Ideas: MikeMirzayanov

**Tutorial**

Tutorial is loading...

**Solution**

```
#include <bits/stdc++.h>
using namespace std;
int main()
{
int t;
cin >> t;
while (t--)
{
int k;
cin >> k;
for (int i = 1; ; i++)
{
if (i % 3 == 0 || i % 10 == 3)
continue;
if (--k == 0)
{
cout << i << '\n';
break;
}
}
}
}
```

**Tutorial**

Tutorial is loading...

**Solution**

```
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
int main()
{
int t;
cin >> t;
while (t--)
{
ll a, b, c;
cin >> a >> b >> c;
ll n = 2 * abs(a - b);
if (a > n || b > n || c > n)
cout << -1 << '\n';
else
{
ll d = n / 2 + c;
while (d > n) d -= n;
cout << d << '\n';
}
}
return 0;
}
```

**Tutorial**

Tutorial is loading...

**Solution**

```
#include <bits/stdc++.h>
using namespace std;
int main()
{
int t;
cin >> t;
while (t--)
{
int k;
cin >> k;
int a = 1;
int x = 1;
int i = 1;
while (k >= x + a)
{
x += a;
a += 2;
i += 1;
}
int m = k - x + 1;
if (m <= i)
cout << m << ' ' << i << '\n';
else
cout << i << ' ' << (i - (m - i)) << '\n';
}
}
```

**Tutorial**

Tutorial is loading...

**Solution**

```
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const ll P2LIM = (ll)2e18;
int solve(string s, string t)
{
int tp = 0;
int sp = 0;
int taken = 0;
while (sp < s.length() && tp < t.length())
{
if(s[sp] == t[tp])
{
taken++;
tp++;
}
sp++;
}
return (int)s.length() - taken + (int)t.length() - taken;
}
vector<string> ts;
int main()
{
for (ll p2 = 1; p2 <= P2LIM; p2 *= 2)
ts.push_back(to_string(p2));
int t;
cin >> t;
while (t--)
{
string n;
cin >> n;
int ans = n.length() + 1;
for (auto p2 : ts)
ans = min(ans, solve(n, p2));
cout << ans << '\n';
}
return 0;
}
```

1560E - Polycarp and String Transformation

**Tutorial**

Tutorial is loading...

**Solution**

```
#include <bits/stdc++.h>
using namespace std;
int cntsrc[26]; // don't forget to memset it but not cnt
int* cnt = cntsrc - 'a'; // so cnt['a'] = cntsrc[0] and so on
pair<string, string> decrypt(string s)
{
string order;
reverse(s.begin(), s.end());
for (auto c : s)
{
if (!cnt[c])
order.push_back(c);
cnt[c]++;
}
int m = order.length();
int originalLength = 0;
for (int i = 0; i < m; i++)
originalLength += cnt[order[i]] / (m - i);
reverse(order.begin(), order.end());
return { string(s.rbegin(), s.rbegin() + originalLength), order };
}
string encrypt(pair<string, string> p)
{
string result = p.first;
for (auto c : p.second)
{
string temp;
for (auto d : p.first)
if (d != c)
{
temp.push_back(d);
result.push_back(d);
}
p.first = temp;
}
return result;
}
int main()
{
int t;
cin >> t;
while (t--)
{
memset(cntsrc, 0, sizeof(cntsrc));
string s;
cin >> s;
auto ans = decrypt(s);
auto check = encrypt(ans);
if (check == s)
cout << ans.first << ' ' << ans.second << '\n';
else
cout << "-1\n";
}
return 0;
}
```

1560F1 - Nearest Beautiful Number (easy version)

**Tutorial**

Tutorial is loading...

