# Find d to maximize the number of zeros in array c[] created as c[i] = d*a[i] + b[i] in C++

## Concept

With respect of two given arrays of M integers, assume an array C, where the i-th integer will be d*a[i] + b[i] where d is indicated as any arbitrary real number. Our task is to display or print d such that array C has largest number of zeros and also prints the number of zeros.

## Input

a[] = {15, 40, 45}
b[] = {4, 5, 6}

## Output

Value of d is: -0.133333
The number of zeros in array C is: 1
If we choose d as -0.133333 then we get one zero in the array C which is the maximum possible.

## Methods

We follow the below mentioned steps to solve the above problem −

• We rewrite the equation as d = -b[i]/a[i]
• Implement hash-table to count the largest number of occurrence of any real number to obtain the value of d.
• Now,we conclude that number of zeros will be the largest count + (number of pairs a[i] and b[i] where both are 0).

## Example

Live Demo

// C++ program to implement the above
// approach
#include <bits/stdc++.h>
using namespace std;
// Shows function to find the value of d
// and find the number of zeros in the array
void findDandZeros1(int a[], int b[], int m){
// Shows hash table
unordered_map<long double, int> mpp1;
int count1 = 0;
// Performs iteration for i-th element
for (int i = 0; i < m; i++) {
// Now if both are not 0
if (b[i] != 0 && a[i] != 0) {
long double val1 = (long double)(-1.0 * b[i]) /
(long double)(a[i]);
mpp1[val1] += 1;
}
// Now if both are 0
else if (b[i] == 0 && a[i] == 0)
count1 += 1;
}
// Used to find max occurring d
int maxi1 = 0;
for (auto it : mpp1) {
maxi1 = max(it.second, maxi1);
}
// Used to print the d which occurs max times
for (auto it : mpp1) {
if (it.second == maxi1) {
cout << "Value of d is: "
<< it.first << endl;
break;
}
}
// Used to print the number of zeros
cout << "The number of zeros in array C is: "
<< maxi1 + count1;
}
// Driver code
int main(){
int a[] = { 15, 40, 45 };
int b[] = { 4, 5, 6 };
int m = sizeof(a) / sizeof(a[0]);
findDandZeros1(a, b, m);
return 0;
}

## Output

Value of d is: -0.133333
The number of zeros in array C is: 1

Updated on: 24-Jul-2020

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