netman's blog

Codeforces Round #260 — Editorial
By netman, 10 years ago, translation, In English

Warning: my English is very bad.

456A - Laptops

Solution: 7407613;

In this task you need to check the existense of such pair i and j, such that i ≠ j, a[i] < a[j], b[i] > b[j]. If such i and j exist, Alex is happy.

There is very simple solution. Let's check that for all i a[i] = b[i]. If this condition is true we should print "Poor Alex". We can easy prove it. Let's sort arrays a and b like pair of numbers in increasing order. We can see that Alex is happy if we have at least one inversion in array b, i.e there is such pair i and j that b[i] > b[j] и i < j (). i.e it means that array b is not sorted and it's means that a ≠ b.

456B - Fedya and Maths

Solutions: 7407625, 7407631;

In this task you need to calculate formula that given in the statement, but it's hard to calculate it with the naive way.

But we can transform our formula to this:

This formula is right because 5 is prime number and it's coprime with 1, 2, 3, 4.

φ(5) = 4

To solve this task we should be able to calculate remainder of division n by 4 and calculate formula for small n.

Asymptotics — .

There is also another solution. It uses a fast exponentiation, but not binary exponentiation. The idea of this exponentiation is the same as that of the binary exponentiation. Let we want to fast calculate xnmodP. Algorithm is very simple. Let process digits of n moving from end to begin. Let Result — current result and K — x(10i), i — number of the currently processed digit (digits are numbered from the end. Used 0-indexation). During processing of digits, we must update result: , c[i] — i-th digit of the number n (digits are numbered from the end).

Asymptotics — .

456C - Boredom / 455A - Boredom

Solutions: 7407649, 7407655;

In this task we need to maximize the sum of numbers that we took. Let precalc array cnt. cnt[x] — number of integers x in array a. Now we can easily calculate the DP:

f(i) = max(f(i - 1), f(i - 2) + cnt[i]·i), 2 ≤ i ≤ n;

f(1) = cnt[1];

f(0) = 0;

The answer is f(n).

Asymptotics — O(n).

456D - A Lot of Games / 455B - A Lot of Games

Solutions: 7407663, 7407670;

To solve this problem we need the prefix tree(trie), which will have all the strings from the group. Next we will calculate the two DP: win[v] — Can player win if he makes a move now (players have word equal to prefix v in the prefix tree(trie)). lose[v] — Can player lose if he makes a move now (players have word equal to prefix v in the prefix tree(trie)).

if v is leaf of trie, then win[v] = false; lose[v] = true;

Else win[v] = (win[v] or (not win[i])); lose[v] = (lose[v] or (not lose[i])), such i — children of vertex v.

Let's look at a few cases:

If win[v] = false, then second player win (first player lose all games).

If win[v] = true и lose[v] = true, then first player win (he can change the state of the game in his favor).

If win[v] = true and lose[v] = false, then if , then first player win, else second player win.

Asymptotics — .

456E - Civilization / 455C - Civilization

Solutions: 7407681, 7407683;

You can see that the road system is a forest. For efficient storage component we need to use DSU. First, we need to build the initial system of roads. For each component of the initial road system, we must find the diameter of component. This can be done using a DFS or BFS. Let a — any vertex of component. Let b — furthest vertex from vertex a. Let c — furthest vertex from vertex b. Diameter equal to distance from b to c. This algorithm for finding the diameter is correct only for tree. For each component in the DSU, we know its diameter.

Now it is very easy to answer the query of the $1$st type: To know the component which contains the vertex x and output diameter of this component. Query of the $2$nd type also very easy to process: Let u — of component in which lie the vertex x, v — of component in which lie the vertex y. If u ≠ v, then we can merge components: The diameter of the new component is computed as follows:

Asymptotics — O(n·A - 1(n)), где A - 1(n) — inverse Ackermann function.

