pikmike's blog

Educational Codeforces Round 98 Editorial
By pikmike, history, 6 days ago, translation, In English

1452A - Robot Program

Idea: BledDest

Tutorial
Solution (BledDest)

1452B - Toy Blocks

Idea: adedalic

Tutorial
Solution (adedalic)

1452C - Two Brackets

Idea: BledDest

Tutorial
Solution (pikmike)

1452D - Radio Towers

Idea: BledDest

Tutorial
Solution (BledDest)

1452E - Two Editorials

Idea: BledDest

Tutorial
Solution (pikmike)

1452F - Divide Powers

Idea: adedalic

Tutorial
Solution (adedalic)

1452G - Game On Tree

Idea: adedalic

Tutorial
Solution 1 (pikmike)
Solution 2 (BledDest)
 
 
 
 
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Comments Comments (82)
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6 days ago, # |
  Vote: I like it +18 Vote: I do not like it

What about rating updates?

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6 days ago, # |
  Vote: I like it +28 Vote: I do not like it

I think, in tutorial G, Alice and Bob had been swapped. It's Alice who has one starting vertex, and it's Bob who chases her, not vice versa.

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    6 days ago, # ^ |
    ← Rev. 2   Vote: I like it +10 Vote: I do not like it

    Oh, indeed. I've been told the problem with them reversed and I haven't read the actual statement haha. Will fix in a sec, thanks.

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6 days ago, # |
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Can anyone explain problem A's solution a bit more. I couldn't get it!

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    6 days ago, # ^ |
      Vote: I like it -8 Vote: I do not like it

    See let min(x,y)=a

    Then, we can first go to (a,a) in exactly a*2 steps. After that we just have to increment in one direction and the best way to do that is by first waiting then moving because it always takes comparatively less number of steps,i.e, 2.

    Also note we can always reach (a,a) in two possible ways by first moving right or left, so when we take steps from (a,a) we can always increment one step without waiting.

    So, answer is (a*2)+1+max(y-x-1)*2 when (y-x-1)>=0 else answer is simply (a*2) when x==y

    You can look at my submission 98961942. Hope you find it helpful !

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      3 days ago, # ^ |
      ← Rev. 3   Vote: I like it 0 Vote: I do not like it

      can we write second condition when x!=y as 2*max(x,y)-1 ?? if not please give some examples sorry i didn't read the editorial before

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6 days ago, # |
  Vote: I like it 0 Vote: I do not like it

why i get tle in test case 20 of problem E

my submission : 99017296

logic

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    6 days ago, # ^ |
      Vote: I like it +5 Vote: I do not like it

    Comparator for sorting should follow strict weak ordering. If $$$a=b$$$ then it should always return false, otherwise it's undefined behavior.

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6 days ago, # |
← Rev. 3   Vote: I like it +14 Vote: I do not like it

If anyone didn't understand B. Here is an easy solution-

For solution to exist let us consider an element any index i. Then, for solution to exist we should be able to increment all values at all indexes to the max value in the array because we can't decrement the max value anyway.

Thus, a[i]>=(a[max]-a1)+(a[max]-a2)......(a[max]-a[max])
or, a[i]>=a[max]*n-1-(S-a[i]) where S is total sum of all elements.
or, S>=a[max]*n-1;

So solution boils down to two cases-

1. When S<a[max]*n-1 then the answer is just the difference of these two.

2. If S>a[max]*n-1 then (S-a[max]*n-1) should be equally divisible by (n-1), so just increment S until divisible by (n-1) and the answer is difference of the two.

You can look at my submission here

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6 days ago, # |
  Vote: I like it -39 Vote: I do not like it

My code gives me wrong answer in test case 3 any one help Question no B

void solve() { ll n; cin>>n;

ll a[n];
ll mx = 0 ;
for (ll i= 0;i<n;i++)
{
    cin>>a[i] ;
    mx = max(mx, a[i]);
}

if (n==2)
{
    cout<<0<<endl;
    return ;
}

ll sum = accumulate(a , a+n , 0) ;

ll temp = mx*(n-1)*(1ll) ;

if (sum == temp)
cout<<0<<endl;
else if(sum <temp)
cout<<abs(sum-temp)<<endl;
else
{
    for (ll i=1;i<=100000;i++)
    {
        if (((n-1)*i*(1ll)) == sum)
        {
            cout<<0<<endl;
            return ;
        }
        else if (((n-1)*i*(1ll)) > sum)
        {
            cout<<(abs(n-1)*i*(1ll) - sum)<<endl;
            return;
        }
    }
}

}

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6 days ago, # |
  Vote: I like it 0 Vote: I do not like it

Proof by Induction for problem D is great but can someone tell me if there is a mathematical proof for that?

