# 1570 Dot Product of Two Sparse Vectors

Given two sparse vectors, compute their dot product.

Implement class `SparseVector`:

• `SparseVector(nums)` Initializes the object with the vector `nums`
• `dotProduct(vec)` Compute the dot product between the instance of SparseVector and `vec`

A sparse vector is a vector that has mostly zero values, you should store the sparse vector efficiently and compute the dot product between two SparseVector.

Follow up: What if only one of the vectors is sparse?

Example 1:

``````Input: nums1 = [1,0,0,2,3], nums2 = [0,3,0,4,0]
Output: 8
Explanation: v1 = SparseVector(nums1) , v2 = SparseVector(nums2)
v1.dotProduct(v2) = 1*0 + 0*3 + 0*0 + 2*4 + 3*0 = 8
``````

Example 2:

``````Input: nums1 = [0,1,0,0,0], nums2 = [0,0,0,0,2]
Output: 0
Explanation: v1 = SparseVector(nums1) , v2 = SparseVector(nums2)
v1.dotProduct(v2) = 0*0 + 1*0 + 0*0 + 0*0 + 0*2 = 0
``````

Example 3:

``````Input: nums1 = [0,1,0,0,2,0,0], nums2 = [1,0,0,0,3,0,4]
Output: 6
``````

Constraints:

• `n == nums1.length == nums2.length`
• `1 <= n <= 105`
• `0 <= nums1[i], nums2[i] <= 100`
 `````` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 `````` ``````class SparseVector: def __init__(self, nums: List[int]): self.data = {} for i, v in enumerate(nums): if v != 0: self.data[i] = v # Return the dotProduct of two sparse vectors def dotProduct(self, vec: 'SparseVector') -> int: res = 0 for i, v in vec.data.items(): if i in self.data: res += self.data[i] * v return res # Your SparseVector object will be instantiated and called as such: # v1 = SparseVector(nums1) # v2 = SparseVector(nums2) # ans = v1.dotProduct(v2) ''' Without using a hash table ''' class SparseVector: def __init__(self, nums: List[int]): self.pairs = [] for index, value in enumerate(nums): if value != 0: self.pairs.append([index, value]) def dotProduct(self, vec: 'SparseVector') -> int: result = 0 p, q = 0, 0 while p < len(self.pairs) and q < len(vec.pairs): if self.pairs[p][0] == vec.pairs[q][0]: result += self.pairs[p][1] * vec.pairs[q][1] p += 1 q += 1 elif self.pairs[p][0] < vec.pairs[q][0]: p += 1 else: q += 1 return result``````