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Jesse has broken into a sporting goods store to steal some training equipment. He can only carry out a certain amount of stuff before it gets too heavy. In addition, Jesse can only make one trip in and out of the store before the cops arrive, so he wants to be sure to get the most value out of the stuff he takes. Input for the program will be as below. The first line will contain how much Jesse can carry. This line is followed by a single item per line. Each of these lines will contain the name of the item, the number of items available, each individual item’s weight and its value. There will be up to 10 different items. Output the number of each item type he should take to maximize his value as well as the max value.

Jesse has broken into a sporting goods store to steal some training equipment. He can only carry out a certain amount of stuff before it gets too heavy. In addition, Jesse can only make one trip in and out of the store before the cops arrive, so he wants to be sure to get the most value out of the stuff he takes. Input for the program will be as below. The first line will contain how much Jesse can carry. This line is followed by a single item per line. Each of these lines will contain the name of the item, the number of items available, each individual item’s weight and its value. There will be up to 10 different items. Output the number of each item type he should take to maximize his value as well as the max value.

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C++
Jesse the Body-Building Burglar

Jesse has broken into a sporting goods store to steal some training equipment. He can only carry out a certain amount of stuff before it gets too heavy. In addition, Jesse can only make one trip in and out of the store before the cops arrive, so he wants to be sure to get the most value out of the stuff he takes. Input for the program will be as below. The first line will contain how much Jesse can carry. This line is followed by a single item per line. Each of these lines will contain the name of the item, the number of items available, each individual item’s weight and its value. There will be up to 10 different items. Output the number of each item type he should take to maximize his value as well as the max value.
 
Example File:
100
Barbell 1 25 10
Plate 4 40 12
Ball 5 30 15
Rope 10 5 10
Bench 1 50 20
Output:

10 Rope, 1 Bench 120

Attached file is the JBB dynamic programming
The image displays a spreadsheet with a dynamic programming table used for solving the knapsack problem. Below is a detailed transcription and explanation suitable for an educational website. **Spreadsheet Overview:** The spreadsheet shows a table that helps determine the maximum value achievable within given weight constraints using various items. This is an example of the classic "knapsack problem." **Columns and Rows:** - **Columns A to AH (1 to 34):** Each column from A to E includes item names (Barbell, Plate, Ball, Rope, Bench), weights, and values. - **Column A:** Item Names. - **Columns B to C:** Item weights and values. - Items and corresponding weights and values: - Barbell: Weight 4, Value 25 - Plate: Weight 5, Value 40 - Ball: Weight 3, Value 30 - Rope: Weight 10, Value 50 - Bench: Weight 1, Value 50 - **Columns F to AH:** Corresponds to weight capacities from 0 to 25. **Rows 5 to 26:** - Represent cumulative weight limits available in the knapsack (0 to 21). **Dynamic Programming Table:** - **Row 6 (under weights 0 to 25):** Displays the optimized values that can be accommodated in the knapsack for each weight capacity. - **Values in the Table:** - As you move down the rows and across the columns, values represent the maximum achievable value at each weight capacity and item number. **Description of the Table Evolution:** - In this problem, the goal is to find the maximum value for each weight capacity. - The table populates by deciding whether to include each item in the knapsack or not, updating the cell with the maximum of including or excluding an item as you iterate over rows. **Explanation of Technique:** - The dynamic programming approach uses these cumulative computations to ensure optimal substructure, avoiding redundant calculations and effectively constructing solutions for larger problems based on smaller subproblems. This table is a visual and computational aid for understanding dynamic programming applications in optimization problems, showcasing efficient ways to solve complex decision-making scenarios using computational techniques.
Transcribed Image Text:The image displays a spreadsheet with a dynamic programming table used for solving the knapsack problem. Below is a detailed transcription and explanation suitable for an educational website. **Spreadsheet Overview:** The spreadsheet shows a table that helps determine the maximum value achievable within given weight constraints using various items. This is an example of the classic "knapsack problem." **Columns and Rows:** - **Columns A to AH (1 to 34):** Each column from A to E includes item names (Barbell, Plate, Ball, Rope, Bench), weights, and values. - **Column A:** Item Names. - **Columns B to C:** Item weights and values. - Items and corresponding weights and values: - Barbell: Weight 4, Value 25 - Plate: Weight 5, Value 40 - Ball: Weight 3, Value 30 - Rope: Weight 10, Value 50 - Bench: Weight 1, Value 50 - **Columns F to AH:** Corresponds to weight capacities from 0 to 25. **Rows 5 to 26:** - Represent cumulative weight limits available in the knapsack (0 to 21). **Dynamic Programming Table:** - **Row 6 (under weights 0 to 25):** Displays the optimized values that can be accommodated in the knapsack for each weight capacity. - **Values in the Table:** - As you move down the rows and across the columns, values represent the maximum achievable value at each weight capacity and item number. **Description of the Table Evolution:** - In this problem, the goal is to find the maximum value for each weight capacity. - The table populates by deciding whether to include each item in the knapsack or not, updating the cell with the maximum of including or excluding an item as you iterate over rows. **Explanation of Technique:** - The dynamic programming approach uses these cumulative computations to ensure optimal substructure, avoiding redundant calculations and effectively constructing solutions for larger problems based on smaller subproblems. This table is a visual and computational aid for understanding dynamic programming applications in optimization problems, showcasing efficient ways to solve complex decision-making scenarios using computational techniques.
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