Finding all subsets of a list of positive integers using backtracking

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The discussion centers on a Python 3 solution for generating all subsets of a list of integers using backtracking. The provided code defines a `backtrack` function that recursively builds subsets by appending the current subset to a results list (`ans`) and iterating through the input list (`nums`). The function takes three parameters: the list of numbers, the starting index for iteration, and the current subset being constructed. The `subsets` function initiates the backtracking process by calling `backtrack` with the starting index set to 0 and an empty current subset. The output for the input list [1, 2, 3] is all possible subsets, including the empty set. To better understand the backtracking mechanism, users are encouraged to trace the code execution line by line, use print statements for debugging, or utilize debugging tools in an IDE. Additional resources, such as examples from Rosetta Code, are suggested for further learning about generating power sets in Python.
Andrew1235
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The following Python 3 code is provided as the solution to this problem (https://leetcode.com/problems/subsets/solution/) that asks to find all subsets of a list of integers. For example, for the list below the output is [[], [1], [1, 2], [1, 2, 3], [1, 3], [2], [2, 3], [3]].

I am not familiar with backtracking. Can someone explain how the code works?

alist = [1,2,3]

ans = []

def backtrack(nums, start, curr):

ans.append(curr)

for i in range(start, len(nums)):

backtrack(nums, i+1, curr + [nums])

def subsets(nums):
backtrack(nums, 0, [])
return ans

print(subsets(alist))
 
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Andrew1235 said:
The following Python 3 code is provided as the solution to this problem (https://leetcode.com/problems/subsets/solution/) that asks to find all subsets of a list of integers. For example, for the list below the output is [[], [1], [1, 2], [1, 2, 3], [1, 3], [2], [2, 3], [3]].

I am not familiar with backtracking. Can someone explain how the code works?

Python:
alist = [1,2,3]

ans = []

def backtrack(nums, start, curr):
 
    ans.append(curr) 
    
    for i in range(start, len(nums)):
 
        backtrack(nums, i+1, curr + [nums[i]])

def subsets(nums):     
    backtrack(nums, 0, [])
    return ans
   
print(subsets(alist))
You need to put
Python:
[/color] before your code and
[/color] afterwards if you want it to be readable.

Python:
alist = [1,2,3]
ans = []

def backtrack(nums, start, curr): 
    ans.append(curr)     
    for i in range(start, len(nums)): 
        backtrack(nums, i+1, curr + [nums[i]])

def subsets(nums):     
    backtrack(nums, 0, [])
    return ans
   
print(subsets(alist))
 
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Andrew1235 said:
I am not familiar with backtracking. Can someone explain how the code works?
The best (only?) way to understand it is to work through it line by line. You can do this on paper, or by inserting print statements in the code, or by using the 'watch' facitilty of an IDE and stepping through the code.
 
What pbuk said. At the very least, adding
Python:
print("backtrack called with)
print(" nums =",nums)
print(" start =",start)
print(" curr =",curr)
to the beginning of the backtrack function will show you how it's working through the data. First run it with a two element list, then a three element list, etcetera.
 
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