1154A - Restoring Three Numbers

Idea: MikeMirzayanov

**Tutorial**

Tutorial is loading...

**Solution**

```
#include <bits/stdc++.h>
using namespace std;
int main() {
#ifdef _DEBUG
freopen("input.txt", "r", stdin);
// freopen("output.txt", "w", stdout);
#endif
vector<int> a(4);
for (int i = 0; i < 4; ++i) {
cin >> a[i];
}
sort(a.begin(), a.end());
cout << a[3] - a[0] << " " << a[3] - a[1] << " " << a[3] - a[2] << endl;
return 0;
}
```

Idea: MikeMirzayanov

**Tutorial**

Tutorial is loading...

**Solution**

```
#include <bits/stdc++.h>
using namespace std;
int main() {
#ifdef _DEBUG
freopen("input.txt", "r", stdin);
// freopen("output.txt", "w", stdout);
#endif
int n;
cin >> n;
vector<int> a(n);
for (int i = 0; i < n; ++i) {
cin >> a[i];
}
sort(a.begin(), a.end());
a.resize(unique(a.begin(), a.end()) - a.begin());
if (a.size() > 3) {
cout << -1 << endl;
} else {
if (a.size() == 1) {
cout << 0 << endl;
} else if (a.size() == 2) {
if ((a[1] - a[0]) % 2 == 0) {
cout << (a[1] - a[0]) / 2 << endl;
} else {
cout << a[1] - a[0] << endl;
}
} else {
if (a[1] - a[0] != a[2] - a[1]) {
cout << -1 << endl;
} else {
cout << a[1] - a[0] << endl;
}
}
}
return 0;
}
```

Idea: le.mur

**Tutorial**

Tutorial is loading...

**Solution**

```
#include <bits/stdc++.h>
using namespace std;
int main() {
#ifdef _DEBUG
freopen("input.txt", "r", stdin);
// freopen("output.txt", "w", stdout);
#endif
vector<int> a(3);
cin >> a[0] >> a[1] >> a[2];
vector<int> idx({0, 1, 2, 0, 2, 1, 0});
int full = min({a[0] / 3, a[1] / 2, a[2] / 2});
a[0] -= full * 3;
a[1] -= full * 2;
a[2] -= full * 2;
int ans = 0;
for (int start = 0; start < 7; ++start) {
int day = start;
vector<int> b = a;
int cur = 0;
while (b[idx[day]] > 0) {
--b[idx[day]];
day = (day + 1) % 7;
++cur;
}
ans = max(ans, full * 7 + cur);
}
cout << ans << endl;
return 0;
}
```

Idea: MikeMirzayanov

**Tutorial**

Tutorial is loading...

**Solution**

```
#include<bits/stdc++.h>
using namespace std;
int a, b, maxa;
void use_battery(int s)
{
if(s == 1) a = min(a + 1, maxa);
--b;
}
void use_accum()
{
--a;
}
int main()
{
int ans = 0;
int n;
cin >> n >> b >> a;
maxa = a;
vector<int> s(n);
for(int i = 0; i < n; i++) cin >> s[i];
for(int i = 0; i < n; i++)
{
if(a == 0 && b == 0)
break;
else if(a == 0)
use_battery(s[i]);
else if(b == 0)
use_accum();
else if(s[i] == 1 && a < maxa)
use_battery(s[i]);
else use_accum();
ans++;
}
cout << ans << endl;
}
```

Idea: MikeMirzayanov

**Tutorial**

Tutorial is loading...

**Solution**

```
#include <bits/stdc++.h>
using namespace std;
int main() {
#ifdef _DEBUG
freopen("input.txt", "r", stdin);
// freopen("output.txt", "w", stdout);
#endif
int n, k;
cin >> n >> k;
vector<pair<int, int>> a(n);
for (int i = 0; i < n; ++i) {
cin >> a[i].first;
a[i].second = i;
}
sort(a.rbegin(), a.rend());
queue<int> q;
for (int i = 0; i < n; ++i) {
q.push(a[i].second);
}
set<int> idx;
for (int i = 0; i < n; ++i) {
idx.insert(i);
}
string ans(n, '0');
int who = 0;
while (!idx.empty()) {
while (!idx.count(q.front())) {
q.pop();
}
int pos = q.front();
q.pop();
vector<int> add;
auto it = idx.find(pos);
for (int i = 0; i <= k; ++i) {
add.push_back(*it);
if (it == idx.begin()) break;
--it;
}
it = next(idx.find(pos));
for (int i = 0; i < k; ++i) {
if (it == idx.end()) break;
add.push_back(*it);
++it;
}
for (auto it : add) {
idx.erase(it);
ans[it] = '1' + who;
}
who ^= 1;
}
cout << ans << endl;
return 0;
}
```

Idea: MikeMirzayanov

**Tutorial**

Tutorial is loading...

