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1570. Dot Product of Two Sparse Vectors

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Description

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 <= 10^5
• 0 <= nums1[i], nums2[i] <= 100

Solutions

Python3

class SparseVector:
    def __init__(self, nums: List[int]):
        self.v = {}
        for i, num in enumerate(nums):
            if num != 0:
                self.v[i] = num

    # Return the dotProduct of two sparse vectors
    def dotProduct(self, vec: 'SparseVector') -> int:
        res = 0
        if len(self.v) > len(vec.v):
            self.v, vec.v = vec.v, self.v
        for i, num in self.v.items():
            if i not in vec.v:
                continue
            res += num * vec.v[i]
        return res


# Your SparseVector object will be instantiated and called as such:
# v1 = SparseVector(nums1)
# v2 = SparseVector(nums2)
# ans = v1.dotProduct(v2)

Java

class SparseVector {

    private Map<Integer, Integer> v;

    SparseVector(int[] nums) {
        v = new HashMap<>();
        for (int i = 0; i < nums.length; ++i) {
            if (nums[i] != 0) {
                v.put(i, nums[i]);
            }
        }
    }

	// Return the dotProduct of two sparse vectors
    public int dotProduct(SparseVector vec) {
        int res = 0;
        if (v.size() > vec.v.size()) {
            Map<Integer, Integer> t = v;
            v = vec.v;
            vec.v = t;
        }
        for (Map.Entry<Integer, Integer> entry : v.entrySet()) {
            int i = entry.getKey(), num = entry.getValue();
            res += num * vec.v.getOrDefault(i, 0);
        }
        return res;
    }
}

// Your SparseVector object will be instantiated and called as such:
// SparseVector v1 = new SparseVector(nums1);
// SparseVector v2 = new SparseVector(nums2);
// int ans = v1.dotProduct(v2);

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