Knapsack Problem using Greedy Technique Introduction | Lec 47 | Design & Analysis of Algorithm
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- เผยแพร่เมื่อ 25 ส.ค. 2024
- Kanpsack Problem Definition
Given a Knapsack of capacity C/M and n items of weight {w1, w2, w3,…….wn} and profits {p1, p2, p3,…….pn}, the objective is to choose a subset of n objects that fits into the knapsack and that maximizes the total profit
GREEDY STRATEGY
Select the item with maximum profit that fits into the knapsack
Select the item with minimum weight that fits into the knapsack
Calculate Pi/Wi , select the item with maximum Pi/Wi
Knapsack Problem Design
Consider a knapsack with capacity C or M
Select the items from the list of n items with weight Wi and Profit Pi
Obtain solution such that
Sum of weights must not exceed knapsack capacity C
Optimal selection is object feasible and reaches maximum profit
The optimal solution is feasible object that reaches maximum profit
The problem can be stated as
Maximize ∑_(𝑖=1)^𝑛▒〖𝑃𝑖 𝑋𝑖〗
Subject to ∑_(𝑖=1)^𝑛▒〖𝑊𝑖 𝑋𝑖〗 ≤ C or M
with 0 ≤ 𝑋𝑖 ≤ 1, 1 ≤ 𝑖 ≤ n
The profits & weights are positive numbers
This video explains Definition and steps to solve knapsack problem using Greedy Technique
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