455D - Serega and Fun

Solutions: 7407693, 7407699, 7407703;

Let's change the query type 1 to two more simple requests:

Erase a number from r-th position. Insert this number after (l - 1)-th position.

Now let's keep our array as blocks. In each block will store the numbers themselves in such a manner as in the array a and will store an array cnt. cnt[x] — number of integers x in block. This requires O(n sqrtn) space.

Now we can fast process the queries of the 1st type. We can erase number from r-th position in operations. And we can insert this number after (l - 1)-th position in operations. Also we can fast recalc cnt after transformations.

Also we can fast process the queries of the

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O (\ sqrt n) $ numbers are in blocks, which are partly lie within the boundaries of the query.

To keep the size of the blocks close to , we need rebuild our structure after each -th query of the 1st type. We can rebuild structure in O(n) operations.

Asymptotics — .

455E - Function

Solutions: 7407711, 7452418;

In this problem you should quickly be able to compute the function described in the statement.

You may notice that this task is equivalent to next task:

Go through the array a, starting from the position of y, making (x - 1) step. Step might be: step to the left or to stay in place.

Function is calculated as follows: , ki — how many times we visited the i th element of the array a.

For a fixed l is clear, it is most optimally that a minimum on the interval [l, y] has been visited by (x - (y - l)) times, and all the other numbers once.

You may notice that optimally to a[l] was a minimum.

From all this we can conclude that for a fixed l answer is — sum[y] - sum[l] + a[l]·(x - (y - l)), where sum — an array of prefix sums of array a.

Above formula can be written as follows:

sum[y] - sum[l] + a[l]·(x - (y - l)) = sum[y] - sum[l] + a[l]·(x - y + l) = sum[y] - sum[l] + a[l]·l + a[l]·(x - y) = sum[y] + (a[l]·(x - y) + a[l]·l - sum[l])

You may notice that in brackets something like the equation of the line — K·X + B. That's very similar to the equation of the line: a[l]·(x - y) + a[l]·l - sum[l], where K = a[l], X = (x - y), B = a[l]·l - sum[l].

Now we must find minimum for all l and fixed X = (x - y).

We have n lines, i. e. for every element in array a one line (Ki, Bi).

Answer for query equal to:

, where (Ki, Bi) — i-th line. Ki = a[i], Bi = a[i]·i - sum[i].

For fast answer calculation we must use Convex Hull Trick with segment tree. In every vertex of segment tree we keep all lines for segment of this vertex. This requires space, because each line lies in vertices. And we can answer query in operations. Because we visit vertices and each vertex need in operations. You can learn the theory about Convex Hull Trick here.

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10 years ago, # |
← Rev. 14   Vote: I like it +42 Vote: I do not like it

Problem D could be solve by Splay which invented by Darooha in O(nlog2n) without the ungraceful part.

It is hard to answer the query if you only have one Splay. The key point is to build more splays with each different k (k-splay). Let's call the splay with all elements 0-splay.

Thus, for query, you can find the interval of [l, r] on the k-splay by a variation of select() function. The different of it between the regular is not use rank of the node but the rank of the corresponding node on the 0-splay.

For modification, you should also adjust the position of a node in 0-splay and the corresponding k-splay. So for each node, we add one more field to store the corresponding node in another splay.

struct node{
    node *child[2],*parent,*corresponding; 
    int size, key; 
    ...
}

Check my submission or vfleaking's for detail.

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    10 years ago, # ^ |
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    Do u know Russian?

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    10 years ago, # ^ |
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    Why is O(nlog2n) ? I think just O(nlogn) .

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      7 years ago, # ^ |
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      Because is a implicit treap with keys linked to nodes in others implicit treaps for all k. O.o cool. code

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        5 years ago, # ^ |
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        Can you explain the logic?

