Educational Codeforces Round 154 Editorial

#	User	Rating
1	ecnerwala	3649
2	Benq	3581
3	orzdevinwang	3570
4	Geothermal	3569
4	cnnfls_csy	3569
6	tourist	3565
7	maroonrk	3531
8	Radewoosh	3521
9	Um_nik	3482
10	jiangly	3468

#	User	Contrib.
1	maomao90	174
2	awoo	164
3	adamant	161
4	TheScrasse	159
5	nor	158
6	maroonrk	156
7	-is-this-fft-	152
8	SecondThread	147
9	orz	146
10	pajenegod	145

Tutorial

Solution (BledDest)

#include<bits/stdc++.h>
 
using namespace std;
 
int main()
{
	int t;
	cin >> t;
	for(int i = 0; i < t; i++)
	{
		string s;
		cin >> s;
		if(s.find("1") < s.find("3"))
			cout << 13;
		else
			cout << 31;
		cout << endl;
	}
}

1861B - Two Binary Strings

Idea: Roms

Tutorial

Solution (Roms)

#include <bits/stdc++.h>
 
using namespace std;
 
int main() {
    int t;
    cin >> t;
    for (int tc = 0; tc < t; ++tc) {
        string a, b;
        cin >> a >> b;
        bool ok = false;
        for (int i = 0; i + 1 < a.size(); ++i) {
            if (a[i] == b[i] && a[i] == '0' && a[i + 1] == b[i + 1] && a[i + 1] == '1') {
                ok = true;
            }
        }
        
        if (ok) 
            puts("YES");
        else
            puts("NO");
    }
    return 0;
}

1861C - Queries for the Array

Idea: BledDest

Tutorial

Solution 1 (Roms)

#include <bits/stdc++.h>
 
using namespace std;
 
const int N = 200000;
 
int main() {
    int t;
    cin >> t;
    for (int tc = 0; tc < t; ++tc) {
        string s;
        cin >> s;
        int maxSortedPref = 0;
        int minNotSortedPref = 0;
        int bal = 0;
        bool good = true;
        
        for (auto c : s) {
            if (c == '+') {
                ++bal;
            } else if (c == '-') {
                --bal;
                maxSortedPref = min(maxSortedPref, bal);
                if (bal < minNotSortedPref)
                    minNotSortedPref = 0;
            } else if (c == '1') {
                maxSortedPref = max(maxSortedPref, bal);
            } else {
                if (bal <= 1) {
                    good = false;
                    break;
                }
                if (minNotSortedPref == 0 || minNotSortedPref > bal)
                    minNotSortedPref = bal;
            }
            if(minNotSortedPref <= maxSortedPref && minNotSortedPref != 0) {
                good = false;
                break;
            }
        }
        
        if (good)
            puts("YES");
        else
            puts("NO");
    }
    return 0;
}

Solution 2 (BledDest)

#include<bits/stdc++.h>
 
using namespace std;
 
vector<int> has0, has1;
vector<vector<int>> g;
 
bool ans;
 
bool dfs(int x, int d)
{
	if(has0[x] && (has1[x] || d <= 1))
		ans = false;
	bool res = false;
	for(auto y : g[x])
		res |= dfs(y, d + 1);
	if(has0[x] && res)
		ans = false;
	return res || has1[x];
}
 
void solve()
{
	ans = true;
	has0.push_back(0);
	has1.push_back(0);
	g.push_back(vector<int>());
	int ts = 1;
	
	string s;
	cin >> s;
	vector<int> st = {0};
	for(auto x : s)
	{
		int cur = st.back();
		if(x == '0')
			has0[cur] = 1;
		if(x == '1')
			has1[cur] = 1;
		if(x == '+')
		{
			g[cur].push_back(ts);
			st.push_back(ts);
			ts++;
			has0.push_back(0);
			has1.push_back(0);
			g.push_back(vector<int>());
		}
		if(x == '-')
			st.pop_back();
	}
	
	dfs(0, 0);
	cout << (ans ? "YES\n" : "NO\n");
	
	has0.clear();
	has1.clear();
	g.clear();
}
 
int main()
{
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	int t;
	cin >> t;
	for(int i = 0; i < t; i++)
		solve();
}

