 ≤N, W; ≤ 2.10³
i
0≤ C≤2·10³

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