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          4 years ago, # ^ |
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          sorry for forgetting this comment, today someone reminded me. The idea is not very complicated, you just have to keep a treap of all the possible values ​​in "a", and one for each of them, rotating a range can be seen as removing the last of the range and putting it before the range, now If I only had the first query then it would be enough with the treap that has all the values, but since it is not like that, the trick is that the implicit keys of the other treaps, use the order they have in the main treap, this allows us not to have worrying about adding 1 to each value that was in the range [l, r-1], note that the structure of those treaps does not change (except the position r), this is treated separately, but it is only one that is treated differently instead of r — l + 1 positions.

          int order(int t) { //find relative position
	int sum = 0;	
	bool is_right = 1;
	while (t) {
		if (is_right) {
			sum += cnt(T[t].l) + 1;
                }
		upd(p[t]);
		is_right = T[p[t]].r == t;
		t = p[t];
	}
	return sum-1;
}
 
 
void split(int t, int& l, int& r, int key, bool type, int add = 0) {
        //type 1 is treap[0] and 0 others
	int cur_key = type ? cnt(T[t].l) + add : order(T[t].fake);
	if(t == 0) l = r = 0;
	else if(cur_key < key) 
		split(T[t].r, T[t].r, r, key, type, type? cur_key+1 : 0), l = t;
	else
		split(T[t].l, l, T[t].l, key, type, add), r = t;
	upd(t);
}
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    8 years ago, # ^ |
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    really inspiring

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    8 years ago, # ^ |
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    My solution using Treap.

    Any balanced tree with father pointers would work. Treap is easier to write.

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10 years ago, # |
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Can anybody explain about How to implement the trie using an array instead of pointer??

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    10 years ago, # ^ |
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    I've used to implement tree with a 2-d array [if you guarantee 2 child for every node] the array will look like this


    a
bc//b and c are the childs of a
defg//d and e are the childs of b
hijklmno//l and m are the childs of f

    if you want to reach the first child of the i-th node in the j'th level : level=j+1,id=2*i

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      10 years ago, # ^ |
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      but how we can implement trie (prefix tree) using it??

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    10 years ago, # ^ |
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    You could see my code here 7393354

    Y use a trie using a vector of pairs and Grundy number to solve the game I know that my code couldn't be clear but I hope it could help you

    Sorry for my english too

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    10 years ago, # ^ |
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    You do it like with the standard trie, but replace pointers with array indices and node allocation with index advance:

    // Array of nodes. If trie[i].next[x] is 0, then there is no path with
// character x from the node i. Otherwise it is an index of the next
// node.
struct trie_node
{
    int data;
    int next[26];
};
trie_node trie[100005];

// Number of allocated nodes, 1 by default for trie root
int count = 1; 

void insert(const string& s)
{
    int p = 0; // Index of the current node, 0 by default for root

    for (char c : s)
    {
        int x = c - 'a';
        if (trie[p].next[x] == 0)
        {
            // This is a leaf, attach new node to it.
            // For new node, take trie[count], and increase count.
            trie[p].next[x] = count++;
        }

        // Advance to the next node
        p = trie[p].next[x];
    }

    trie[p].data++;
}

    .data is the information we want to store in tree nodes. For example, it can hold the number of strings ending in this node, like it does in the insert() function above.

    As an exercise write a contains_prefix(s) function for this structure.

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      10 years ago, # ^ |
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      A full structure of Trie should be a more bit representing "is some word ends here"

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10 years ago, # |
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can some one explain "how to use the convex Hull Trick with segment Tree" in DIV-1 E

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    10 years ago, # ^ |
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    Remainder: convex hull trick lets us maintain k linear functions of the form fi(x) = aix + bi and answer efficiently (in time proportional to number of functions) to the queries Q(x) = min1 ≤ i ≤ k fi(x) (given x).

    Now we will be able to solve the problem if we can answer a bit more general kind of queries: we consider only lines with indices from given L and R; formally, Q(x, L, R) = minL ≤ i ≤ R fi(x).