1861D - Sorting By Multiplication

Idea: Roms

Tutorial

Solution (Roms)

#include <bits/stdc++.h>
 
using namespace std;
 
const int N = 200 * 1000 + 5;
 
int t;
int n;
int a[N];
 
int main() {
    cin >> t;
    for (int tc = 0; tc < t; ++tc){
    	cin >> n;
    	for (int i = 0; i < n; ++i)
    	    cin >> a[i];
    	
    	int cnt = 0;
    	for (int i = 1; i < n; ++i)
    	    cnt += (a[i - 1] >= a[i]);
    	    
    	int res = n, cnt2 = 0;
        for (int i = 0; i <= n; ++i) {
            bool isMultipliedByNegative = (i > 0);
            res = min(res, isMultipliedByNegative + cnt + cnt2);
            
            if (i + 1 < n)
                cnt -= (a[i] >= a[i + 1]);
            if (i > 0)
                cnt2 += (a[i - 1] <= a[i]);
        }
        
        cout << res << endl;
    }
}

1861E - Non-Intersecting Subpermutations

Idea: BledDest

Tutorial

Solution (BledDest)

#include<bits/stdc++.h>
 
using namespace std;
 
const int MOD = 998244353;
 
int add(int x, int y)
{
	x += y;
	while(x >= MOD) x -= MOD;
	while(x < 0) x += MOD;
	return x;
}
 
int sub(int x, int y)
{
	return add(x, -y);
}
 
int mul(int x, int y)
{
	return (x * 1ll * y) % MOD;
}
 
int binpow(int x, int y)
{
	int z = 1;
	while(y > 0)
	{
		if(y & 1) z = mul(z, x);
		x = mul(x, x);
		y /= 2;
	}
	return z;
}
 
int main()
{
	int n, k;
	cin >> n >> k;
	int ans = 0;
	vector<vector<int>> dp(n + 1, vector<int>(k, 0));
	dp[0][0] = 1;
	for(int i = 0; i < n; i++)
	{
		int cur = 0;
		for(int j = k - 1; j >= 1; j--)
		{
			cur = add(cur, dp[i][j]);
			dp[i + 1][j] = cur;
		}
		for(int j = k - 1; j >= 0; j--)
		{
			int nxt = (j + 1) % k;
			dp[i + 1][nxt] = add(dp[i + 1][nxt], mul(dp[i][j], k - j));
		}
		ans = add(ans, mul(dp[i + 1][0], binpow(k, n - (i + 1))));
	}
	cout << ans << endl;
}

1861F - Four Suits

Idea: BledDest

Tutorial

Solution (BledDest)

#include<bits/stdc++.h>
 
using namespace std;
 
const int K = 4;
const int N = 2 * int(1e6) + 43;
 
pair<long long, long long> operator+(const pair<long long, long long>& a, const pair<long long, long long>& b)
{
	return make_pair(a.first + b.first, a.second + b.second);
}
 
pair<long long, long long> operator-(const pair<long long, long long>& a, const pair<long long, long long>& b)
{
	return make_pair(a.first - b.first, a.second - b.second);
}
 
// prefix sums for an array of pairs
vector<pair<long long, long long>> pref_sums(const vector<pair<long long, long long>>& a)
{
	int n = a.size();
	vector<pair<long long, long long>> ans(n);
	ans[0] = a[0];
	for(int i = 1; i < n; i++)
		ans[i] = ans[i - 1] + a[i];
	return ans;
}
 
