This Java program generates all possible subsets (the power set) of a given array using backtracking

Reference Youtube video:Link This Java program generates all possible subsets (the power set) of a given array using backtracking. Let's break it down step by step. Let given array be [1, 2, 3]. Understanding the Code The program consists of two main functions: subsets(int[] nums): Initializes the result list (list) to store all subsets. Sorts the input array (though sorting is unnecessary in this case). Calls the helper function backtrack() to generate subsets. backtrack(List list, List tempList, int [] nums, int start): Adds the current subset (tempList) to the result list (list). Iterates through the numbers in nums, adding one element at a time to tempList, and recursively explores further subsets. After recursion, removes the last element to backtrack and explore other possibilities. Step-by-Step Execution Let's assume the input is: nums = [1, 2, 3] Step 1: Start Execution subsets(nums) is called with nums = [1, 2, 3] list is initialized as an empty list: list = [] backtrack() is called with: backtrack(list, tempList = [], nums = [1, 2, 3], start = 0) Step 2: First Call to backtrack tempList = [] is added to list list = [[]] For Loop Iteration 1 (i = 0): Add 1 to tempList → tempList = [1] Call backtrack(list, tempList = [1], nums, start = 1) Step 3: Second Call to backtrack tempList = [1] is added to list list = [[], [1]] For Loop Iteration 1 (i = 1): Add 2 to tempList → tempList = [1, 2] Call backtrack(list, tempList = [1, 2], nums, start = 2) Step 4: Third Call to backtrack tempList = [1, 2] is added to list list = [[], [1], [1, 2]] For Loop Iteration 1 (i = 2): Add 3 to tempList → tempList = [1, 2, 3] Call backtrack(list, tempList = [1, 2, 3], nums, start = 3) Step 5: Fourth Call to backtrack tempList = [1, 2, 3] is added to list list = [[], [1], [1, 2], [1, 2, 3]] start = 3 (out of bounds), so the function returns Backtrack: Remove 3 → tempList = [1, 2] Step 6: Backtrack to Third Call Continue loop in Third Call (i = 2 finished) Backtrack: Remove 2 → tempList = [1] For Loop Iteration 2 (i = 2): Add 3 to tempList → tempList = [1, 3] Call backtrack(list, tempList = [1, 3], nums, start = 3) Step 7: Fifth Call to backtrack tempList = [1, 3] is added to list list = [[], [1], [1, 2], [1, 2, 3], [1, 3]] Backtrack: Remove 3 → tempList = [1] Backtrack: Remove 1 → tempList = [] Step 8: Backtrack to Second Call For Loop Iteration 2 (i = 1): Add 2 to tempList → tempList = [2] Call backtrack(list, tempList = [2], nums, start = 2) Step 9: Sixth Call to backtrack tempList = [2] is added to list list = [[], [1], [1, 2], [1, 2, 3], [1, 3], [2]] For Loop Iteration 1 (i = 2): Add 3 to tempList → tempList = [2, 3] Call backtrack(list, tempList = [2, 3], nums, start = 3) Step 10: Seventh Call to backtrack tempList = [2, 3] is added to list list = [[], [1], [1, 2], [1, 2, 3], [1, 3], [2], [2, 3]] Backtrack: Remove 3 → tempList = [2] Backtrack: Remove 2 → tempList = [] Step 11: Backtrack to First Call For Loop Iteration 3 (i = 2): Add 3 to tempList → tempList = [3] Call backtrack(list, tempList = [3], nums, start = 3) Step 12: Eighth Call to backtrack tempList = [3] is added to list list = [[], [1], [1, 2], [1, 2, 3], [1, 3], [2], [2, 3], [3]] Backtrack: Remove 3 → tempList = [] All iterations complete. Return list. Final Output [[], [1], [1, 2], [1, 2, 3], [1, 3], [2], [2, 3], [3]] Key Takeaways Backtracking Approach: We explore subsets recursively, adding and removing elements (backtracking). The tempList is used to build subsets, and each state is stored in list. Time Complexity: O(2^n) → Since each element can either be included or not, we generate 2^n subsets. Space Complexity: O(2^n * n) → Each subset requires space, and there are 2^n subsets, each taking up to O(n) space. Recursive Tree Visualization: The recursive function creates a tree where each level corresponds to choosing or skipping an element. This step-by-step breakdown explains how subsets are generated recursively using backtracking.

nums = [1, 2, 3]

  backtrack(list, tempList = [], nums = [1, 2, 3], start = 0)

[[], [1], [1, 2], [1, 2, 3], [1, 3], [2], [2, 3], [3]]

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