    How can we do it? Let's make a segment tree! Let's say we have such m that 2m ≥ n. Then the root contains the convex hull of lines having indices [0, 2m - 1], its left child contains [0, 2m - 1 - 1], right child [2m - 1, 2m - 1] and so on. We can costruct all these hulls one by one; without any optimizations it gives us time .

    Now let's say we have to answer the query Q(x, L, R). Then we just "break" the interval [L, R] into base intervals (in the same way a segment tree does) and for each of such base intervals we find its minimum at x. Now we see that the answer is the smallest of these minima. It doesn't matter that we consider some groups of lines from interval [L, R] separately — still, we can just take the smallest of the results.

    What's the time? We have base intervals, for each of them we can compute the answer in , so total time is . There are some ways which let us compute all answers off-line in , but it's not the subject :P

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      10 years ago, # ^ |
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      aix + bi -> aix + bi

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      10 years ago, # ^ |
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      @mnbvmar would you like to provide a neat and clean implimentation of convex hull Trick .It is a great help for me and naive learner's like me

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10 years ago, # |
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Hi. I'm new to DP. Can someone please explain me where did the formula for problem div2 C or div1 A come from? Implementing it is not hard but I have problem with the formula. Why should f[i] be as said in the editorial? I don't understand...

I would be thankful if someone could give me more explanation about it. Thanks

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    10 years ago, # ^ |
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    A more straightforward formula looks like this

    Let f[i][0] = max. answer considering numbers <= i && doesn't choose i, f[i][1] = max. answer choose i

    Then f[i][0] = max(f[i-1][0],f[i-1][1]), and f[i][1] = f[i-1][0] + cnt[i]*i

    Actually this is doing the same thing as the formula in editorial.

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      10 years ago, # ^ |
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      I am confused as to what cnt[i] is supposed to represent. What exactly does cnt[] store?

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        10 years ago, # ^ |
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        cnt[i] is the number of the times that the number i has appeared in the input list. It can be calculated while reading the input.

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        8 years ago, # ^ |
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        cnt[i] represent the frequency of the number "i"

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      10 years ago, # ^ |
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      Shouldn't the statement be this:

      dp[i][0] = dp[i - 1][1];
dp[i][1] = dp[i - 1][0] + cnt[i] * i;

      Because if we don't choose i, then we definitely have to choose i-1 to remove i.

      And if we have to choose i then we will have to not choose i-1 => dp[i - 1][0] and for choosing all occurrences of i we get cnt[i]*i

      Any help regarding this would be greatly appreciated.

      Thanks

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      8 years ago, # ^ |
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      before doing boredom question try this one simpler version of boredom https://www.hackerearth.com/problem/algorithm/choosing-the-judges-7/description/

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    8 years ago, # ^ |
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    Warning: please take this explanation with a pinch of salt, because I'm myself new to DP, and it may thus be incorrect ...

    First, we pre-compute the frequency of occurrence of each element in Alex's sequence (using the array "freq", say)

    dp[i] stores the maximum sum that Alex can get using the numbers from 1 to i. Thus, dp[0] is 0, and dp[1] is freq[1] (i.e., number of '1's in the sequence)

    For i = 2 to 10^5 (10^5 being the maximum possible value of any number in Alex's sequence according to the given constraints), dp[i] is calculated using the inference that each set of "i"s (if at all they occur in the sequence) can either all be picked OR not picked at all:

    dp[i] = max(I, II), where:

    I = dp[i-1] represents the situation where "i" isn't picked at all (As "i" isn't picked at all, none of the "i-1"s will be deleted, and the sum will be the same as the one calculated for dp[i-1])

    II = dp[i-2] + (freq[i] * i) represents the situation where all "i"s are picked (As all the "i"s are picked, all the "i-1"s WILL be deleted, and we cannot consider dp[i-1] at all, given that dp[i-1] was itself computed while considering the situation where all the "i-1"s may be picked. Instead, we use dp[i-2]; the sum computed therein is safe to use, given that none of the "i-2"s will be deleted when the "i"s are picked. Also, as we are picking all the "i"s, our previous sum (i.e., dp[i-2]) will increase by (freq[i] * i))

    Final answer will just be dp[100000].

