1570. Dot Product of Two Sparse Vectors

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1570. Dot Product of Two Sparse Vectors

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 vectorefficiently and compute the dot product between two SparseVector.

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

Example 1:

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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:

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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:

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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

Hints/Notes

Solution

Language: C++

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class SparseVector {
public:
    vector<pair<int, int>> vals;

    SparseVector(vector<int> &nums) {
        for (int i = 0; i < nums.size(); i++) {
            if (nums[i]) {
                vals.push_back({i, nums[i]});
            }
        }
    }

    // Return the dotProduct of two sparse vectors
    int dotProduct(SparseVector& vec) {
        int res = 0;
        auto vals2 = vec.getValues();
        int m = vals.size(), n = vals2.size(), i = 0, j = 0;
        while (i < m && j < n) {
            if (vals[i].first == vals2[j].first) {
                res += vals[i++].second * vals2[j++].second;
            } else if (vals[i].first > vals2[j].first) {
                j++;
            } else {
                i++;
            }
        }
        return res;
    }

    vector<pair<int, int>> getValues() {
        return vals;
    }
};

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