# Count of a, b & c after n seconds for given reproduction rate in C++

Given three numbers 'a', 'b' and 'c' as input. The goal is to find the count/value of 'a', 'b' and 'c' after n seconds such that the rate of reproductions are:-

• Every a changes to b after every 2 seconds
• Every b changes to c after every 5 seconds
• Every c changes to 2 a after every 12 seconds.

## Let us understand with examples.

For Example

Input - n_seconds = 62  a = 1 b = 1 c = 1

Output - Count of a after n seconds for given reproduction rate is: 0

Count of b after n seconds for given reproduction rate is: 33

Count of c after n seconds for given reproduction rate is: 1

Explanation - After 60 seconds, a's will be 32, b = 0, c = 0.

After 2 more seconds, all b's will become c, c=1. All a become b, b=33.

Input - n_seconds = 20  a = 1 b = 1 c = 1

Output - Count of a after n seconds for given reproduction rate is: 0

Count of b after n seconds for given reproduction rate is: 0

Count of c after n seconds for given reproduction rate is: 6

Explanation

1 sec :-  a=1, b=1, c=1

2 sec :-  a=0, b=2(1+1) , c=1          → a to b after 2 seconds

4 sec :-  a=0, b=2 , c=1                  → a to b after 2 seconds

5 sec :-  a=0, b=0 , c=3 (1+2)        → b to c after 5 seconds

6 sec :-  a=0, b=0 , c=3                  → a to b after 2 seconds

8 sec :-  a=0, b=0 , c=3                  → a to b after 2 seconds

10 sec :-  a=0, b=0 , c=3               → b to c after 5 seconds

12 sec :-  a=6 (0+2*3), b=0 , c=0     → c to 2a after 12 seconds

14 sec :-  a=0, b=6(0+6) , c=0          → a to b after 2 seconds

15 sec :-  a=0, b=0 , c=6(0+6)         → b to c after 5 seconds

16 sec :-  a=0, b=0 , c=6                  → a to b after 2 seconds

18 sec :-  a=0, b=0 , c=6                  → a to b after 2 seconds

20 sec :-  a=0, b=0 , c=6                 → b to c after 5 seconds

## Approach used in the below program is as follows

The LCM of seconds will be 60 ( 2, 5, 12 ). So the changes in a, b and c after every 60 seconds will be :

60 seconds → a= 32, b=0, c=0

120 seconds → a= 32*32 , b=0, c=0

180 seconds → a= 32*32*32 , b=0, c=0.

For seconds as multiples of 60 calculate a's as above. For non-multiples, calculate nearest multiple temp and then traverse from temp+1 to input seconds and calculate using mod 2, 5 or 12.

• Take numbers a, b and c as input.
• Take n_seconds as time in seconds.
• Function reproduction_rate(int n_seconds, int a, int b, int c) takes all parameters and prints the count of a, b & c after n seconds for given reproduction rate.
• Take temp = n_seconds / 60 as multiples of 60 below n_seonds.
• Calculate a = (int)pow(32, temp) as given in formula. ( atemp )
• Now update temp = 60 * temp for nearest multiple of 60 less or equal to n_seconds.
• Now traverse using for loop from i=temp+1 to i=n_seconds.
• If the number i is multiple of 2 then update b by adding a and a with 0.
• If the number i is multiple of 5 then update c by adding b and b with 0.
• If the number i is multiple of 12 then update a by adding 2c and c with 0.
• At the end of for loop, print the final values of a, b and c.

## Example

Live Demo

#include <bits/stdc++.h>
using namespace std;

void reproduction_rate(int n_seconds, int a, int b, int c) {
int temp = n_seconds / 60;
a = (int) pow(32, temp);
temp = 60 * temp;

for (int i = temp + 1; i <= n_seconds; i++) {
if (i % 2 == 0) {
b = b + a;
a = 0;
}
if (i % 5 == 0) {
c = c + b;
b = 0;
}
if (i % 12 == 0) {
a = a + (2 * c);
c = 0;
}
}
cout << "Count of a after n seconds for given reproduction rate is: " << a << "\n";
cout << "Count of b after n seconds for given reproduction rate is: " << b << "\n";
cout << "Count of c after n seconds for given reproduction rate is: " << c;
}
int main() {
int n_seconds = 72;
int a = 2;
int b = 1;
int c = 1;
reproduction_rate(n_seconds, a, b, c);
return 0;
}

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

## Output

Count of a after n seconds for given reproduction rate is: 68
Count of b after n seconds for given reproduction rate is: 0
Count of c after n seconds for given reproduction rate is: 0