# sparse vector 实现add，dot和cos

```dart
Add these operations to your library: Addition, dot product, and cosine. Formulae for each are provided below; 
we’re more interested in you writing the code than whether you’ve memorized the formula. For each operation, your code should throw an error if the two input vectors are not equal length.
Sample input/output:
//Note: This is pseudocode. Your actual syntax will vary by language.
v1 = new vector(5)
v1[0] = 4.0
v1[1] = 5.0
. from: 1point3acres.com/bbs 
v2 = new vector(5)
v2[1] = 2.0
v2[3] = 3.0. From 1point 3acres bbs

v3 = new vector(2)
print v1.add(v2) //should print [4.0, 7.0, 0.0, 3.0, 0.0]
print v1.add(v3) //error -- vector lengths don’t match

print v1.dot(v2) //should print 10
print v1.dot(v3) //error -- vector lengths don’t match

print v1.cos(v2) //should print 0.433
print v1.cos(v3) //error -- vector lengths don’t match


Formulae:
Addition
a.add(b) = [a[0]+b[0], a[1]+b[1], a[2]+b[2], ...]
Dot product
a.dot(b) = a[0]*b[0] + a[1]*b[1] + a[2]*b[2] + ...

Cosine
a.cos(b) = a.dot(b) / (norm(a) * norm(b))
//norm(a) = sqrt(a[0]^2 + a[1]^2 + a[2]^2 + ...). 
```


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