**Solution**

```
#include <bits/stdc++.h>
using namespace std;
string solve1(string n)
{
string res(n.length(), '9');
for (char c = '8'; c >= '0'; c--)
{
string t(n.length(), c);
if (t >= n)
res = t;
}
return res;
}
string solve2(string n)
{
string res = solve1(n);
for(char a = '0'; a <= '9'; a++)
for (char b = a + 1; b <= '9'; b++)
{
bool n_ok = true;
for (int i = 0; i < n.length(); i++)
{
if (n[i] < b)
{
string t = n;
if (t[i] < a) t[i] = a;
else t[i] = b;
for (int j = i + 1; j < n.length(); j++)
t[j] = a;
if (res > t)
res = t;
}
if(n[i] != a && n[i] != b)
{
n_ok = false;
break;
}
}
if (n_ok) return n;
}
return res;
}
string solve()
{
string n;
int k;
cin >> n >> k;
if (k == 1) return solve1(n);
else return solve2(n);
}
int main()
{
int t;
cin >> t;
while (t--)
cout << solve() << '\n';
return 0;
}
```

1560F2 - Nearest Beautiful Number (hard version)

**Tutorial**

Tutorial is loading...

**Short solution**

```
#include <bits/stdc++.h>
using namespace std;
string solve()
{
string n;
int k;
cin >> n >> k;
while (true)
{
set<char> s;
for (auto c : n) s.insert(c);
if (s.size() <= k) return n;
s.clear();
int ptr = 0;
for (; ; ptr++)
{
s.insert(n[ptr]);
if (s.size() > k)
{
while (n[ptr] == '9')
ptr--;
n[ptr]++;
for (int i = ptr + 1; i < n.size(); i++)
n[i] = '0';
break;
}
}
}
}
int main()
{
int t;
cin >> t;
while (t--)
cout << solve() << '\n';
return 0;
}
```

**Long solution**

```
#include <bits/stdc++.h>
using namespace std;
string solveFillingSuffix(string& n, char d, int from)
{
for (int i = from; i < n.length(); i++)
n[i] = d;
return n;
}
void decAt(map<char, int>& d, char c)
{
if (d.count(c))
{
d[c]--;
if (d[c] == 0) d.erase(c);
}
}
string solve()
{
string n;
int k;
cin >> n >> k;
map<char, int> d;
int pref = 0;
while (pref < n.length())
{
if (d.count(n[pref]))
{
d[n[pref++]]++;
continue;
}
if (d.size() == k) break;
d[n[pref++]]++;
}
if (pref == n.length())
return n;
while (true)
{
if (n[pref] == '9')
{
decAt(d, n[--pref]);
continue;
}
if (d.size() < k)
{
d[++n[pref]]++;
return solveFillingSuffix(n, d.size() < k ? '0' : d.begin()->first, pref + 1);
}
auto it = d.upper_bound(n[pref]);
if (it == d.end())
{
decAt(d, n[--pref]);
continue;
}
n[pref] = it->first;
return solveFillingSuffix(n, d.begin()->first, pref + 1);
}
}
int main()
{
int t;
cin >> t;
while (t--)
cout << solve() << '\n';
return 0;
}
```

Very Good Round with Balanced Problemsets! Problem C was very interesting to me. Thanks!

How dare you say something wholesome here? No wonder you got downvoted. /s

It seems that you get downvotes too.):

They are just spoilt children don't mind them.

C was pretty similar to a CSES Problem-

https://cses.fi/problemset/task/1071

Thanks Man!

Great problemset and quick editorial.

Thank you for the round! Problems were interesting and of the right difficulty for a Div. 3.

For problem F1, there's a simpler solution:

Simply generate all beautiful numbers for $$$k = 2$$$, my program counts about $$$80,000$$$. Link

Can you please explain what i,j,k,l,m denote in your code?

`i`

and`j`

are the two digits that are in the number.`k`

is the number of digits in the number. I use`l`

as a bitmask to determine which digits are`i`

and which are`j`

. Then I loop over the digits of the bitmask with`m`

and construct the new number, which I insert into the set. I don't let`i == j`

by setting`j = i + 1`

since that is already covered when the bitmask is all 0 or 1.Got it. Thanks!

Prob C was very interesting ngl.

