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en/Greedy Algorithms/Fractional Knapsack.md

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+# Knapsack Problem (Greedy algorithm)
+
+#### Problem Statement
+
+Given a set of items, each with weight and a value, determine the number of each item included in a collection so that the total weight is less than or equal to the given limit and the total value is as large as possible.
+
+##### Greedy method will always provide an optimal solution with fractional knapsack problem.
+
+#### Time Complexity
+
+O(log n) Worst Case     
+O(1) Best Case (If middle element of initial array is the target element)
+
+#### Space Complexity
+
+O(1) For iterative approach          
+O(1) For recursive approach *if tail call optimization is used*, O(log n) due to recursion call stack, otherwise
+
+#### Example
+
+```
+Lets assume the capacity of knapsack, W = 60
+value = [280, 100, 120, 120]  
+weight = [40, 10, 20, 24]
+
+Ratio(V/W) = 7,10,6,5
+Say those items as A,B,C,D
+next, the items should be sorted in descending order based on the ratio of value by weight to get maximum profit
+First and foremost, B was picked since its weight is smaller than the knapsack's capacity. The next item, A, is chosen since the knapsack's available capacity is more than A's weight. C is now the next item on the list. However, the entire item cannot be chosen because the knapsack's remaining capacity is less than C's weight.
+As a result, the C proportion (60–50)/20)
+The knapsack's capacity is now equal to the specified items.
+As a result, no more items can be chosen.
+
+10 + 40 + 20*(10/20) = 60 is the total weight of the chosen goods.
+
+100+280+120*(10/20)=380+60=440 is the total profit.
+
+This is the most suitable option.
+
+We won't be able to make more money by combining diverse things.
+
+```
+
+#### Code Implementation Links
+
+- [C++](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/greedy_algorithms/knapsack.cpp)
+- [Python](https://github.com/TheAlgorithms/Python/tree/master/knapsack)
+- [C-Sharp](https://github.com/TheAlgorithms/C-Sharp/tree/master/Algorithms/Knapsack)
+
+#### Video Explanation
+
+[A CS50 video explaining the Greedy Algorithm](https://www.youtube.com/watch?v=Ou9OA0yQCYA)