From the Knapsack DP matrix given above, what is the maximum profit earned when the Capacity = 4 weights available = [2,3,4]
From the Knapsack DP matrix given above, what is the maximum profit earned when the Capacity = 4 weights available = [2,3,4]
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![Knapsack 0/1 problem:
Given N items where each item has some weight and profit associated with it and also given
a bag with capacity W, [i.e., the bag can hold at most W weight in it]. The task is to put the
items into the bag such that the sum of profits associated with them is the maximum
possible.
Given the problem is solved using a dynamic programming approach and the matrix derived
is given below, answer the below set of questions by analyzing the DP matrix.
weights = [2, 3, 4, 5], profits = [1, 2, 5, 6], Capacity W = 8
Capacity
2
3
Profits weights|0
1
2
5
16
14
|->
5
10
0
O
10
1 2 3 4
0 O
0 1 1
0 1
0 1
O
10
1
2 2
2
5
2
O
15
50
1
356
6
O
1
3
6
18
00378
7
10 10
1
3
7
7
1
18](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1942d21f-1f68-402e-935c-586383b38458%2Ff06238d2-408c-42a8-a3b2-d72e4f11ec4d%2Fw3spskh_processed.png&w=3840&q=75)
Transcribed Image Text:Knapsack 0/1 problem:
Given N items where each item has some weight and profit associated with it and also given
a bag with capacity W, [i.e., the bag can hold at most W weight in it]. The task is to put the
items into the bag such that the sum of profits associated with them is the maximum
possible.
Given the problem is solved using a dynamic programming approach and the matrix derived
is given below, answer the below set of questions by analyzing the DP matrix.
weights = [2, 3, 4, 5], profits = [1, 2, 5, 6], Capacity W = 8
Capacity
2
3
Profits weights|0
1
2
5
16
14
|->
5
10
0
O
10
1 2 3 4
0 O
0 1 1
0 1
0 1
O
10
1
2 2
2
5
2
O
15
50
1
356
6
O
1
3
6
18
00378
7
10 10
1
3
7
7
1
18
![From the Knapsack DP matrix given above,
what is the maximum profit earned when
the
Capacity = 4
weights available = [2,3,4]
5
1
8
2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1942d21f-1f68-402e-935c-586383b38458%2Ff06238d2-408c-42a8-a3b2-d72e4f11ec4d%2F7ys2kvi_processed.png&w=3840&q=75)
Transcribed Image Text:From the Knapsack DP matrix given above,
what is the maximum profit earned when
the
Capacity = 4
weights available = [2,3,4]
5
1
8
2
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