    My implementation of the above logic (C++): http://codeforces.me/contest/456/submission/18021003

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      8 years ago, # ^ |
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      Thank You for the explanation!

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      8 years ago, # ^ |
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      Hello.
      Could you help me?
      problem C div 2.
      link to task
      How is it possible to get 16 from this test case?
      5
      5 3 5 3 4
      Windboy hell_hacker RaghavN

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        4 years ago, # ^ |
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        we would choose the numbers 3 and 5. so the required sum would be : (6+10)=16.

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      8 years ago, # ^ |
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      Alternative way is to use a 2 dimensional dp.
      dp[i][0] represents max value you can get from 1 to i and not picking i.
      dp[i][1] represents max value from 1 to i and picking i.
      The relations for each i are:
      Base case- dp[0][0]=dp[0][1]=0;
      dp[i][0]=max(dp[i-1][0],dp[i-1][1])'
      dp[i][1]=freq[i]*i+dp[i-1][0];

      Then answer would be max(dp[100000][0],dp[100000][1]).

      I personally find that single dimensional dp can sometimes be tough to understand so I use 2d normally.

      Implementation:21918844

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      5 years ago, # ^ |
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      Sorry for bringing up such an old thread, could you please explain why the final answer should be dp[100000] instead of dp[n] which is specific to the test case? Thanks

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        5 years ago, # ^ |
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        n is not specific to the test case. Look again, n is the size of the array. You are confusing it with the maximum integer of the array which would in fact be specific to the test case.

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        5 years ago, # ^ |
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        Yes, you can also say that the answer is dp[n]. In fact, dp[100000] will be equal to dp[n], because freq[i] (for i > n) will be 0 and therefore the value of dp[n] will propagate upwards to n=100000.

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          5 years ago, # ^ |
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          What about this case:

          3
3 5 8

          The answer could be dp[8] or dp[100000], but dp[3] doesn't work. I don't think anything in the problem statement implies that n is greater than the maximum element.

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10 years ago, # |
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In the tutorial of Problem 456B - Fedya and Maths

I can't really understand the transformation of the equation if anyone can explain.

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    10 years ago, # ^ |
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    we know from modulo theory examples : 3%5=-2%5, 4%5=-1%5 so new equation is - (1)^n+(2)^n+(3)^n+(4)^n=(1)^n+(2)^n+(-2)^n+(-1)^n - so for n==odd answer is simply "0" for n==even which are multiple of 4 answer is =4 and for n==even which is not multiple of 4 ans is zero. take a pen and paper do some work on it you can get that idea and the complexity of this solution is O(1) .

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10 years ago, # |
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for the problem 1, going by logic of tutorial and so many other solutions, Alex should be happy for the following data set: (2 1) (3 4) But we can see clearly, it is not so. Am I missing anything?. Thanks.

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    10 years ago, # ^ |
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    Limitations: 1 ≤ ai, bi ≤ n. Your data set is incorrect.

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10 years ago, # |
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In the editorial of problem D div2, Consider the example 2 1 abas abacaba now the player one can win and loose the game. so win[root]=true and loose[root]=true.so according to editorial its answer should be first.But the answer is second.Let's consider these moves a--b--a--s using this prefix the player 2 will win? Can anyone explain this to me??

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    10 years ago, # ^ |
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    From my debug printing of my AC submission: Starting player can FORCE win? false , can FORCE lose? false Second ``

    In fact, if we merge the two given strings we get something like this:

    aba — s \ caba

    There are only two possible games. Both share the initial "aba" prefix. The starting player must pick the second a, so the non-starting player can force a win (by choosing the "s") or a lose (by choosing the "c"). So, the starting player outcome only depends on what the non-starting one decides. In this case, we have k = 1, so the Second player can directly win. In fact, in this case the optimal strategy for the second player is winning every game, since the loser player will be the starting one.

