0/1 Knapsack Problem to print all possible solutions

Given weights and profits of N items, put these items in a knapsack of capacity W. The task is to print all possible solutions to the problem in such a way that there are no remaining items left whose weight is less than the remaining capacity of the knapsack. Also, compute the maximum profit.
Examples: 

Input: Profits[] = {60, 100, 120, 50} 
Weights[] = {10, 20, 30, 40}, W = 40 
Output: 
10: 60, 20: 100, 
10: 60, 30: 120, 
Maximum Profit = 180 
Explanation: 
Maximum profit from all the possible solutions is 180
Input: Profits[] = {60, 100, 120, 50} 
Weights[] = {10, 20, 30, 40}, W = 50 
Output: 
10: 60, 20: 100, 
10: 60, 30: 120, 
20: 100, 30: 120, 
Maximum Profit = 220 
Explanation: 
Maximum profit from all the possible solutions is 220 

Approach: The idea is to make pairs for the weight and the profits of the items and then try out all permutations of the array and including the weights until their is no such item whose weight is less than the remaining capacity of the knapsack. Meanwhile after including an item increment the profit for that solution by the profit of that item. 

Below is the implementation of the above approach:

10: 60, 20: 100, 
10: 60, 30: 120, 
20: 100, 30: 120, 
Maximum Profit = 220

Time complexity : O(N! * N), where N is the number of items. The code uses permutation to generate all possible combinations of items and then performs a search operation to find the optimal solution. 

Space complexity : O(N), as the code uses a map and set to store the solution, which has a maximum size of N.