**Solution**

```
#include <bits/stdc++.h>
using namespace std;
const int INF = 1e9;
int main() {
#ifdef _DEBUG
freopen("input.txt", "r", stdin);
// freopen("output.txt", "w", stdout);
#endif
int n, m, k;
cin >> n >> m >> k;
vector<int> a(n);
for (int i = 0; i < n; ++i) {
cin >> a[i];
}
sort(a.begin(), a.end());
a.resize(k);
reverse(a.begin(), a.end());
vector<int> offers(k + 1);
for (int i = 0; i < m; ++i) {
int x, y;
cin >> x >> y;
if (x <= k) {
offers[x] = max(offers[x], y);
}
}
vector<int> pref(k + 1);
for (int i = 0; i < k; ++i) {
pref[i + 1] = pref[i] + a[i];
}
vector<int> dp(k + 1, INF);
dp[0] = 0;
for (int i = 0; i < k; ++i) {
dp[i + 1] = min(dp[i + 1], dp[i] + a[i]);
for (int j = 1; j <= k; ++j) {
if (offers[j] == 0) continue;
if (i + j > k) break;
dp[i + j] = min(dp[i + j], dp[i] + pref[i + j - offers[j]] - pref[i]);
}
}
cout << dp[k] << endl;
return 0;
}
```

Idea: MikeMirzayanov

**Tutorial**

Tutorial is loading...

**Solution**

```
#include <bits/stdc++.h>
using namespace std;
const int INF = 1e9;
const int N = 10 * 1000 * 1000 + 11;
int n;
vector<int> a;
int mind[N];
pair<int, int> mins[N];
vector<pair<int, int>> divs;
void build_sieve() {
vector<int> pr;
mind[0] = mind[1] = 1;
for (int i = 2; i < N; ++i) {
if (mind[i] == 0) {
pr.push_back(i);
mind[i] = i;
}
for (int j = 0; j < int(pr.size()) && pr[j] <= mind[i] && i * pr[j] < N; ++j) {
mind[i * pr[j]] = pr[j];
}
}
}
void add_to_mins(int curd, int idx) {
if(mins[curd].first == -1)
mins[curd].first = idx;
else if(mins[curd].second == -1)
mins[curd].second = idx;
}
void rec(int pos, int curd, int idx) {
if (pos == int(divs.size())) {
add_to_mins(curd, idx);
return;
}
int curm = 1;
for (int i = 0; i <= divs[pos].second; ++i) {
rec(pos + 1, curd * curm, idx);
curm *= divs[pos].first;
}
}
void add(int idx) {
int value = a[idx];
divs.clear();
while (value > 1) {
int d = mind[value];
if (!divs.empty() && divs.back().first == d) {
++divs.back().second;
} else {
divs.push_back(make_pair(d, 1));
}
value /= d;
}
rec(0, 1, idx);
}
int main() {
#ifdef _DEBUG
freopen("input.txt", "r", stdin);
// freopen("output.txt", "w", stdout);
#endif
cin >> n;
a.resize(n);
for (int i = 0; i < n; ++i) {
cin >> a[i];
}
for(int i = 0; i < N; i++)
mins[i] = make_pair(-1, -1);
build_sieve();
vector<pair<int, int> > vals;
for(int i = 0; i < n; i++)
vals.push_back(make_pair(a[i], i));
sort(vals.begin(), vals.end());
for (int i = 0; i < n; ++i) {
if(i > 1 && vals[i].first == vals[i - 2].first) continue;
add(vals[i].second);
}
long long l = INF * 1ll * INF;
int ansi = -1, ansj = -1;
for (int i = 1; i < N; ++i) {
pair<int, int> idxs = mins[i];
if (idxs.second == -1) continue;
long long curl = a[idxs.first] * 1ll * a[idxs.second] / i;
if (l > curl) {
l = curl;
ansi = min(idxs.first, idxs.second);
ansj = max(idxs.first, idxs.second);
}
}
cout << ansi + 1 << " " << ansj + 1 << endl;
return 0;
}
```

Could somebody explain the LCM question clearly ? I could not understand the editorial

Link of Code

In your code, you're sorting the input array, so complexity is still O(nlogn).

