discrete_optimization/knapsack/knapsack.py

from collections import namedtuple

Result = namedtuple("Result", ['objective', 'is_optimal', 'xs'])
Item = namedtuple("Item", ['index', 'value', 'weight'])
Knapsack = namedtuple("Knapsack", ['count', 'capacity', 'items'])
Node = namedtuple("Node", ['index', 'value', 'room', 'estimate', 'path'])


def solve_knapsack_greedy(knapsack):
    remaining_capacity = knapsack.capacity
    current_value = 0
    xs = [0] * knapsack.count

    for item in knapsack.items:
        if remaining_capacity >= item.weight:
            remaining_capacity -= item.weight
            current_value += item.value
            xs[item.index] = 1

    return Result(current_value, 0, xs)


def solve_knapsack_dynamic(knapsack):
    value_column = [0 for _ in range(knapsack.capacity + 1)]
    # Keep track for each item for what capacities we take
    # the respective item. This allows us to backtrack the items
    # for the optimal solution later.
    item_taken = {i: set() for i in range(len(knapsack.items))}

    for item in knapsack.items:
        new_column = list(value_column)
        for capacity in range(knapsack.capacity + 1):
            if item.weight <= capacity:
                # Calculate the new value for the capacity if we take the item.
                new_value = item.value + value_column[capacity - item.weight]
                if new_value > value_column[capacity]:
                    new_column[capacity] = new_value
                    item_taken[item.index].add(capacity)

            # There is no else case because new_colum contains the right values
            # from the previous item so we only have to update when the new
            # value is better.
        value_column = new_column

    objective = value_column[-1]
    # Dynamic programing computes the best posible solution.
    is_optimal = 1

    # Reconstruct which items are used for the optimal solution.
    xs = []
    current_index = knapsack.items[-1].index
    current_capacity = knapsack.capacity
    while current_index >= 0:
        if current_capacity in item_taken[current_index]:
            current_capacity -= knapsack.items[current_index].weight
            xs.append(1)
        else:
            xs.append(0)
        current_index -= 1
    xs.reverse()

    return Result(objective, is_optimal, xs)


def solve_knapsack_depth_first_search(knapsack):
    knapsack.items.sort(key=lambda item: item.value / float(item.weight),
                        reverse=True)

    def get_estimate(current_value, current_index, remaining_capacity):
        estimated_value = current_value
        for item in knapsack.items[current_index:]:
            if item.weight <= remaining_capacity:
                estimated_value += item.value
                remaining_capacity -= item.weight
            else:
                v = int((remaining_capacity / float(item.weight)) * item.value)
                estimated_value += v
                return estimated_value
        return estimated_value

    estimate = get_estimate(0, 0, knapsack.capacity)
    nodes = [Node(0, 0, knapsack.capacity, estimate, [])]
    num_items = len(knapsack.items)
    best_value = 0
    best_path = []

    while nodes:
        current_node = nodes.pop()
        current_index = current_node.index

        if current_node.room < 0:
            continue

        if current_node.estimate < best_value:
            continue

        if current_node.value > best_value:
            best_value = current_node.value
            best_path = list(current_node.path)

        if current_index == num_items:
            continue

        current_item = knapsack.items[current_index]

        # Right child - do not take current_item
        new_index = current_index + 1
        new_value = current_node.value
        new_room = current_node.room
        new_estimate = get_estimate(new_value, new_index, new_room)
        if new_estimate > best_value:
            new_path = current_node.path + [0]
            r = Node(new_index, new_value, new_room, new_estimate, new_path)
            nodes.append(r)

        # Left child - take current_item
        new_index = current_index + 1
        new_room = current_node.room - current_item.weight
        if new_room >= 0:
            new_value = current_node.value + current_item.value
            new_estimate = get_estimate(new_value, new_index, new_room)
            new_path = current_node.path + [1]
            n = Node(new_index, new_value, new_room, new_estimate, new_path)
            nodes.append(n)

        # If we sort the items by estimate here it becomes
        # best first search.
        # nodes.sort(key=lambda node: node.estimate)

    def correct_path(path):
        path = path + [0] * (num_items - len(path))
        values = zip(path, knapsack.items)
        path = [v[0] for v in sorted(values, key=lambda value: value[1].index)]
        return path

    return Result(best_value, 0, correct_path(best_path))


def input_data_to_knapsack(input_data):
    lines = input_data.split('\n')
    item_count, capacity = map(int, lines[0].split())

    items = []
    for i in range(1, item_count + 1):
        line = lines[i]
        value, weight = map(int, line.split())
        items.append(Item(i - 1, value, weight))

    k = Knapsack(item_count, capacity, items)
    return k


def result_to_output_data(result):
    # prepare the solution in the specified output format
    output_data = str(result.objective) + ' ' + str(result.is_optimal) + '\n'
    output_data += ' '.join(map(str, result.xs))
    return output_data


if __name__ == '__main__':
    file_location = "./data/ks_60_0"
    with open(file_location, 'r') as input_data_file:
        input_data = input_data_file.read()
    k = input_data_to_knapsack(input_data)
    print(result_to_output_data(solve_knapsack_dynamic(k)))
    print(result_to_output_data(solve_knapsack_depth_first_search(k)))