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    10 years ago, # ^ |
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    In the test you given win[root]=false and lose[root]=false. Check that again!

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      10 years ago, # ^ |
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      Correct me if I am wrong. the above test case can be written as Let' name them:_________________________________________________________________________________ (1)a--(2)b--(3)a--(4)s _______________|_____________________________________________________ __________________(5)c--(6)a--(7)b--(8)a

      Now in the 4th node

      win[4]=false

      win[3]=true

      win[2]=false

      win[1]=true

      similarly

      loose[8]=true

      loose[7]=false

      loose[6]=true

      loose[5]=false

      loose[4]=true

      loose[3]= loose[4]|loose[5] =true

      loose[2]=false

      loose[1]=true

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10 years ago, # |
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would anyone like to explain for problem E DIV-1 how we got this relation Function is calculated as follows: , ki — how many times we visited the i th element of the array a.

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10 years ago, # |
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netman in your code of Problem E of DIV 1 Can you explain the algorithm of function addline() and mergeCHs() ,how these function works ? it will be great help !!! sorry for my bad english

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    10 years ago, # ^ |
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    addLine() — it is adding line to Convex Hull. In my structure all lines are in decreasing order of K. And we can easily add line to structure in O(1) operations. You can draw a lines in the order of decreasing K to better understand this.

    If our lines are in decreasing order of K in structure, we can easily merge 2 structures. Add all lines in decreasing order to new structure in O(n + m) operations, where n and m — sizes of 2 structures.

    Read this article to better understand.

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      10 years ago, # ^ |
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      netman in your addline() function the first if condition you do this bb=max(b[l-1],bb) i did not get the idea why you did this . please explain it

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        10 years ago, # ^ |
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        Ohh... sorry... In right solution must be bb=min(b[l-1],bb).

        Tests very weak and my solution with this bug passed tests :(

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10 years ago, # |
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Can anyone give me detail explain for solution of problem D div 1 ?

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10 years ago, # |
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I agree. Your English is very bad :P. But can you please make someone else post in English? I cannot understand the tutorials properly. :(

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10 years ago, # |
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opening solution 7452418 of PROBLEM 455E — FUNCTIONS shows "you are not allowed to view the requested page". Why is that? Please fix it! Thanks

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10 years ago, # |
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netman can you please tell what does f(i) denote in the editorial for problem C of Div2.?

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    10 years ago, # ^ |
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    f(i) — maximal sum if we delete all numbers that smaller or equal to i.

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      10 years ago, # ^ |
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      thanks :)

      netman if it is so, then how would f(n) give answer to original problem, as any number lies between 1 and 10^5 and is also independent of value of n.

      there could be a test case like 


      3
1 9 10000

      So, I think the answer should be f(max(a[i])) [for all i in range(1, n)]

      Please correct me if I am wrong. I am quite weak at DP.

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        10 years ago, # ^ |
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        You are right =)

        Answer is f(maxA).

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10 years ago, # |
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Can someone please explain 456C — Boredom / 455A — Boredom ?

f(i) = max(f(i - 1), f(i - 2) + cnt[i]·i), 2 ≤ i ≤ n;

According to what I understood, the above statement does the following:

  1. f(i-1) Here the number i-1 is selected at some point number which removes all the occurrences of the number i, hence there is no term cnt[i]·i

  2. f(i-2)+cnt[i]·i Here the number i-2 is selected at some point which removes all the occurrences of number i-1 and then we are separately removing all the occurrences of the number i which is the term cnt[i]·i

  3. Then we are taking the maximum of the above two calculated values.

But it can be possible that we do not select the number i-1 in f(i-1) and also we do not select the number i-2 in f(i-2).

So how is this correct? Any help would be greatly appreciated.