Oh sorry, I missed that:)

You don't need a nlogn sort algorithm in your code. You can do linearly too

you can use counting sort

E can be solved using Linked List if O(n). you just need to implement the operations. since every student will be chosen exactly once so the time complexity is O(n). code: 52920413

sorting?

If you use a non-comparing sort algorithm. It could be done in linear time.

I don't know of any non-comparison sort algorithm that works in

`O(n)`

time. The best I know of is works in O($$$n\sqrt {log(log(n)}$$$). Can you tell one that works in linear time.Counting sort

OK, that would work in this case, as it also depends on the range of input, won't work for larger ranges.

if you read my submission you can see that I didn't sort anything!!!

Can you explain your O(n) solution.

build a Linked List and every time you are removing a student remove him and his k left and his k right students from the Linked List.

But finding the max in remaining list will take O(n). so it will be O(n*n) solution.

You don't need to find that and nor need to sort it. Since all students are between 1 to N and occur exactly once just create an array to point out their location in the linked list.Whenever you remove a student just clear this pointer.Keep a pointer to last maximum player used and decrement this until a player which exists in the linked list!

Honestly for the first time I saw the use of linked list making a solution optimal. Very good approach

could you tell me about solution you mentioned in first line or provide a link (in problem G).

Such a fine editorial !

My approach to problem G :

let

G = gcd(A,B)

so we can writeA = GRB = GSNow,

lcm(A,B) = AB/gcd(A,B) = AB/G = GRSWe need to minimize

GRSHere G is common factors between two numbersRis uncommon factors in numberASis uncommon factors in numberBSo we iterate on

G(which will be <= 10^7) and for eachGwe store smallest two multiples ofGwhich are present in our array. Say those multiples areA,B.Now

G(A/G)(B/G)(lets denote it withZ) is our best possible answer withGas gcd.We find minimum value of

Zfor all the possible values ofGand print corresponding indices as required.NOTEThe declaration of

A = GRandB = GSrequiresRandSto be coprime (gcd(R,S) = 1).While finding

ZforG, We may havegcd(A,B) > Gbut it will always be multiple ofG(think why). Thusgcd(R,S) = kNow

gcd(A,B) = kG. Even if answerZstored forGwill beG(A/G)(B/G)=Gk,^{2}RSwhen calculation answer

ZforkG (G')as gcd we will getZasG'(A/G')(B/G')=kGRSwhich is actual answer.Link to my solution!

Ca you exaplain your code little bit?? Thanks in advance.

take a look at my code , I believe its the same idea for each x in range of 1e7 get the minimum two numbers ( a , b ) which are divisible by x

the answer will be ( a * b / x )

C++ Solution

My code was a bit messy! Thanks RamiZk for providing an excellent implementation! vivek_4_0 you can have a look at his implementation it's super clean and easy to understand.

My pleasure

What is the time complexity of your solution?

`O(Nlog(N))`

Thanks for the explanation! It helped :)

Glad I could help! :)

Really easy to understand :).

Successfully implemented my submission based on your approach. As per your

Note: So basically we are ignoring those G whose gcd(A, B) = kG, because, there will be a gauranteed G' which is gcd of same (A,B) but provides a better(minimum) LCM.Also, you don't need to check for

`if(m < a[i])`

and`if(m < b[i])`

, as this will never happen. (sincemis directely proportional tojgiven a fixedi). i.e. (my soln)Yup you got it right!

Yes I could have ignored that. Just a messy implementation on my part.

Thanks for sharing your implementation! :)

in problem c: why we take the modules day:=(day+1)%7 ?

To wrap around. Suppose start day is 5 and you want to iterate till 5 more days, doing day = day + 1 gives you 5, 6, 7, 8, 9(but you have only 7(0 to 6) days). When you do (day+1)%7, it wraps around after 6 like 5, 6, 0, 1, 2.

That because we want the index of the current day If you just increase it, day will be bigger than the last index of the vector (last index =6) so you want the day to go to the first element after the last one, so you put day%7 Let's say that the day =6 and there is nothing after 6 and you want it to go back to first element, day=(6+1)%7 = 0, and you are again on the index 0 Actually you also can do it like this : If day == 7: day = 0 :))

the problem G. As far as I know, $$$\sum_{i \le x}d(i) = O(x \log x)$$$, where $$$d(i)$$$ is the number of divisors of n. So time complexity is equal $$$O(a \log a)$$$, maybe it is equal $$$O(n \log a + a)$$$. Can you point me other $$$O(a \log a)$$$ simple solution?