Completely agree ! Pre-computing all powers of 2 upto 10^18

That was D i guess

One great observation was that the leading row in the table was forming an arithmetic progression with common difference of 2.Great problem

Well, not the row elements, but the differences between consecutive elements form an arithmetic progression with a common difference of 2. This is because $$$\sum\limits_{i=0}^{k}2k+1 = k^2$$$ and every element in first row will obviously be $$$k^2 + 1$$$ and numbers $$$2k+1$$$ form an arithmetic progression with a common difference of 2.

Using this, we can also solve it in less than $$$\mathcal O(\sqrt k)$$$. The time complexity will depend on how you calculate the square root.

Great approach can you please give me this particular solution....if you don't mind pls

Pardon the late response. Here's the pseudocode.

This works in $$$\mathcal O(1)$$$ once you calculate square root.

gives me old spoj problems vibe.

I liked all problems. For F I made a dp with bitmasks (normal dp on digits), you could've set the constraints to disallow this solution, because it was pretty brainless (no cases to think about, just "brute-force")

O(T * 2^LEN * LEN), where LEN is the number of digits of N.

But don't you think this thing is above Div3 level for like 98% official particpants of Div3?

idk I never went to Div3 before, thinking carefully about many cases can be harder and more tricky.

yeah, that's your tunnel vision right there.

I implemented a similar solution (126326225) with complexity O(LEN * 1024) per test case. However, I feel considering a Div. 3 round, it wouldn't be brainless for official participants to think of a Digit DP there. However, what could have been changed was that instead of bombarding with 10^4 test cases, the length of the number could have been increased to let's say N <= 10^1000.

Could you elaborate on how the recurrence of the dp worked?

Isn't it O(T*2^LEN)?

EDIT: No, there is popcount in every recursion

You can avoid popcount by having a 4th argument (which you don't need to use for memoization). So, ll dp[1<<10][10][2] but the function ll solve(int mask, int pos, bool flag, int popcount) { ... } . But this does not change the complexity

I did the same solution and it got hacked. Did yours pass?

linkret I see no do major difference in our approach ( sorry , if there is) Can you tell why mine is TLE ? Here is my submission 126427896

I think it's better to always count the bits, and immediately return INF if there are too many, instead of just doing it in the end.

Hey [user:linkert] even after that , for clearing the array the whole complexity is (10^4 * 2^10 * 10 * 2) . Shouldn't it be TLE ?

2*10^8 is fast enough for Codeforces, even 10^9 is, too. My solution is about 100ms.

Counting bits worked and AC

Hey , can you explain the approach a bit too?

DP (memoized recursion). Use a bitmask to remember which digits from 0 to 9 have already been used. The number of 1s in this bitmask will tell you the number of different digits you had used: it must not exceed K.

In the DP, try out every possible digit for the current position, and move to the next position, adding it to the bitmask.

Also you will need to keep track of a 3rd state, weather the number you are currently building (from left to right) is already larger than the target number N, or not. Whenever you choose a digit larger than the corresponding digit of N, from then on you will always be larger and those dp states are allowed to choose any digits. But if you are not already larger than N, then it is not allowed to choose the current digit that is LESS than the corresponding digit of N. And if you choose the same digit, then the next recursion call still has to be careful (since it is not yet larger). You can google "digit dp" to get a better explanation about this part.

Thanks alot , great explanation

Just curious, how did you come up with problem E? What motivated this particular string construction?

It was a nice problem :)

A clean solution for C$$$sqrt()$$$ runs in $$$O(logK)$$$

I'm not pretty good at math, so I solved C using binary search.

I noticed that the last number of the $$$i_{th}$$$ row is $$$i^2$$$, so I do a binary search to find the row which $$$n$$$ belongs to. Then the starting number of the new column is $$$i^2 + 1$$$ (let's call this $$$start$$$), thus the number $$$corner$$$ at the position $$$(i + 1, i + 1)$$$ is $$$start + i$$$.

