Combination Sum II

Moderate

0/80

Average time to solve is 30m

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75 upvotes

Asked in companies

Problem statement

You are given an array ‘arr’ of ‘n’ positive integers.

You are also given a positive integer ‘target’.

Your task is to find all unique combinations of elements of array ‘arr’ whose sum is equal to ‘target’. Each number in ‘arr’ may only be used once in the combination.

Elements in each combination must be in non-decreasing order and you need to print all unique combinations in lexicographical order.

Note:

In lexicographical order, combination/array  ‘a’  comes before array ‘b’ if at the first index 'i' where 'a[i]' differs from 'b[i]', 'a[i]' < 'b[i]  or length of 'a' is less than 'b'.

Example:

Input: ‘arr’ = [1, 2, 3, 1], ‘target’ = 5. 

Output: [[1,1,3], [2,3]]

Explanation:
All possible valid combinations with sum = 5 in lexicographical order are -:
(1, 1, 3)
(2, 3)

Detailed explanation ( Input/output format, Notes, Images )

Input Format:

Then the first line of input contains two space-separated integers  ‘n’ and ‘target’ denoting the number of elements in ‘arr’ and the ‘target'.

The second line of input contains 'n' space-separated integers the elements of array ‘arr’.

Output Format:

Print all possible valid combinations in a separate line in the lexicographical order. Elements in each combination must be in non-decreasing order.

Note:

You do not need to print anything, it has already been taken care of. Just implement the given function.

Sample Input 1:

7 8
10 1 2 7 6 1 5

Sample Output 1:

Explanation For Sample Input 1:

Here ‘n’ = 7, 'arr' = [10, 1, 2, 7, 6, 1 , 5], and ‘target’ = 8
All unique combinations whose sum of elements is 8 are -:     

(1, 1, 6)  because, 1 + 1 + 6 = 8
(1, 2, 5)  because,  1 + 2 + 5 = 8
(1, 7)  because, 1 + 7 = 8                                                                                                               
(2, 6)  because,  2 + 6 = 8

Note that, elements in each combination are in non-decreasing order and all unique combinations are arranged in lexicographical order.

Sample Input 2:

5 5
1 2 3 1 5

Sample Output 2:

1 1 3
2 3
5

Expected Time Complexity:

Try to do this in O(2^n).

Constraints:

1 <= n <= 20
1 <= arr[i] <= 30
1 <= target <= 500

Time Limit: 1 sec

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