Count Pairs of Consecutive Zeros in C++

We have a sequence generator that starts with 1. At each step 0 becomes 10 and 1 becomes 01. So following changes will occur at consecutive steps −

Step 1 − 01

Step 2 − 1001

Step 3 − 01101001 ……

The goal is to find the number of pairs of consecutive 0’s for a given number of steps.

If input step is 1 pair of 0’s - 0, input step is 2 pair of 0’s - 1, input step is 3 pair of 0’s 1

Step 4 − 1001011001101001

Step 5 − 01101001100101101001011001101001

We can observe that sequence is increasing in powers of 2 and repeats itself after length 12 and for every 12 characters. So, these 12 length sequences have 2 pairs of consecutive 0’s.

For steps S number of 12 length patterns will be 2S /12

Number of consecutive 2 patterns = 1 (initial) + 2 X S ( for rest of 12 length repetitions )

Let us understand with examples.

Input − steps = 5

Output − Count of Pairs Of Consecutive Zeros are − 5

Explanation − As shown above sequence at 5th step is −

Step 5: 01101001100101101001011001101001
Number of pairs of 0’s is 5.
Also with formula : tmp=25
/12= 32/12 = 2, pairs=1+ 2 x 2 = 5

Input − steps = 10

Output − Count of Pairs Of Consecutive Zeros are − 171

Explanation − With formula − tmp=210/12= 1024/12 = 85, pairs=1+ 2 x 85 = 171

The approach used in the below program is as follows

We will take the number of steps as input and check if steps=1 then the number of pairs of consecutive 0’s is 0. If steps = 2 or 3 then the number of such pairs is 1.

Otherwise, calculate using formula tmp=2input/12 and pairs=1+2*tmp.

• Take a variable decimal as input for steps.

• Function Zero_pairs(int decimal) takes decimal and returns Count of Pairs Of Consecutive Zeros for that step.

• Take the initial count as 0.

• If decimal<=1, return 0.

• If decimal==2 or decimal==3. Then return 1.

• Else calculate temp=(pow(2,decimal))/12 and calculate count as 2*temp + 1.

• Return count as result.

Example

 Live Demo

#include<bits/stdc++.h>
using namespace std;
int Zero_pairs(int decimal){
   int count = 0;
   if(decimal <=1){
      count = 0;
   }
   else if(decimal == 2 || decimal == 3){
      count = 1;
   }
   else{
      int temp = (pow(2, decimal) / 12);
      count = 2 * temp + 1;
   }
   return count;
}
int main(){
   int decimal = 7;
   cout<<"Count of Pairs Of Consecutive Zeros are: "<<Zero_pairs(decimal);
   return 0;
}

Output

If we run the above code it will generate the following output −

Count of Pairs Of Consecutive Zeros are: 21