# LeetCode 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 _SparseVecto&#x72;_&#x61;nd `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`

## Solution

[English Version in Youtube](https://youtu.be/yzaZJCCjV7M)

[中文版解答Youtube Link](https://youtu.be/Ns_gNGRhGd8)

[中文版解答Bilibili Link](https://www.bilibili.com/video/BV1FZ4y1w7tQ/)

```
class SparseVector {
public:
    
    vector<pair<int, int>> idx_value_pairs;
    
    SparseVector(vector<int> &nums) {
        for (int i = 0; i < nums.size(); i++) {
            if (nums[i] == 0) continue;
            
            idx_value_pairs.push_back({i, nums[i]});
        }
    }
    
    // Return the dotProduct of two sparse vectors
    int dotProduct(SparseVector& vec) {
        int i = 0, j = 0;
        int result = 0;
        
        while (i < idx_value_pairs.size() && j < vec.idx_value_pairs.size()) {
            if (idx_value_pairs[i].first < vec.idx_value_pairs[j].first) {
                i++;
            } else if (idx_value_pairs[i].first > vec.idx_value_pairs[j].first) {
                j++;
            } else {
                result += (idx_value_pairs[i].second * vec.idx_value_pairs[j].second);
                i++;
                j++;
            }
        }
        
        return result;
    }
};

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