# How to store a Sparse Vector efficiently?

A sparse vector is a vector that has a large number of zeros so it takes unwanted space to store this zeroes.

The task is to store a given sparse vector efficiently without storing the zeros.

Examples:

```Input: vector = { 2, 0, 0, 0, 0,
3, 0, 4, 0, 0,
0, 1, 5, 0, 0,
0, 0, 0, 0, 0,
0, 0, 4, 0, 0,
0, 2, 0, 0, 0,
0, 0, 0, 3, 0,
0, 0, 1, 0, 0,
0, 0, 5 }
Output: {2, 3, 4, 1, 5,
4, 2, 3, 1, 5}
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach:
To store the sparse vector efficiently, a vector of pairs can be used. The First element of pair will be the index of spare vector element(which is non-zero) and the second element will be the actual element.

Below is the implementation of the above approach:

## C++

 `// C++ program to store sparse vectors ` `// with the help of vector of pair ` ` `  `#include ` `using` `namespace` `std; ` ` `  `// Store the sparse vector ` `// as a vector of pairs ` `vector > ` `convertSparseVector(vector<``int``> v) ` `{ ` `    ``vector > res; ` `    ``for` `(``int` `i = 0; i < v.size(); i++) { ` `        ``if` `(v[i] != 0) { ` `            ``res.push_back(make_pair(i, v[i])); ` `        ``} ` `    ``} ` `    ``return` `res; ` `} ` ` `  `// Print the vector of pairs ` `void` `print(vector > res) ` `{ ` ` `  `    ``for` `(``auto` `x : res) { ` `        ``cout << ``"index: "` `<< x.first ` `             ``<< ``" -> value: "` `             ``<< x.second << endl; ` `    ``} ` `} ` ` `  `// Driver function ` `int` `main() ` `{ ` ` `  `    ``// Get the sparse vector ` `    ``vector<``int``> v{ 2, 0, 0, 0, 0, ` `                   ``3, 0, 4, 0, 0, ` `                   ``0, 1, 5, 0, 0, ` `                   ``0, 0, 0, 0, 0, ` `                   ``0, 0, 4, 0, 0, ` `                   ``0, 2, 0, 0, 0, ` `                   ``0, 0, 0, 3, 0, ` `                   ``0, 0, 1, 0, 0, ` `                   ``0, 0, 5 }; ` ` `  `    ``// Get the stored vector of pairs ` `    ``vector > res ` `        ``= convertSparseVector(v); ` ` `  `    ``// Print the vector of pairs ` `    ``print(res); ` ` `  `    ``return` `0; ` `} `

## Python 3

 `# Python3 program to store sparse vectors ` `# with the help of vector of pair ` ` `  `# Store the sparse vector ` `# as a vector of pairs ` `def` `convertSparseVector(v): ` `    ``res ``=` `[] ` `    ``for` `i ``in` `range``(``len``(v)): ` `        ``if` `(v[i] !``=` `0``): ` `            ``res.append([i, v[i]]) ` ` `  `    ``return` `res ` ` `  `# Print the vector of pairs ` `def` `printf(res): ` `    ``for` `x ``in` `res: ` `        ``print``(``"index:"``, x[``0``],  ` `              ``" -> value:"``, x[``1``]) ` ` `  `# Driver Code ` `if` `__name__ ``=``=` `'__main__'``: ` `     `  `    ``# Get the sparse vector ` `    ``v ``=` `[``2``, ``0``, ``0``, ``0``, ``0``, ` `         ``3``, ``0``, ``4``, ``0``, ``0``, ` `         ``0``, ``1``, ``5``, ``0``, ``0``, ` `         ``0``, ``0``, ``0``, ``0``, ``0``, ` `         ``0``, ``0``, ``4``, ``0``, ``0``, ` `         ``0``, ``2``, ``0``, ``0``, ``0``, ` `         ``0``, ``0``, ``0``, ``3``, ``0``, ` `         ``0``, ``0``, ``1``, ``0``, ``0``, ` `         ``0``, ``0``, ``5``] ` ` `  `    ``# Get the stored vector of pairs ` `    ``res ``=` `convertSparseVector(v) ` ` `  `    ``# Print the vector of pairs ` `    ``printf(res) ` ` `  `# This code is contributed by Surendra_Gangwar `

Output:

```index: 0 -> value: 2
index: 5 -> value: 3
index: 7 -> value: 4
index: 11 -> value: 1
index: 12 -> value: 5
index: 22 -> value: 4
index: 26 -> value: 2
index: 33 -> value: 3
index: 37 -> value: 1
index: 42 -> value: 5
```

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