Non-Adjacent Combination Sum - Amazon Top Interview Questions


Problem Statement :


You are given a list of positive integers nums and an integer k. Return whether there exists a combination of integers in nums such that their sum is k and none of those elements are adjacent in the original list.

Constraints

n * k ≤ 100,000 where n is the length of nums

Example 1

Input

nums = [1, 2, 2, 3]
k = 4

Output

True

Explanation

We can pick [1, 3] since they are non-adjacent and sums to 4

Example 2

Input

nums = [1, 3, 1]
k = 4

Output

False

Explanation

We can't pick [1, 3] or [3, 1] since they are adjacent.


Solution :



title-img 




                        Solution in C++ :

bool solve(vector<int>& nums, int k) {
    if (k == 0) return true;
    bitset<100005> has, nohas;
    nohas.set(0);
    for (int num : nums) {
        bitset<100005> nhas, nnohas;
        nhas = (nohas << num);
        if (nhas[k]) return true;
        nnohas = (has | nohas);
        has = nhas;
        nohas = nnohas;
    }
    return false;
}
                    




                        Solution in Python : 
                            
class Solution:
    def solve(self, nums, k):
        @lru_cache(None)
        def f(total, idx):
            if total > k:
                return False
            if total == k:
                return True
            if idx >= len(nums):
                return False

            return f(total + nums[idx], idx + 2) or f(total, idx + 1)

        return f(0, 0)


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