In problem D, in the second example 6 2 1 1 0 0 1 0 1

How is the answer 3? It should be 5 right? Because we can use a battery in first segment so battery decreases by one and accumulator increases by one ==> b=1 , a=2. For the next 2 segments we use 2 accumulators ==> b=1,a=0. The for the fourth segment we use a battery ==> b=0,a=1.For the fifth we use the accumulator!

Can anybody explain how the answer is 3?

It is mentioned in the question that charge of accumulator cannot exceed it's maximum capacity. "If the current segment is exposed to sunlight and the robot goes through it using the battery, the charge of the accumulator increases by one

(of course, its charge can't become higher than it's maximum capacity)."So when we make first move using battery the charge of accumulator wont increment to 2 as it is already at it's maximum capacity (1).

I just figured it out and saw your comment. Thanks :)

Because it was said about optimization, I would like to give some. First, the provided code find all divisors any number $$$a$$$ in not $$$O(d(a))$$$, because to find one divisor required between $$$\Omega(k)$$$ and $$$O(d(n))$$$, where $$$k$$$ is the amount of unique prime divisors. it needs to be changed by itarative algorithm. Second it's necessary to sort the array a. I thinks both tips will reduce the running time.

Solution of E NlogN: https://codeforces.com/contest/1154/submission/52892001 Create segment Tree with = on segment and take maximum on segment Also create segment tree with add on segment and sum on segment And segment tree for calc Ans, with = on segment, and take value in the point

it's very hard way to solve this problem)) We can also solve it using set of pair (value, index) and two array left[n], right[n], which point for unchosen elemnts indexes of their left and right closest unchosen elements.

I know this, but I write them, because this hard, special for this))

Thanks for hosting the nice round. I don't quite understand the iterator part of the problem E. If I didn't read it wrong, the iterator

`--it`

and`++it`

are supposed to refer to the original index of the students. If it is so, how do we deal with cases when the next students the couch has to choose is out of reach of k steps (i.e. some of them in between have be chosen in previous rounds)?The students that already been chosen in between are getting removed from the set at the end of each turn. In the editorial, it is written that we iterate the "add" array (that holds all students that were picked in the current turn) and delete all students in the "add" array from the total students set. Thus, in the next turn, the "students in between" that have already been chosen aren't in the students set anymore.

I have changed my opinion about Div3 contests. In this contest the last 3 problem was intresting ans usefull for some experts, imho

Can Anyone help me finding bug in my Recursive DP approach on problem F : https://codeforces.com/contest/1154/submission/52944910 Thanks in Advance..

Update: Done !! Recursive DP solution: https://codeforces.com/contest/1154/submission/52951559

In problem F editorial can someone please explain this statement

"If shovel A is for free, then we may "swap" shovels A and C, otherwise we may swap shovels A and B, and the answer won't become worse"Can't understand the same :(

I think two swap A and C would mean

include C in previous offer instead of A and buy A in next offer. Similarly for A and B.F can be solved in O(k^2). First, any deals requiring us buy more than k shovels can be immediately discarded since the problem tells us to buy exactly k shovels. We are left with a subset of deals that have us buy between 1 and k shovels. This means that if we have an array deals[] with each element i corresponding to us having to buy i number of shovels we can simply find the maximum free for every index of this array. therefore, we since this array is size k, instead of running through every single deal, we only have to run through these, giving the solution a time complexity of k^2

Can you please elaborate your solution? I don't think only knowing the maximum amount of free shovels that can be bought will solve the problem.

https://codeforces.com/blog/entry/66560?#comment-506047

I tried to explain a similar solution to problem F here. Hope it helps!

Thanks a lot! It helped :)

Hi, In question D, the editorial says to use accumulator if we can't increase it and specifies if the optimal solution does this in reverse(using battery first at current time and accumulator ahead) then usage of battery does not grant us any additional charges and we can swap our decisions at this point, I am unable to wrap my head around this statement. Does this mean that had we used battery we would have battery capacity one less than now, and accumulator same, and if we don't use it then we have capacity on battery 1 more than it would have been in optimal solution but accumulator charge is one less, how is this a win-win situation ?

Hello can anyone explain this paragraph further more I can't get its idea:

Why should the sets of shovels for all purchases be consecutive subarrays? Suppose it's not so: let's pick two purchases such that they are "mixed" in the array of costs, i. e. there exists at least one shovel A bought in the first purchase such that there exists a shovel B cheaper than it and a shovel C more expensive than it, both bought in the second purchase. If shovel A is for free, then we may "swap" shovels A and C, otherwise we may swap shovels A and B, and the answer won't become worse. So, we can do it until all purchases correspond to subsegments in the array of costs.