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I've found out that there is a direct solution (i didn't get it myself, I just found out by searching, I solved the problem with while bucle like almost everybody).

Ok, I updated it, with the input example 10 2 2 and i tried to remove the python stuff and leave only the math symbols :) If anyone has a suggestion how to better rewrite the question is welcome :)

Well, not sure about this formula but if you wanted to use one yourself, think about the steps you would take if you were doing the exchange of wrappers by hand; by the way, not the best code to write as it's confusing and you are writing over the money variable instead of creating a new one. First you buy as many chocolates as you want, chocolates = money/cost . Now you eat those chocolates and exchange all the wrappers possible for extra ones, let's call it extras = chocolates / extra .

BUT you could have leftover chocolates so let's see how many, remainders = chocolates % extra . Since we got extras , we can add it to the remainders and see if it is enough for more chocolates, super_extras = (extras + remainders) / extra . Remember that all of this is integer division so it'll round down.

Finish by adding to the total chocolates += extras + super_extras and you're done! You have to tweak it a bit to get edge cases but that part should be trivial. Use the same logic to see where those terms you wrote came from. I think if you rearrange what I showed you'll get the same thing.

Chk this :Worked for all test cases:
for(int a1=0;a1

no = n/c;
int wrapper = no;
int rem = 0;
while(wrapper>=m){
rem = wrapper/m;
no = no +rem;
rem = rem + wrapper%m;
wrapper = rem;
}
System.out.println(no);
}

Yeah! You are right and the description is easy. I sloved this problem with the same way. The following is my AC code :)

int main() {
/* Enter your code here. Read input from STDIN. Print output to STDOUT */
int t,n,c,m;
cin>>t;
while(t--){
cin>>n>>c>>m;
int answer=0;
// Computer answer(the total of chocolates Bob eats)
// answer consists of two parts: directly buy with money and exchange with wrapper
int answer1 = n / c; // the number of buying with money
answer += answer1;
int answer2 = 0; // the number of exchanging with wrapper
int wrapper = answer1 / m; // the number of first exchange with wrapper
int remain = answer1 % m; // the number of first remain wrapper
answer2 += wrapper;
int available = wrapper + remain;
while (available / m != 0) {
wrapper = available / m;
remain = available % m;
answer2 += wrapper;
available = wrapper + remain;
}
answer += answer2;
cout<<answer<<endl;
}
return 0;
}

t = int(raw_input().strip())
for a0 in xrange(t):
n,c,m = raw_input().strip().split(' ')
n,c,m = [int(n),int(c),int(m)]
result = 0
ch = n / c
result +=ch
while True:
ch_w = ch / m
result += ch_w
ch_r = ch % m
ch = ch_w + ch_r
if ch < m:
break
print result

@ansonete: This is indeed the cleanest solution, and the logic is simple: for every m wrappers you get a candy, candy = wrapper, i.e. for every m wrappers you get 1 wrapper back. Thus, the actual "wrapper price" of one candy is (m - 1) rather than m. Now, dividing your original number of wrappers by the "reduced price" is unfair - you still have to pay "full price" (i.e. full m) for the very first "exchange candy". Thus, let us first put m aside to make sure we get our first free candy. So the amount of wrappers to divide by reduced price is (boughtCandy - m). Now, the total number of candies is:

boughtCandy = money / cost

total = boughtCandy + 1 + (boughtCandy - m) / (m - 1)

where 1 is the candy we bought for the m we put aside in the first place. This can be simplified as follows:

total = boughtCandy + (m - 1)/(m - 1) + (boughtCandy - m) / (m - 1)

= boughtCandy + (m - 1 + boughtCandy - m) / ( m - 1 )

## Chocolate Feast

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I've found out that there is a direct solution (i didn't get it myself, I just found out by searching, I solved the problem with while bucle like almost everybody).

## Code

Does anyone know the math basis or where this comes from, or where can I read about this?

Thanks!

@ ansonete, it's recommended to write formula instead of code snippet. Will be easier for non-python programmar :)

Ok, I updated it, with the input example 10 2 2 and i tried to remove the python stuff and leave only the math symbols :) If anyone has a suggestion how to better rewrite the question is welcome :)

Well, not sure about this formula but if you wanted to use one yourself, think about the steps you would take if you were doing the exchange of wrappers by hand; by the way, not the best code to write as it's confusing and you are writing over the

`money`

variable instead of creating a new one. First you buy as many chocolates as you want,`chocolates = money/cost`

. Now you eat those chocolates and exchange all the wrappers possible for extra ones, let's call it`extras = chocolates / extra`

.BUT you could have leftover

`chocolates`

so let's see how many,`remainders = chocolates % extra`

. Since we got`extras`

, we can add it to the`remainders`

and see if it is enough for more chocolates,`super_extras = (extras + remainders) / extra`

. Remember that all of this is integer division so it'll round down.Finish by adding to the total

`chocolates += extras + super_extras`

and you're done! You have to tweak it a bit to get edge cases but that part should be trivial. Use the same logic to see where those terms you wrote came from. I think if you rearrange what I showed you'll get the same thing.For just one test case input() There needs changing in condition. What if super_extras is more than m. Then more candies.

Chk this :Worked for all test cases: for(int a1=0;a1

Thanks for your comment. You are right, the code is confusing due the name of the variables :) I updated it.

I am not able to figure out the mistake in this code any help wud be appreciated

## include

## include

## include

## include

int main() { long int a,b,c,t,d,e; scanf("%ld",&t); while(t--) { scanf("%ld %ld %ld",&a,&b,&c); e=a/b; d=e;

return 0; }

Yeah! You are right and the description is easy. I sloved this problem with the same way. The following is my AC code :)

Similar approach using python:

I too, would also like to know about this.

thanks for the solution, it reminds me of the meme "code works: no idea why"

sir if you the logic behind it then pls help me to understand that thank you

@ansonete: This is indeed the cleanest solution, and the logic is simple: for every m wrappers you get a candy, candy = wrapper, i.e. for every m wrappers you get 1 wrapper back. Thus, the actual "wrapper price" of one candy is (m - 1) rather than m. Now, dividing your original number of wrappers by the "reduced price" is unfair - you still have to pay "full price" (i.e. full m) for the very first "exchange candy". Thus, let us first put m aside to make sure we get our first free candy. So the amount of wrappers to divide by reduced price is (boughtCandy - m). Now, the total number of candies is:

`boughtCandy = money / cost`

`total = boughtCandy + 1 + (boughtCandy - m) / (m - 1)`

where 1 is the candy we bought for the m we put aside in the first place. This can be simplified as follows:

`total = boughtCandy + (m - 1)/(m - 1) + (boughtCandy - m) / (m - 1)`

`= boughtCandy + (m - 1 + boughtCandy - m) / ( m - 1 )`

`= boughtCandy + (boughtCandy - 1)/(m - 1)`

Et voila!

That was brilliant Anna, thanks ;)

thats wrong bud... check for 2nd case of 1st test case

Awesome explanation. Thanks a lot.

My idea was same as you but i am getting runtime error for test case 5.could u help me?

int t,n,m,c; int wrappers,count;

for(int i =0;i

}

/*The main logic is above u can compare it easily */

Amazing :)

Here you can find formula with the proof http://www.geeksforgeeks.org/g-fact-42/

I'm trying to understand how this problem can be mapped to a n-ary tree.

I've tried several approaches but couldn't succeed.

Could you explain the approach you have in mind?

Thanks!