Thanks

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    10 years ago, # ^ |
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    Lets say that the numbers are contained in an array of srtucts a[], and it is sorted by the number in it.

    That struct contains the current number and time it is writen.

    The idea is that there is no sense to chose f(i-2), without chosing "i" too, because all numbers are >= 0. So we will either chose the current (ith) number or we will skip it. That means if(a[i-1].numb == a[i].numb-1) we must call a rec(i-2) + a[i].numb * a[i].cnt, because we already deleted all (a[i]-1) elements. But if(a[i-1].numb != a[i].numb-1) => there are no elements equal to a[i] — 1 and that means we can simply call rec(i-1) + a[i].numb * a[i].cnt. If we want to skip the current element we just call rec(i-1).

    From this => rec(i) = max(rec(i-1), ((a[i].numb == a[i-1].numb + 1) ? rec(i-2) : rec(i-1)) + a[i].numb * a[i].cnt)

    And after that you need just to do memoization.

    EDIT: The answer will be rec(N). Let the the array be 1-indexed ans rec(0) = 0, rec(1) = a[1].numb*a[1].cnt.

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9 years ago, # |
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Can someone please explain this test case in 455A ?

5

4 2 3 2 5

how this output is 9?

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    9 years ago, # ^ |
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    choose any 2 -> delete 3

    choose another 2

    choose 5 -> delete 4

    total 9

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      9 years ago, # ^ |
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      how many times i have to choose?

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        9 years ago, # ^ |
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        In this case just 3 times (2,2,5). But anyway number of choosing doesn't really matter to optimal choosing. We can get optimal value by more than one way

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9 years ago, # |
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My solution for Div. 2 B is much simpler. Check if the number is divisible by 4 (check the last two digits), if it is divisible then the answer is 4. Otherwise the answer is 0. I don't know how to prove it but I got Accepted.

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9 years ago, # |
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In C, n should actually be max[a[i]]

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9 years ago, # |
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can someone explain problem D more gracefully , like more of explanation with simple words? (sqrt decomposition method)

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    9 years ago, # ^ |
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    Divide an array into blocks. For each block, you have cnt[block_id][x] -> how many x's we have in this block. To do a shift operation, you need to delete last element and insert it before first one. To delete and insert element, you can find where this element is located and delete it (this will take O(sqrt(N)) because size of each block is O(sqrt(N))). But after several queries, some blocks will be too small and some will be too large. That's why you need fully re-construct your sqrt-decomposition after some number of queries.

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      9 years ago, # ^ |
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      how can we mantain which element is last in the block the block? i think this will consume o(n) , beacause as we perform a cycle shift , a new element acquires the new position. I was thinking about keeping sqrt(n)queues and then for a shift we always a sqrt operations .. what say?

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        9 years ago, # ^ |
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        Look, let us have a two arrays: vector all[numberOfBlocks] and also cnt[numberOfBlocks][maxNumber] to maintain information in blocks. How to do a shift operations? Shift operation is deleting R'th number and inserting it in L'th position.

        Now we need insertion and deletion functions.
        Take a look at my insertion:

        void insert(int pos, int value) {
  // We traverse all blocks
  for (int block_id = 1; block_id <= numberOfBlocks; block_id++) {
    if (all[block_id].size() < pos) {
      /* if this block is smaller than the position we need, then we skip
      this block and decrease our pos by block's size */
      pos -= all[block_id].size();
    } else {
      /* when we found a block where our pos is located, we just insert
      needed value */
      cnt[block_id][value]++;
      all[block_id].insert(all[block_id].begin() + pos, value);
      return;
    }
  }
}

        By doing the shift, we change the sizes of blocks. After N queries, some blocks can have no element, while others have O(N) elements. But to make our blocks as close to sqrt(N) as possible, we can totally re-build our decomposition every sqrt(N) queries.