// for an array of pairs denoting linear functions, evaluate
// them in the corresponding points
vector<long long> eval(const vector<pair<long long, long long>>& a)
{
	int n = a.size();
	vector<long long> ans(n);
	for(int i = 0; i < n; i++)
		ans[i] = a[i].first * i + a[i].second;
	return ans;
}
 
void solve()
{
	int n;
	scanf("%d", &n);
	vector<vector<int>> a(n, vector<int>(K));
	for(int i = 0; i < n; i++)
		for(int j = 0; j < K; j++)
			scanf("%d", &a[i][j]);
	vector<int> b(K);
	for(int i = 0; i < K; i++)
		scanf("%d", &b[i]);
	
	int deck_size = 0;
	for(int i = 0; i < K; i++)
		deck_size += b[i];
	
	// calculate the remaining number of cards for each player
	long long full = deck_size;
	for(int i = 0; i < n; i++)
		for(int j = 0; j < K; j++)
			full += a[i][j];
	vector<int> remain(n, full / n);
	for(int i = 0; i < n; i++)
		for(int j = 0; j < K; j++)
			remain[i] -= a[i][j];
	
	// for every player, calculate the maximum number of cards
	// they already have among all suits
	// and store it in a multiset
	vector<int> min_val(n);
	for(int i = 0; i < n; i++)
		min_val[i] = *max_element(a[i].begin(), a[i].end());
	multiset<int> min_vals;
	for(int i = 0; i < n; i++)
		min_vals.insert(min_val[i]);
	
	// for every mask of suits and every player, calculate
	// the number of cards in those suits they already have
	vector<vector<int>> already_has(1 << K, vector<int>(n));
	for(int mask = 0; mask < (1 << K); mask++)
		for(int i = 0; i < n; i++)
			for(int j = 0; j < K; j++)
				if(mask & (1 << j))
					already_has[mask][i] += a[i][j];
	// for every mask of suits and every player, calculate the
	// maximum value of x such that if that player can receive 
	// no more than x cards in each suit, the vertex of that
	// player should belong to T in the cut
	vector<vector<int>> max_x(1 << K, vector<int>(n));
	for(int mask = 0; mask < (1 << K); mask++)
		for(int i = 0; i < n; i++)
		{
			int suits = __builtin_popcount(mask);
			if (suits == 0) max_x[mask][i] = N - 2;
			else
			{
				// incoming edges have capacity of
				// x - a[i][j]
				int incoming = -already_has[mask][i];
				// outgoing edge has capacity of remain[i]
				// find the maximum x such that
				// suits * x + incoming < remains[i]
				int x = (remain[i] - incoming) / suits;
				x = min(x, N - 2);
				max_x[mask][i] = x;
			}
		}
	
	// for every mask and for all players, calculate the sum of 
	// values they add to the cut if they can have no more than
	// x cards of each suit in the mask
	vector<vector<long long>> add_to_cut(1 << K, vector<long long>(N));
	for(int mask = 0; mask < (1 << K); mask++)
	{
		int suits = __builtin_popcount(mask);
		vector<pair<long long, long long>> aux(N);
		for(int i = 0; i < n; i++)
		{
			// for the i-th player, they add remains[i] to
			// the minimum cut if x > max_x[mask][i]
			// otherwise, they add
			// suits * x - already_has[mask][i]
			int incoming = -already_has[mask][i];
			// add [suits * x - incoming] on segment [0, max_x]
			int x = max_x[mask][i];
			pair<long long, long long> f1 = {suits, incoming};
			aux[0] = aux[0] + f1;
			aux[x + 1] = aux[x + 1] - f1;
			// add remain[i] on [max_x + 1, N)
			pair<long long, long long> f2 = {0, remain[i]};
			aux[x + 1] = aux[x + 1] + f2;
			aux[N - 1] = aux[N - 1] - f2;
		}
		// sum up those functions and evaluate them
		add_to_cut[mask] = eval(pref_sums(aux));
	}
	