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    6 days ago, # ^ |
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    If we have a tower with power p, it will cover 2p-1 spots, thus the length of the subsegment covered by a tower is always odd.Now we need to find a way to divide a length of n into a number of odd length subsegments. This can be done via dynammic programming, which reduces to finding the nth Fibonacci number. In the end , just divide this by 2^n.

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      6 days ago, # ^ |
      ← Rev. 2   Vote: I like it 0 Vote: I do not like it

      I'm sorry but I didn't need the proof for the solution to this problem. I was wondering how did that function get reduced to just finding the Fibonacci number for a particular input.(which was proved by Induction by the Editorialist)

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        6 days ago, # ^ |
          Vote: I like it +19 Vote: I do not like it

        f(n) = f(n-1) + f(n-3) + f(n-5) + .... f(n-2) = f(n-3) + f(n-5) + .... thus f(n) = f(n-1) + f(n-2) Is this what you were looking for?

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          6 days ago, # ^ |
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          Yeah exactly, thanks for putting it that way. Made it so easy to understand.

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        6 days ago, # ^ |
          Vote: I like it +14 Vote: I do not like it

        Here's the intuitive proof I came up with while upsolving.

        First let's solve it like a normal dp problem (forgetting about the fibonacci numbers). We sweep from left to right. Let $$$dp[i]$$$ mean the number of ways to cover only the first $$$i$$$ positions.

        How do our transitions work? First, $$$dp[0] = 1$$$ because there is one way to cover the first $$$0$$$ positions (don't have any towers at all). Now loop over all i's (from left to right).

        Consider the current $$$dp[i]$$$. We can cover some range with exactly one tower if and only if the length of the segment is odd (so we can put the tower in the midpoint). So $$$dp[i]$$$ is equal to the sum of all dp values where the index has a different parity than i (so $$$dp[i] = dp[i-1]+dp[i-3]+dp[i-5]...$$$). Though this would work, it runs in $$$O(n^2)$$$, so it needs to be optimized.

        The optimization is pretty simple. Because you don't care about the actual values of all previous dp's but just the parity. So instead of storing the whole dp array, just have it store 2 values, $$$dp[0]$$$ and $$$dp[1]$$$. $$$dp[0]$$$ stores the numbers of ways to cover an even prefix, and $$$dp[1]$$$ stores the number of ways to cover an odd prefix.

        You still loop from 1 to n but the transitions are now $$$dp[i \mod 2] = dp[i \mod 2] + dp[1-(i \mod 2)]$$$. This is exactly the Fibonacci recurrence.

        Hope this was helpful! Thanks!

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          6 days ago, # ^ |
            Vote: I like it +1 Vote: I do not like it

          That's a really nice way to think about it. Thanks.

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          5 days ago, # ^ |
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          hey thanks for sharing your idea . I have implemented the same idea with bottom up DP. but i am not able to do the same with top down DP. Can you please help me with that ?

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          4 days ago, # ^ |
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          @PurpleCrayon how did you come up with the idea that dp[i] is equal to the sum of all dp values where the index has a different parity than i ??

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          31 hour(s) ago, # ^ |
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          Nice explanation!

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    6 days ago, # ^ |
      Vote: I like it +2 Vote: I do not like it

    I had a different approach to this problem which is quite intuitive imo. We are effectively choosing a subset out of $$$n$$$ towers such that the sum of powers of those towers cover the entire range $$$1-n$$$.This is equivalent to number of odd integral solutions of the equation $$$ p_1 + p_2 + ... + p_r = n $$$.This can be found out easily by converting it to the form $$$ (2*x_1 + 1) + (2*x_2 + 1) + .. + (2*x_r + 1) = n $$$ and finding non negative integral solution for $$$x_1 , x_2 ,... x_r$$$. Multiply this with the probability of choosing $$$r$$$ towers = $$$1/{2^{n}}$$$ to get the required answer solution

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      5 days ago, # ^ |
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      Thank you very much! It's a great solution.

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      4 days ago, # ^ |
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      i am sorry, this might sound dumb but in you solution , ncr(d+x-1,x-1) here what are you actually choosing and from what

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        4 days ago, # ^ |
          Vote: I like it 0 Vote: I do not like it

        number of non negative integral solutions of the equation $$$x_1 + x_2 + ... +x_r=d$$$ is $$$d+r-1\choose r-1$$$

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6 days ago, # |
← Rev. 2   Vote: I like it +5 Vote: I do not like it

Why this Solution do not get TLE in problem G? I solved only with bfs/dfs. There is some property?

