added Fractional Knapsack

Author: minhyeong-joe

Greedy/FractionalKnapsack/README.md

@@ -0,0 +1,25 @@
+# Fractional Knapsack
+
+## Problem:
+
+Given `weights`: list of weights where `weights[i]` represents the weight of `i-th` item,
+`values` : list of values where `values[i]` represents the value of `i-th` item,
+and `capacity`, total weight available,
+Find the maximum values that can be achieved within the limit of total weight.
+
+**Unlike, 0-1 Knapsack Problem, a fraction/portion of an item can be used**
+
+## Example:
+
+```
+weights = [1,2,3]
+values = [6,10,12]
+capacity = 5
+
+Output: 24
+Explanation: Whole of first two items and 2/3 of the last item
+             weight = 1+2+(2/3)*3 = 5
+             value = 6+10+(2/3)*12 = 24
+```
+
+## Note:

Greedy/FractionalKnapsack/solution.py

@@ -0,0 +1,23 @@
+from collections import defaultdict
+
+
+def fractionalKnapsack(weights, values, capacity):
+    maxValue = 0
+    unitValues = defaultdict(int)
+    for i in range(len(weights)):
+        unitValues[values[i]/weights[i]] += weights[i]
+    while capacity:
+        valueToAdd = max(unitValues)
+        weightToAdd = min(capacity, unitValues[valueToAdd])
+        maxValue += valueToAdd * weightToAdd
+        unitValues[valueToAdd] -= weightToAdd
+        if unitValues[valueToAdd] == 0:
+            del unitValues[valueToAdd]
+        capacity -= weightToAdd
+    return maxValue
+
+
+weights = [2, 1, 3]
+values = [10, 6, 12]
+capacity = 5
+print(fractionalKnapsack(weights, values, capacity))

README.md

@@ -86,6 +86,7 @@ Languages used: Java and Python
 
 - [Assign Cookies](Greedy/AssignCookies)
 - [Car Pooling](Greedy/CarPooling)
+- [Fractional Knapsack](Greedy/FractionalKnapsack)
 - [Maximize Sum after K Negations](Greedy/MaximizeSumAfterKNegations)
 - [Maximum Score Words](Greedy/MaximumScoreWords)
 - [Score After Flipping Matrix](Greedy/ScoreAfterFlippingMatrix)