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}

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++

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// C++ program to store sparse vectors
// with the help of vector of pair
  
#include <bits/stdc++.h>
using namespace std;
  
// Store the sparse vector
// as a vector of pairs
vector<pair<int, int> >
convertSparseVector(vector<int> v)
{
    vector<pair<int, int> > 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<pair<int, int> > 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<pair<int, int> > res
        = convertSparseVector(v);
  
    // Print the vector of pairs
    print(res);
  
    return 0;
}

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Python 3

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# 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

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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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