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    4 days ago, # ^ |
    ← Rev. 3   Vote: I like it +5 Vote: I do not like it

    As in Tutorial, this solution is at most $$$O(nlog^2n)$$$

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6 days ago, # |
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@BledDest Can you give more explanation how problem D can be solved. I didn't get the point how the probability can be considered as Fibonacci number. Please help me to understand.

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6 days ago, # |
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In Problem D Editorial

How this statement is true?

Covering all towns can be expressed as splitting n into the sum of several positive odd integers

Anyone, Please Explain.

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    6 days ago, # ^ |
      Vote: I like it +1 Vote: I do not like it

    Each town that has power must power itself, and an equal number of towns either side of it.

    Suppose it powers K towns to its left, then it must also power K towns to its right. So in total it powers 2*K+1 towns.

    All the towers together power N towns, and the set is partitioned such that no town is powered twice. As such,

    N = sum (i = 1 to j) (2*Ki + 1), where there are j towns receiving power directly, and the ith town powers Ki either side of it.

    The numerator of the answer is the number of unique sets of j and K1,...,Kj such that the equality holds.

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6 days ago, # |
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What is the logic of taking max of the array in calculation of k for B?

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    6 days ago, # ^ |
      Vote: I like it 0 Vote: I do not like it

    We need an end state where each of the n-1 boxes has exactly (TOTAL)/(n-1). Suppose we choose one of the non-max boxes to redistribute: then all the boxes must have at least the max starting value, since we cannot take any away. Therefore max*(n-1) is a lower bound for the total number.

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      2 days ago, # ^ |
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      yeah but why would there be atleast max in each box?

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        47 hours ago, # ^ |
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        Because if there is one box with max, we can't take any out of this box (if redistributing from any of the others). So that box must finish with at least max, and we require all the boxes to finish with the same number, so they must also have at least max.

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6 days ago, # |
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i successfully solved 1st problem by this=> ```