I finally check whether $$$n$$$ exceeds $$$corner$$$ or not, if it does then the answer is $$$(i + 1, i + corner + 1 - n)$$$, else the answer is $$$(n - start + 1, i + 1)$$$

Here's my submission

pretty smart vision :)

I solved using the same approach!

Also, binary search was not necessary for finding the nearest square since the constraints allowed a linear search algorithm. :)

Why does the short solution in F2 work in m^2 ? Couldn't figure it out:(

Btw problems are pretty good!!

Suppose n = 789152352 and k = 3. Then the algorithm takes you to:

789200000

789300000

789400000

789500000

789600000

789700000

Now this is a special point in the algorithm. The fourth character of the number is now among the 3 previously used digits, and now you just have to fill the 0's.

This act of "filling in the 0's" is O(M^2). (For each of the 0's, you have to do O(M * B) work where B the base, in this case the number is base 10 so B = 10. And there are O(M) 0's. So in total it is O(M^2 * B). Or just O(M^2) since B = 10, is a constant.)

There is another case, where you have to "loop around" because the character that was being incremented (in this case the 1 got incremented to 2, 3, .., then 7) hit 9 and then looped back around to 0. For example, if:

n = 456713538, k = 3. Then you have to do:

456800000

456900000

457000000

But you still end up with a state where now you just have to "fill in the 0's". Again O(M^2).

Example test cases were really handy for giving AC in one go..

DigitForcesMy O(1) solution to the problem C. CLICK

it is O(40000 * 100)

Oh my bad, I thought anything that goes on before any input is taken comes into compile time. So I mistook my O(40000*100) as O(1) as it didn't depend on n. Thanks for helping, a newbie here :)

As a newbie I just wanted to show my solution and hopefully get some feedback ( which apparently I got ). Maybe my rating is what made you all to downvote. I was working hard, but now I'll double my hard work. Ciao :)

Problem

`A`

could be solved in $$$\mathcal{O}(1)$$$ time complexity:Let's define $$$f(x)$$$ to be $$$1$$$ if Polycarp likes $$$x$$$, and $$$0$$$ otherwise. Then, $$$f(x)$$$ is cyclic, and its cycle's length is $$$lcm(3, 10) = 30$$$.

We can compute the number of liked numbers among the first $$$30$$$ positive integers, let's call it $$$M$$$. Let's also say that there are $$$T$$$ contiguous ranges of size 30 between 1 and the number we're looking for (excluding that number).

Then $$$T \cdot M < K$$$, which means that $$$T = \left\lceil\frac{K}{M}\right\rceil - 1$$$. Now, we just need to find the $$$(K-T\cdot M)$$$-th liked number strictly greater than $$$30\cdot T$$$, which is less than 30 steps away from $$$30\cdot T$$$.

great!!!

Can anyone tell me that in the problem B can there be any testcase like:-

1 2 2

as 2 people are in the circle 1 is next to 2 and we have to output the person next to 2.

While I am hacking my solution by myself it's showing invalid input

No a,b,c should be distinct

Dhanyavad Mitr.

but in the problem it is mention that : Each test case consists of one line containing three

distinctintegers a,b,c.I think it was a good round, at least for new users like me.

MrPaul_TUser the solutions to problems A, B and C are possible in O(1) too. Will it be fine if you can please publish my O(1) solutions?

Problemset was great. First 3 questions were easy to solve. I got stuck at D and wasn't able to solve.

I solved D 30s after contest got over. Worst feeling ever :/

I submitted E after a min, and man I felt sed cause my rank was pretty low and I hadn't solved D

E was easier to observe, but I wasted all my time on F1 and couldn't even solve it. Bad luck for me.

atleast you solved D orz ;)

" Let's iterate a prefix of n starting from the empty one so that the prefix will be the prefix of x. This prefix must contain only the digits a and b"can someone explain what this means. Problem F1Look at my submission for problem D. Link: https://codeforces.com/contest/1560/submission/126381278

Why this is getting TLE

I submitted your code in pypy3 it passed

https://codeforces.com/contest/1560/submission/126414861

Oh! Thanks alot from now on I'll be submitting in pypy3

MathForces

For problem С is possible to generate arithmetic progression, and in solution use lower_bound

Problem C can be easily done, first get the square root of k (bcz every row starts with square number), then start counting from top most box of next column.

