# 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 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

• class SparseVector {
public Map<Integer, Integer> d = new HashMap<>(128);

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

// Return the dotProduct of two sparse vectors
public int dotProduct(SparseVector vec) {
var a = d;
var b = vec.d;
if (b.size() < a.size()) {
var t = a;
a = b;
b = t;
}
int ans = 0;
for (var e : a.entrySet()) {
int i = e.getKey(), v = e.getValue();
ans += v * b.getOrDefault(i, 0);
}
return ans;
}
}

// 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);

• class SparseVector {
public:
unordered_map<int, int> d;

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

// Return the dotProduct of two sparse vectors
int dotProduct(SparseVector& vec) {
auto a = d;
auto b = vec.d;
if (a.size() > b.size()) {
swap(a, b);
}
int ans = 0;
for (auto& [i, v] : a) {
if (b.count(i)) {
ans += v * b[i];
}
}
return ans;
}
};

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

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

# Return the dotProduct of two sparse vectors
def dotProduct(self, vec: "SparseVector") -> int:
a, b = self.d, vec.d
if len(b) < len(a):
a, b = b, a
return sum(v * b.get(i, 0) for i, v in a.items())

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


• type SparseVector struct {
d map[int]int
}

func Constructor(nums []int) SparseVector {
d := map[int]int{}
for i, x := range nums {
if x != 0 {
d[i] = x
}
}
return SparseVector{d}
}

// Return the dotProduct of two sparse vectors
func (this *SparseVector) dotProduct(vec SparseVector) (ans int) {
a, b := this.d, vec.d
if len(a) > len(b) {
a, b = b, a
}
for i, x := range a {
if y, has := b[i]; has {
ans += x * y
}
}
return
}

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

• class SparseVector {
d: Map<number, number>;

constructor(nums: number[]) {
this.d = new Map();
for (let i = 0; i < nums.length; ++i) {
if (nums[i] != 0) {
this.d.set(i, nums[i]);
}
}
}

// Return the dotProduct of two sparse vectors
dotProduct(vec: SparseVector): number {
let a = this.d;
let b = vec.d;
if (a.size > b.size) {
[a, b] = [b, a];
}
let ans = 0;
for (const [i, x] of a) {
if (b.has(i)) {
ans += x * b.get(i)!;
}
}
return ans;
}
}

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