	// now we're ready to solve the problem!
	vector<int> ans(n);
	// iterate on the player we want to maximize
	for(int i = 0; i < n; i++)
	{
		// iterate on the suits they will maximize
		for(int j = 0; j < K; j++)
		{
			int d = min(remain[i], b[j]);
			int max_cards = a[i][j] + d;
			b[j] -= d;
			// find the maximum current score over all others
			min_vals.erase(min_vals.find(min_val[i]));
			int max_rival = *min_vals.rbegin();
			min_vals.insert(min_val[i]);
			if(max_rival >= max_cards)
				ans[i] = max(ans[i], 0);
			else
			{
				// binary search on the maximum cards over all
				// opponents
				int L = max_rival - 1;
				int R = max_cards;
				while(R - L > 1)
				{
					int mid = (L + R) / 2;
					long long min_cut = 1e18;
					long long req_flow = deck_size - remain[i];
					// iterate on the mask of suit vertices
					// which belong to S
					for(int mask = 0; mask < (1 << K); mask++)
					{
						int suits = __builtin_popcount(mask);
						long long cur_cut = 0;
						for(int z = 0; z < K; z++)
							if(!(mask & (1 << z)))
								cur_cut += b[z];
						cur_cut += add_to_cut[mask][mid];
						// don't forget to discard our player
						// from the flow network!
						if(mid > max_x[mask][i])
							cur_cut -= remain[i];
						else
						{
							long long add = mid * suits - already_has[mask][i];
							cur_cut -= add;
						}
						min_cut = min(min_cut, cur_cut);
					}
					if(min_cut < req_flow)
						L = mid;
					else
						R = mid;
				}
				ans[i] = max(ans[i], max_cards - R);
			}
			b[j] += d;
		}
	}
	
	for(int i = 0; i < n; i++)
		printf("%d ", ans[i]);
	puts("");
}
 
int main()
{
	int t = 1;
	for(int i = 0; i < t; i++) solve();
}

#include <bits/stdc++.h> using namespace std; #define all(v) (v).begin(), (v).end() void solve(); signed main() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout.setf(ios::fixed); cout.precision(10); srand(time(NULL)); long long t; cin >> t; while (t--) { solve(); } } void solve() { string s; cin >> s; long long n = s.length(); if (n == 1) { if (s[0] == '0' || s[0] == '-') cout << "NO" << endl; else cout << "YES" << endl; return; } long long flag0 = 0; long long flag1 = 1; long long count = 0; for (long long i = 0; i < n; i++) { if (s[i] == '+') { if (flag0 > 0) flag0++; flag1 = 0; count++; } else if (s[i] == '-') { count--; flag0 = max(0LL, flag0 - 1); } if (s[i] == '0') { if (count <= 1 || flag1) { cout << "NO" << endl; return; } if (flag0 == 0) flag0 = 1; } if (s[i] == '1') { if (flag0) { cout << "NO" << endl; return; } flag1 = 1; } } cout << "YES" << endl; }

void solve() { str s; cin >> s; stack<char> st; int nz = 0; for (int i = 0; i < s.length(); i++) { if (s[i] == '+') { st.push(s[i]); } else if (s[i] == '-') { if (st.empty()) { cout << "NO" << endl; return; } else { if (st.top() == '1' || st.top() == '0') { if (st.top() == '0') nz--; st.pop(); st.pop(); } else st.pop(); } } else { if (st.size() < 2) { if (s[i] == '0') { cout << "NO" << endl; return; } } else { if ((st.top() == '1' && s[i] == '0') || (st.top() == '0' && s[i] == '1')) { cout << "NO" << endl; return; } if (s[i] == '1' && nz != 0) { cout << i << " " << "hello" << endl; cout << "NO" << endl; return; } if (s[i] == '0') { nz++; } if (st.top() == '+') st.push(s[i]); } } } cout << "YES" << endl; }

Comments (50)

Write comment?

SunnyYuan2009

8 months ago, # |

← Rev. 3 →

+27

These solutions explain very clearly.

I'm sad I didn't AC problem D, but it is interesting!

→ Reply

Dr.Mahareeq

+15

thanks for the tutorial

Kirilliym

+12

Good problems, thanks for the round!

imprayas12

← Rev. 2 →

"BledDest is a graph theory lunatic" had me cracked up.

1ightwhite

8 months ago, # ^ |

The point is that the sentence's coming from himself.

