algorithm Greedy Algorithms Continuous knapsack problem
Example
Given items as (value, weight) we need to place them in a knapsack (container) of a capacity k. Note! We can break items to maximize value!
Example input:
values[] = [1, 4, 5, 2, 10]
weights[] = [3, 2, 1, 2, 4]
k = 8
Expected output:
maximumValueOfItemsInK = 20;
Algorithm:
1) Sort values and weights by value/weight.
values[] = [5, 10, 4, 2, 1]
weights[] = [1, 4, 2, 2, 3]
2) currentWeight = 0; currentValue = 0;
3) FOR i = 0; currentWeight < k && i < values.length; i++ DO:
IF k - currentWeight < weights[i] DO
currentValue = currentValue + values[i];
currentWeight = currentWeight + weights[i];
ELSE
currentValue = currentValue + values[i]*(k - currentWeight)/weights[i]
currentWeight = currentWeight + weights[i]*(k - currentWeight)/weights[i]
END_IF
END_FOR
PRINT "maximumValueOfItemsInK = " + currentValue;