ll t;
cin >> t;
while (t--) {
    ll x, y;
    cin >> x >> y;
    ll z = abs(x - y);
    ll ans = (x + y) + ((z > 0) ? z - 1 : 0);
    print(ans);
}

``` but i am thinking can it be solvable using dp like other grid paths problem? i am new at dp so i am having a hard time to think about it.so can anyone help me with this if it is possible to solve using dp

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    5 days ago, # ^ |
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    I have solved using dp. The idea is that the points on the diagonal(assume it is {x,x}) will always take x+x = 2*x. Other points can be reached from diagonal by this sequence. At diagonal -> Move -> Stop -> Move -> Stop

    #include <bits/stdc++.h>
#define ll long long
const unsigned int mod = 1000000007;
using namespace std;

int main() {
    int t; cin>>t;
    // Store the steps taken to reach diagonals
    vector<int> dp(10001,0);
    for(int i=1;i<=10000;i++)
        dp[i] = 2*i;
    while(t--)
    {
        int x,y; cin>>x>>y;
        if(x==y) {
            cout<<x+y<<endl;
        }
        else if(x<y) {
            int ans = dp[x] + (y-x)*2 - 1;
            cout<<ans<<endl;
        }
        else if(x>y) {
            int ans = dp[y] + (x-y)*2 - 1;
            cout<<ans<<endl;
        }
    }
    return 0;
}
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6 days ago, # |
  Vote: I like it +3 Vote: I do not like it

IN PROBLEM B Why (a.sum() + n — 2) / (n — 1) and not (a.sum()) / (n — 1) i didn't get it

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    6 days ago, # ^ |
      Vote: I like it 0 Vote: I do not like it

    the formula to get ceil of(x/y) is (x+(y-1))/y

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      5 days ago, # ^ |
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      Okk. But when I write ceil function, ceil(x/y), it throws an error, but writing (x+y-1)/y goes successful.

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        5 days ago, # ^ |
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        Maybe you forgot to cast long double/float/double type to this fraction. For example: ceil(5 / 2) = ceil(2) = 2, but ceil(5.0 / 2) = ceil(2.5) = 3.

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        4 days ago, # ^ |
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        But actually you should never try to use floating point numbers then use ceil, always opt to integer operations if possible.

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6 days ago, # |
← Rev. 2   Vote: I like it -13 Vote: I do not like it

Why does this give same results, in modular exponentiation?

ll powe(ll x, ll y){
x = x%mod, y=y%(mod-1);
ll ans = 1;
while(y>0){
if (y&1){
ans = (1ll * x * ans)%mod;
}
y>>=1;
x = (1ll * x * x)%mod;
}
return ans;
}

than this

ll powe(ll x, ll y){
x = x%mod;
ll ans = 1;
while(y>0){
if (y&1){
ans = (1ll * x * ans)%mod;
}
y>>=1;
x = (1ll * x * x)%mod;
}
return ans;
}

The only difference is we do y=y%(mod-1) in the first function.

Edit: figured it out its fermat's theorem, thanks everyone

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    6 days ago, # ^ |
      Vote: I like it +1 Vote: I do not like it

    Why don't people use spoiler while commenting there code?

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    6 days ago, # ^ |
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    Isn't your question obvious, let say we want to compute 2^123097521478997542 mod m, then what do you think will be faster computing 2^123097521478997542 mod m or first compute y mod m-1 which will be smaller than equal to y, then compute power?

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    4 days ago, # ^ |
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    The answer is obvious, but I remember there was a problem in which the input size it self exceeds mod-1 and everyone who did pow=pow%(mod-1) in advance got WA, be careful.

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      4 days ago, # ^ |
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      I'm sorry community, I framed it wrong, I actually meant why both lead to same answer.

      A friend of mine later told me its Little Fermat's theorem.

      This was my first comment in codeforces, wasn't aware about the comment standards we need to maintain, are there any resources, on how questions be asked and all?

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6 days ago, # |
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In D problem, if there are 5 cities, the number of ways to break it into sum of odd positive integer is (3)1,3,1 which shows that there are 3 ways,Can anyone help me in understanding how is it the nth fibonacci ie (5)?

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6 days ago, # |
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Why solutions with complexity O(nmk) can get AC for problem E? The example are below: submission 1 and submission 2

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6 days ago, # |
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Can someone explain problem E's solution a bit more.Thanks in advance! xD!!

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5 days ago, # |
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in the editorial of problem b the first para [ceil(sum/n-1)] is the condition when the nephew chooses the box containing the maximum block, right?

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    5 days ago, # ^ |
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    Yes it is the block with max toys after you have added toys.

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5 days ago, # |
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Problem E,why the solution is right?I spend a long time understanding the code,but can't prove it's correctness.The tutorial seems to ignore this.

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    5 days ago, # ^ |
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    you may think that algorithm is incorrect because of prefix and suffix and that one of them may contain some element which should have been in the other one but it doesn't matter because answer for cases like this will not be the final answer anyway because we are considering all possibilities and final answer will be the case where the conditions are satisfied.

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      5 days ago, # ^ |
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      oh!miaoa~zhenbuchuo!thank you for your reply!

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5 days ago, # |
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Why i get tle for B?

submission : 99050069

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    5 days ago, # ^ |
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    whatever error you meet,you can see the data,the data you tle has sum=5e9,and n-1=4,and ma=1e9,your ma should add many times before you can break,so you tle

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5 days ago, # |
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There is another nice approach to Problem D using combinatorics.

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5 days ago, # |
← Rev. 3   Vote: I like it 0 Vote: I do not like it

For the problem D

how can we find the number of ways in which N can represented as sum of odd integers as mentioned in the editorial ??: To be specific using the following method

It can be calculated with dynamic programming with prefix sums.
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4 days ago, # |
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can anybody explain me ...in the problem toy blocks , why are you adding (n-2) to the array sum ? i.e. 4th line in fun main() function

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    2 days ago, # ^ |
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    ceil function, that is to get the smallest greater integer.

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      2 days ago, # ^ |
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      So Can't we use directly ceil() function available in header cmath ?

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        2 days ago, # ^ |
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        Since these are integers, ceil function wont work here.

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4 days ago, # |
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And everyone ignored the pun in editorial of B. Not I but you.

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3 days ago, # |
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Can anyone help me on the modular division given in solution of the problem d?Specifically why he has used 'mod-2' during the divide process?? Any document is also helpful...

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3 days ago, # |
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cin >> a >> b; cout << a + b + abs(a — b) — (a ^ b ? 1 : 0) << endl;

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30 hours ago, # |
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Why the divide function in problem D is mul(x, binpow(y, MOD — 2)) ? I understand the idea behind mul() and binpow(), but why they can perform the divide operation?

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    6 hours ago, # ^ |
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    It uses Fermat's little theorem to calculate Modular multiplicative inverse.

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