JohanXLiebert

Test 3,682nd test case->great work in testing!

ash88

+13

D was looking hard but it is easy

areke

Another easy way to implement E is to just combine the last two states into one. So $$$dp_{i,j}$$$ counts how many of arrays of length $$$i$$$ exist such that the number of elements on the suffix we use is $$$x \equiv j \pmod k$$$ and the current cost of the array is $$$c = j\ /\ k$$$. Then the transitions are the same, but you just reset the partial sum whenever $$$j \equiv 0 \pmod k$$$ since you can never transition to a lower cost.

Submission: 221342327

Aftershock007

Thanks this is really helpful

attky

In problem C, if you have : ++++1-0 when we verify the number elements in the array we have 3 elements but the array has to be sorted.

Edit : I misunderstood the second condition

otiko_lagadze

during contest i had some trouble implementing C (i had same idea as described in approach 1) and using segment trees seemed easier to me. Idea is identical as described in approach 1 but it was easier for me to implement this way, so i thought of sharing it: code.

Legend_11

-19

Can anyone tell me what is wrong with this solution to problem C. Thank you in advance

butterflies

Hi all, it would really help if you can post some insights/hints for the problems of this contest on https://starlightps.org ! Here's a link to the problems: https://starlightps.org/problems/collection/cf-edu-154/. This will help us get more data so users can have a platform to:

share/discover hints/insights on various problems
find similar problems given insights they struggled with.

Check it out if you're interested. Thanks!

recursive_rebel

-11

what is the error in this code, getting WA in test 3, for problem C. I have used a stack-based approach.

hamossa

Can someone find out what is wrong with my code problem c 221486376

variety-jones

Take a look at Ticket 17062 from CF Stress for a counter example.

bigbanginmyhouse

Kevin114514 , How can you make A this much complicated ? His submission (221392540)

ddamel

awoo,BledDest I think in tutorial of problem E, in the paragraph before the last, you should have written: "difference is: $$$dp_{i,j,c}$$$", instead of $$$dp_{i,j+1,c}$$$

because we have according to the second type of transitions

$$$dp_{i+1,j} <== d_{i,j} + d_{i,j+1} + ... + dp_{i,k-1}$$$

$$$dp_{i+1,j+1} <== d_{i,j+1} + d_{i,j+2} + ... + dp_{i,k-1}$$$

difference: $$$dp_{i+1,j}-dp_{i+1,j+1} = dp_{i,j}$$$ and not $$$dp_{i,j+1}$$$

I hope I'm not mistaking, but correct me if I'm wrong...

thx

BledDest

Thank you, this is an error. Will be fixed in a couple of minutes

Siyah

woww clear editorial , tnx awoo , BledDest

I_FloPPed21

at problem B wouldnt the example a = 00010000 b = 00011111 give a no?

ignore the question I didnt read that it ends with 1 and starts with 0

MohamedSameh

thank you for the editorial It was really helpful, I have a question How on earth did you come up with that idea of the last x elements on problem E, You assumed some number and built the dp table on the assumed number, it is my first time to see such a thing I Don't think this sort of things come from practice, and the amazing thing is that most of accepted solutions are the same idea, Is that I'm too dump or you are too smart? Thank You :D

MountainKing

Why you most of the times post the editorial late, it is expected that you should post the editorial as soon as the hacking phase in over.

Sparsely

The title for D in the tutuorial text is Russian, not English. awoo fix it pls, thx

deydhananjoy5

Roms very clean and readable code. Thanks.

stalkkk_19

Hey Author,

I am in trouble to get the Problem B

according to me for the test case

1
1000101
1000100

I am not able to find the way to make this same : (

but according to the Author code

it is printed YES

Can anyone know how to make this equal ??

anonymous_yuvi

According to the question .. both the strings should start with 0 and end with 1's.

So your test case is wrong.

k200154

What's wrong with this solution for C?

1xx55

In your code dealing with '-' :

if (!unsorted.empty() && elements < unsorted.back())
            unsorted.pop_back();

IF shoule be replaced by WHLIE , for the cases like this : ++++000-1 , you need to pop back more than once.

