Combination Sum Ii

# Explanation

1. Problem Understanding :
• You are given a list of integers called
  candidates
  and a target integer called
  target
  .
• The aim is to find all unique combinations in
  candidates
  where the numbers sum up exactly to the
  target
  .
• Each number may be used only once in each combination.
• It is crucial to handle duplicate values in
  candidates
  to avoid generating duplicate combinations in the result.
2. Constraints :
• The length of
  candidates
  can range from 1 to 100.
• Each integer in
  candidates
  can range from 1 to 50.
• The
  target
  value can range from 1 to 30.
3. Approach :
• Sorting : Sort the
  candidates
  list to make it easier to avoid duplicates and to facilitate the "breaking" of loops when a value exceeds the target.
• Backtracking : Use a backtracking approach to build combinations incrementally. This involves:
• Recursive Function : A function that will try to add each candidate to a current combination (path), then recurse to see if a valid combination can be formed.
• Base Case : If the current target becomes zero, the current combination is valid and should be added to the results.
• Skipping Duplicates : When considering a candidate, skip it if it's the same as the previously considered candidate (to avoid duplicates).
Let's start with a very detailed explanation followed by the detailed pseudocode:

# Detailed Steps in Pseudocode

1. Sort the `candidates` list

Sorting helps to streamline the process of skipping duplicates and breaking out of the loop early if a candidate exceeds the target during recursion.

2. Initialize the result list

This will store all the valid combinations found.

3. Define the backtracking function

This function will handle the recursive aspect of exploring potential combinations.
4. Parameters :
• start_index
  : This indicates the current index in
  candidates
  being considered.
• current_path
  : A list keeping track of the current combination being built.
• remaining_target
  : The remaining value needed to reach the target.

4. Base Case

If
remaining_target
is zero, add a copy of the current combination to the result because we've found a valid combination.

5. Iterate over the candidates starting from `start_index`

For each candidate:
5. Check for Duplicates : Skip if the candidate is the same as the previous one to avoid duplicate combinations.
6. Break if Candidate Exceeds Target : If the candidate is greater than the
   remaining_target
   , no point in considering further as the list is sorted.
7. Recursive Call : Add the candidate to the current path and call the backtrack function with updated parameters.

Pseudocode

                                            
function combinationSum2(candidates, target):
# Step 1: Sort the candidates list to handle duplicates and make breaking conditions easier
sort(candidates)

# Step 2: Initialize the result list
result = []

# Step 3: Define the backtracking function
function backtrack(start_index, current_path, remaining_target):
# Step 4: Base Case - If remaining_target is 0, store a copy of current_path in result
if remaining_target == 0:
result.append(copy_of(current_path))
return

# Step 5: Iterate over candidates starting from start_index
for current_index from start_index to length of candidates:
# Skip duplicate candidates to avoid duplicate combinations
if current_index > start_index and candidates[current_index] == candidates[current_index - 1]:
continue

# Break if current candidate exceeds the remaining_target
if candidates[current_index] > remaining_target:
break

# Choose the current candidate by adding it to current_path
current_path.append(candidates[current_index])

# Recur with updated parameters: move to next candidate and reduce the target
backtrack(current_index + 1, current_path, remaining_target - candidates[current_index])

# Un-choose the current candidate to backtrack
current_path.pop()

# Initialize the backtracking with initial parameters
backtrack(0, [], target)

# Step 6: Return the result
return result

                                        

Step-by-Step Explanation

8. Initial Setup :
• Sort the list of candidates.
• Initialize an empty list
  result
  to store the valid combinations.
9. Backtracking Function definition :
• The
  backtrack
  function takes in three parameters:
  start_index
  ,
  current_path
  , and
  remaining_target
  .
• If
  remaining_target
  is zero, it means we have found a valid combination; we make a copy of
  current_path
  and add it to
  result
  .
10. Looping and Conditions :
• We loop through each candidate starting from
  start_index
  .
• Skip duplicates: If the current candidate is the same as the previous one and it's not the first time we are looking at it on this recursive level (i.e.,
  current_index > start_index
  ), continue to the next iteration.
• Stop further exploration if the current candidate exceeds
  remaining_target
  .
• Include the current candidate in
  current_path
  and recurse with updated target.
11. Backtracking :
• After recursive call, remove the last candidate from
  current_path
  to backtrack and explore other possibilities.
12. Returning the Result :
• Finally, return the
  result
  .