Cleaned up knapsack and images directory (#3972)

knapsack/greedy_knapsack.py

@@ -0,0 +1,98 @@
+# To get an insight into Greedy Algorithm through the Knapsack problem
+
+
+"""
+A shopkeeper has bags of wheat that each have different weights and different profits.
+eg.
+profit 5 8 7 1 12 3 4
+weight 2 7 1 6  4 2 5
+max_weight 100
+
+Constraints:
+max_weight > 0
+profit[i] >= 0
+weight[i] >= 0
+Calculate the maximum profit that the shopkeeper can make given maxmum weight that can
+be carried.
+"""
+
+
+def calc_profit(profit: list, weight: list, max_weight: int) -> int:
+    """
+    Function description is as follows-
+    :param profit: Take a list of profits
+    :param weight: Take a list of weight if bags corresponding to the profits
+    :param max_weight: Maximum weight that could be carried
+    :return: Maximum expected gain
+
+    >>> calc_profit([1, 2, 3], [3, 4, 5], 15)
+    6
+    >>> calc_profit([10, 9 , 8], [3 ,4 , 5], 25)
+    27
+    """
+    if len(profit) != len(weight):
+        raise ValueError("The length of profit and weight must be same.")
+    if max_weight <= 0:
+        raise ValueError("max_weight must greater than zero.")
+    if any(p < 0 for p in profit):
+        raise ValueError("Profit can not be negative.")
+    if any(w < 0 for w in weight):
+        raise ValueError("Weight can not be negative.")
+
+    # List created to store profit gained for the 1kg in case of each weight
+    # respectively.  Calculate and append profit/weight for each element.
+    profit_by_weight = [p / w for p, w in zip(profit, weight)]
+
+    # Creating a copy of the list and sorting profit/weight in ascending order
+    sorted_profit_by_weight = sorted(profit_by_weight)
+
+    # declaring useful variables
+    length = len(sorted_profit_by_weight)
+    limit = 0
+    gain = 0
+    i = 0
+
+    # loop till the total weight do not reach max limit e.g. 15 kg and till i<length
+    while limit <= max_weight and i < length:
+        # flag value for encountered greatest element in sorted_profit_by_weight
+        biggest_profit_by_weight = sorted_profit_by_weight[length - i - 1]
+        """
+        Calculate the index of the biggest_profit_by_weight in profit_by_weight list.
+        This will give the index of the first encountered element which is same as of
+        biggest_profit_by_weight.  There may be one or more values same as that of
+        biggest_profit_by_weight but index always encounter the very first element
+        only.  To curb this alter the values in profit_by_weight once they are used
+        here it is done to -1 because neither profit nor weight can be in negative.
+        """
+        index = profit_by_weight.index(biggest_profit_by_weight)
+        profit_by_weight[index] = -1
+
+        # check if the weight encountered is less than the total weight
+        # encountered before.
+        if max_weight - limit >= weight[index]:
+            limit += weight[index]
+            # Adding profit gained for the given weight 1 ===
+            # weight[index]/weight[index]
+            gain += 1 * profit[index]
+        else:
+            # Since the weight encountered is greater than limit, therefore take the
+            # required number of remaining kgs and calculate profit for it.
+            # weight remaining / weight[index]
+            gain += (max_weight - limit) / weight[index] * profit[index]
+            break
+        i += 1
+    return gain
+
+
+if __name__ == "__main__":
+    print(
+        "Input profits, weights, and then max_weight (all positive ints) separated by "
+        "spaces."
+    )
+
+    profit = [int(x) for x in input("Input profits separated by spaces: ").split()]
+    weight = [int(x) for x in input("Input weights separated by spaces: ").split()]
+    max_weight = int(input("Max weight allowed: "))
+
+    # Function Call
+    calc_profit(profit, weight, max_weight)