Then your code will get accepted. :)

Thanks!

Ahmed_Ashraf_f

Any one could help me I don't know what is the wrong in this solution

https://codeforces.com/contest/1861/submission/221355113

++++1-0

thanks

Noobish_Monk

Can someone please explain, what is the partial sum technique mentioned in E and why is it true?

detective...dots

← Rev. 6 →

For problem D can someone explain how can this be sorted in 4 operations? n = 9, a = [10 5 10 9 6 9 8 9 5]

Srbmaury

l=1,r=2,x=3   30  15  10  9  6  9  8  9  5 
l=1,r=4,x=-1 -30 -15 -10 -9  6  9  8  9  5
l=7,r=8,x=2  -30 -15 -10 -9  6  9 16 18  5
l=9,r=9,x=4  -30 -15 -10 -9  6  9 16 18 20

Thanks

grand__warden

Problem C Approach 1(Roms) Can anyone explain why we need to check it after each query? After each query, we can just check that the longest sorted prefix is shorter than the shortest non-sorted prefix

zym

If the current query is '1', then make longest sorted prefix equal current length, which is consistent with the current query. And the shortest non-sorted prefix is consistent with the previous queries. If longest sorted prefix is shorter than the shortest non-sorted prefix, it means the current query is valid based on the previous queries.

If the current query is '0', then make shortest non-sorted prefix=min(shortest non-sorted prefix, cur_length), which is consistent with the current query. Then check the inequality.

armennarkoman

Seems like this editorial doesn't explain why there is no better solution in problem D, which makes prefix with length x negative by several multiplications on negative number

hydra_cody

7 months ago, # ^ |

← Rev. 4 →

HELP, Can anyone prove the solution to Problem D. Why does this approach give an optimal solution? Thanks.

Shaadsajjad

7 months ago, # |

Why Was My Submission Skipped Despite Submitting First https://codeforces.com/blog/entry/120756

jaineshmachhi

Can anyone help me in which test case is this solution going wrong it shows WA on 303 (test case 3)

lyh3.14

6 months ago, # |

I have an easier solution for E.

We can use dp in one dimension. Dp[i] means how many arrays with length i has the subarray from i-k+1 to i, which contains integers 1~k. Fac[i] means the factorial from 1 to i. Pw[i] means the i-th power of k.Every time, dpi has initial value fac[k] * pw[i-k]， because we chose number from 1~k optionally to fill the position 1 ~ i-k+1, and from 1-k+1 to i, the ways is equal to an arrangement of 1~k.

But this may cause duplication, for example. n = 4, k = 3 and for the array 1 2 3 1, we will calculate the contribution in both dp[3] and dp[4], but the cost of this array is 1. To solve this, when we calculate dp[i], we need to minus dp[j] which j is from i — k + 1 to i — 1. Actually we need to minus dp[j] * fac[i-j] because dp[j] only caluculate array of length j. From the position j+1 to i, the ways we fill it is equal to an arrangement of 1~i-j.

Submission: Code

DuongForeverAlone

4 months ago, # ^ |

Your solution is brilliant, although I don't know why the answer is sum of all dp[i] * Pow(k, n — i). It looks like taking any possible from the rest n — i elements, but it will be confused, as I don't know whether there is any duplication or not. Could you explain this part?

Alex_Sense1

5 months ago, # |

In the BledDest approach for problem C, specifically in this line:
"In terms of our tree, it means that a vertex marked with 0 has an ancestor (possibly itself) marked with 1."
Shouldn't it be the other way? find a vertex marked with 1 that has an ancestor marked with 0?

Fugally787

2 months ago, # |

For C, what about the condition where something that is unsorted, is a prefix of something that's unsorted? Isn't that an automatic 'NO' as well?

For example, we have a 1, then we delete some characters without adding any, then we have a 0. That couldn't happen.

DangKhoizzzz

4 days ago, # |

someone know why this submission keep wrong on test 3 problem C pls

my submission

awoo's blog