What difficulty of your solution?

You mean complexity, it will be whatever time you need to calculate the sqrt.

Guys i had submitted solution for E problem with the same logic. It ran fine in my local IDE but codeforces gave wrong answer on test 1. Is this some bug in the codeforces or is there some part of the code which is wrong. Please do let me know.

126357466

Thank you.

it gave WA on my machine too, it is very messy so I couldn't find the mistake, maybe you could add some comments.

Speed of editorial was quick in the round! Thank!

My soln got stuck for f1 as I was unable to place the right characters to go for can someone give explanation of f1

I can't see anyone mentioning it here, but many people have solved A using this method: Precompute an array with

likedintegers ranging from 1 to 1666, and then just output thek-1th element of the array. Are there any drawbacks to this method? It does take more space compared to the other solution, but the time complexity is much lower, O(1). (Correct me if I'm wrong).No, this method works fine but we can calculate till 1000th number instead of storing from 1 to 1666 Hope thats clears it

I solved F1 and F2! At 2 minutes after contests finished. :(

ehh, that sucks, but you know that you are good enough to even Fs in Div3, now you can try increasing speed:)

Thanks for nice comment :)

You did it very fast from A to D. Any tips on how to increase speed?

I try giving virtual contests, would recommend that, or you can do mashup of problems within time limit. Basically, solving problems in a timed environment helps ig.

For problem E, this submission gives different output on CF judge and local machine for some inputs, for e.g. for the i/p string

`v`

Output of the above submission on OJ is

`-1`

, but when I run locally, the o/p is`v v`

.Can anyone please help in figuring out why this is happening.

Thank you.

I submitted your solution with GNU G++17 compiler and it gave Runtime error on test 2. I have faced problem like yours on codeforces too and submitting on GNU G++17 compiler always helped me.

This is my code for F2.

Can you please explain your idea?

It's just to adjust each digit from high to low.

Please explain why you did this way

It's a pity that I didn't attend.

This was a great round!

I have another solution for Problem F2.

First, take the longest prefix of $$$n$$$, such that there are at most $$$k$$$ distinct digits. Let's call that prefix $$$p$$$.

If $$$p = n$$$, the answer is $$$n$$$.

Otherwise, let's call $$$i$$$ as the first index after $$$p$$$ (for example: if $$$n = 199754$$$, $$$k = 3$$$, then $$$p$$$ will be $$$1997$$$ and $$$i$$$ will be $$$4$$$ (indexes start at $$$0$$$)).

Now find the minimum $$$x$$$ such that $$$p$$$ contains $$$x$$$ and $$$x$$$ is greater than $$$i-th$$$ digit of $$$n$$$ ($$$x$$$ can't be equal to $$$i-th$$$ digit of $$$n$$$, because in that case you can choose longer prefix than $$$p$$$).

Now there are $$$2$$$ cases:

Time complexity: $$$O(len$$$ $$$\mathrm{log}$$$ $$$len)$$$, where $$$len$$$ is the number of digits of $$$n$$$. This means that this solution will also work for $$$n \leq 10^{10^5}$$$ or even for bigger $$$n$$$.

My code

https://codeforces.com/problemset/problem/233/A please help me in solving this

May I ask you 1 thing ?

Does this contest rates for people who are having rating under 1600?- If yes, why I have been rated yet ? - I need an answer.If there's no blog updates or notifications saying it's unrated,it will be rated for you. Just wait :)

Thank you very much. I received the scores. :)

Great Contest, I became pupil for the first time.

Congratulations!

Why my $$$O(t2^{10}mk)$$$ solution got $$$Accepted$$$ for problem F2...

upd : got hacked lol

Ah you get hacked,orz!

