Created
May 1, 2021 00:11
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implementation of knapsack problem exploring the state space in a breadth first search manner and using memoization to reduce the exploration space
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| # Author: Pedro Borges | |
| import heapq | |
| import sys | |
| def knapsack(val, wt, total_w): | |
| elements = transform_to_list_dict(val, wt) | |
| open_list = [] | |
| closed_list = [] | |
| # set to mark the nodes already seen | |
| generated_nodes = set() | |
| open_list.append({'state':[], 'remaining': elements}) | |
| while open_list: | |
| # explore and expand | |
| last_poped_state = explore_and_expand(closed_list, open_list, generated_nodes, total_w) | |
| return -heapq.heappop(closed_list)[0] | |
| def explore_and_expand(closed_list, open_list, generated_nodes, total_w): | |
| state = open_list.pop(0) | |
| # explore | |
| state_weight = sum(i['wt'] for i in state['state']) | |
| state_sum = sum(i['val'] for i in state['state']) if state_weight <= total_w else float('-inf') | |
| heapq.heappush(closed_list, (-state_sum, get_hashable(state))) | |
| #expand | |
| expand(state, open_list, generated_nodes) | |
| return state | |
| def expand(state, open_list, generated_nodes): | |
| for i in range(len(state['remaining'])): | |
| copy_values = state['state'].copy() | |
| # appends the child to the state | |
| copy_values.append(state['remaining'][i]) | |
| # removes the child that was append to the state | |
| copy_children = state['remaining'].copy() | |
| copy_children.pop(i) | |
| # appends to be explored | |
| new_state = {'state':copy_values, 'remaining': copy_children} | |
| if tuple(get_hashable(new_state)) not in generated_nodes: | |
| open_list.append(new_state) | |
| # adds to the set of seen nodes | |
| generated_nodes.add(get_hashable(new_state)) | |
| return None | |
| def transform_to_list_dict(val, wt): | |
| res = [] | |
| for i in range(len(val)): | |
| res.append({'val': val[i], 'wt': wt[i]}) | |
| return res | |
| def get_hashable(state): | |
| vals = tuple([i['val'] for i in state['state']]) | |
| wts = tuple([i['wt'] for i in state['state']]) | |
| return vals, wts | |
| val = [60, 100, 120] | |
| wt = [10, 20, 30] | |
| total_w = 50 | |
| res = knapsack(val, wt, total_w) | |
| res |
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