sparse vector in python?

Question

A sparse vector is a vector whose entries are almost all zero, like [1, 0, 0, 0, 0, 0, 0, 2, 0]. Storing all those zeros wastes memory and dictionaries are commonly used to keep track of just the nonzero entries. For example, the vector shown earlier can be represented as {0:1, 7:2}, since the vector it is meant to represent has the value 1 at index 0 and the value 2 at index 7. Write a function that converts a sparse vector into a dictionary as described above.

Examples

>>> convertVector([1, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 0, 4])
{0: 1, 3: 2, 7: 3, 12: 4}
>>> convertVector([1, 0, 1 , 0, 2, 0, 1, 0, 0, 1, 0])
{0: 1, 2: 1, 4: 2, 6: 1, 9: 1}
>>> convertVector([0, 0, 0, 0, 0])
{}

My Code

def convertVector(numbers):
    d = {i: 0 for i in numbers}
    for k, c in enumerate(numbers):
        d[c] = k  # increment its value

    return d
print convertVector([1, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 0, 4])
print convertVector([1, 0, 1 , 0, 2, 0, 1, 0, 0, 1, 0])
print convertVector([0, 0, 0, 0, 0])

Code Returning it as

{0: 11, 1: 0, 2: 3, 3: 7, 4: 12}
{0: 10, 1: 9, 2: 4}
{0: 4}

The problem is it's returning last index, correspond to the value. where as it should return as

   {0: 1, 3: 2, 7: 3, 12: 4}
    {0: 1, 2: 1, 4: 2, 6: 1, 9: 1}
    {}

Any Help?

Answer 1

def convertVector(numbers):
    d = {}
    for k, c in enumerate(numbers):
        if c:
            d[k] = c  
    return d

print convertVector([1, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 0, 4])
print convertVector([1, 0, 1 , 0, 2, 0, 1, 0, 0, 1, 0])
print convertVector([0, 0, 0, 0, 0])

Answer 2

A one liner using conditional dictionary comprehension:

def sparseVector(v): 
    return {n: val for n, val in enumerate(v) if val}

 v1 = [1, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 0, 4]
 v2 = [1, 0, 1 , 0, 2, 0, 1, 0, 0, 1, 0]
 v3 = [0, 0, 0, 0, 0]

 >>> [sparseVector(v) for v in [v1, v2, v3]]
 [{0: 1, 3: 2, 7: 3, 12: 4}, 
  {0: 1, 2: 1, 4: 2, 6: 1, 9: 1}, 
  {}]

if val at the end of the compression means that it will only add the key and value to the dictionary if val does not evaluate to False (i.e. it is not 0, None, etc.).

enumerate(v) goes through an iterable object (e.g. a list) and returns its index value together with the object/value at that location.

n: val adds the value to the dictionary keyed on index value n (only if val is not zero/None).