I think we have the same approach but I break when the value will only rise, that will only take $$$O(2^k \times m \times 2)$$$ memory but $$$O(mk)$$$ query

For problem C, I got my answer wrong on just one number: 999950883 . Can someone please tell why did this happen. Is this number special in some terms? My submission link: https://codeforces.com/contest/1560/submission/126314408

Disliked this contest, 7 constructive/greedy approaches, really? Nothing educational/interesting. Your div.3 #734 was far more better: it had cool dp and graph problems.

I have the same opinion.

Very good Editorial,and very good problem!

especially for problem F2,a short solution and a long solution are very good for readers.

And it is pretty suitable for beginner coders!

:)

is there any other way to guess that 2^18 thing(size of set of powers of 2) for problem D? Thanks

how does problem rating system works I dont think C would be 800 atleast 900, I guess since a lot of people have solved it , it is given 800.

Problem C is similar to the CSES Number Spiral, here is the O(1) solution comparatively easy from the editorial.

`sqrt()`

doesn't work in $$$O(1)$$$. It works in $$$O(\mathrm{log}$$$ $$$n)$$$.why down vote isn't asymptotic complexity of this library function $$$sqrt()$$$ is $$$\mathcal O(logn)$$$

Problem E has the sorting and binary search tags, can someone explain where it can be used in the solution?

Can anyone please explain to me...why in problem D..we are only considering up to power of 2 equal to 18?

yes please anyone?

it is $$$2\cdot10^{18}$$$

Yes...sorry for the mistake..do you know why this upper limit is taken!

In worst we may have to remove either all digit of

`n`

which can be atmost 10 operation as $$$limit$$$ of`n`

is $$$10^9$$$ or we may have to append 9 digit in right of n which increases value of`n`

equal $$$10^{18}$$$ is equivalent to $$$2^{60}$$$ at most. Checking for all 60 power of 2 and and finding min operation to convert it to perfect power of $$$2$$$.In Editorial for D problem I am unable to understand why upper limit is 10^18

Observe that n's upper bound means there's a limit to your answer which is the number you'd get from deleting all digits and adding a single-digit power of two. The question then is how large of a power-of-2 could you construct with any max-digit-length n + that many add-a-digit-to-the-right operations?

The last case in the sample was helpful in that regard: if you bounded your powers of two according to n itself, you'd get an incorrect result for it.

Extra: consider why 10^9 and 10^18 are commonly seen limits...

Disclosure: I didn't think of this during the contest either, womp womp.

edit: uhhhh, this was in the editorial... in which case, sorry for being repetitive...

I really liked this contest, genuinely enjoyed doing problems C,D,E,F.

what kind of error is this?"wrong answer order too long"...everything seems alright...getting all the outputs that are visible, matching...can someone help? string trans problem https://codeforces.com/contest/1560/submission/126609563

Which is 189 number in 5 test case in 1560F1 - Nearest Beautiful Number (easy version) problem?MrPaul_TUser please give that case because there are a huge number of submissions failed on that case and it is interesting to me to know why

in problem c i didn't understand the logic/intution behind statement

"the number belongs to the i-th row and the (i−(m−i))-th column. if(m>i)"can someone explain it pleaseHey guys, this was my 2nd competition abd I could solve only A, B and C, one more than my first competition. But I notice that for most of the question I form the logic almost equal to the editorial but screw up in small details. Any tips and suggestions for me??

This is my approach for problem C. Although this showed WA during the contest but it got accepted now. 126677915

Can anyone please help me with understanding why this code gives TLE though it's mostly similar to the solution given in editorial. https://codeforces.com/contest/1560/submission/126656613

Please someone help me.... why my answer is the wrong test3 for F1. 126757323 above is my submission. also tell me, how to improve my code.

For problem F,May I get the test case for 204th number? I could not know where my submission got the answer wrong. Thanks in advance

https://codeforces.com/contest/1560/submission/129336848