        Rebuild is something like this:

        void reBuild() {
  vector<int> arr; // our array
  // first, clear all information about blocks 
  for (int i = 1; i <= numberOfBlocks; i++) {
    for (auto it : all[i]) {
      cnt[i][it] = 0;
      arr.push_back(it);
    }
    all[i].clear();
  }
  int ptr = 1;
  for (int i = 1; i <= n; i++) {
    /* just add each element one by one, once some block is full, move to
    the next one */
    all[ptr].pb(a[i]);
    cnt[ptr][a[i]]++;
    if (all[ptr].size() == blockSize)
      ptr++;
  }
}

        After re-building, all blocks will have size of O(sqrt(N)).

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9 years ago, # |
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Div 1 Problem D: I don't understand the need for the array wasVals[][] in the author's solution 7407693. Its only use is to set met[block][value]=0.

Couldn't this be done using the array vals[][]. Will there be a scenario where met[block][value]>0 and vals[block][] does not contain the value?

Edit: I just removed wasVals[][] from author's code and it works 17138498. So looks like it is not needed.

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8 years ago, # |
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Sorry but i missed the problem limitation 1<= a[i],b[i] <= n

this was my original comment :D

problem A maybe i miss understood something about the problem statement or solution.. or there is something wrong with the solution..

Sample Input:

2

1 2

2 3

Solution Output:

Happy Alex

because there exists a pair of a[i],b[i] where a[i]!=b[i] but it's wrong due to problem statement we need to find laptop having less price and higher quality..

Sorry for the long run :D

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    5 years ago, # ^ |
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    You saved me man, i was also getting frustrated on this, guess i also missed this 1<= a[i],b[i] <= n

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8 years ago, # |
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Can anyone please explain the logic behind tourist's solution: 7390969 for Div 1, D. Serega and Fun problem. It would be of great help. Thanks in advance.

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7 years ago, # |
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I am new to competitive programming, can anybody tell why my submission to Boredom is showing time limit exceeding error in eleventh testcase ?

Also, I don't understand the syntax used in the official C++ solution for boredom, but how you create a array containing the number of occurrence of each elements on O(n) time ?

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6 years ago, # |
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For Div2E / Div1C, how can one prove the formula for the new diameter? $$$Diameter_{new} = max(Diameter_u, Diameter_v, \left \lceil{\frac{Diameter_u}{2}}\right \rceil + \left \lceil{\frac{Diameter_v}{2}}\right \rceil + 1)$$$

I understand that in the case that the merged part is not connected to the previous diameter, and is not large enough to affect the diameter, it will be the previous diameter, but how do you prove the last part? I know that it is for the case when the two diameters are going to be connected, but cannot fully understand / prove it. How does it ensure that the diameter is minimum? Why does taking half always work?

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5 years ago, # |
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Div1.C statement make me confuse @@ "Between any pair of cities there either is a single (unique) PATH, or there is no path at all". I don't think graph is forest until I see editorial ><

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5 years ago, # |
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I was trying to solve 456C — Boredom / 455A — Boredom. I wrote the code and it works correctly. The issue is that it shows signed integer overflow for case 42. I have already tried using unsigned long long int but still the problem persists. Moreover, I've seen other codes with no use of long long or anything of that sort. Any help would be appreciated ! Here's my code : https://codeforces.me/problemset/submission/455/75532685

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    5 years ago, # ^ |
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    Try changing int arr[mx]={0}; to unsigned long long arr[mx]={0}; as $$$i * arr_i$$$ can be as big as $$$1e10$$$.

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5 years ago, # |
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The given n doesn't fit in long long for DIV2B. Getting WA on C++14. Changed to pypy3 and AC!!

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4 years ago, # |
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For Div2 D / Div1 B look at this comment.

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4 years ago, # |
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An important point in fedys and maths problem missed by the tutorial setters is that if the result of n % 4 is equal to 0 then the answer is 4 otherwise it is 0. There is no need to do any kind of binary exponentiation or any other mode of fast exponentiation.

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4 years ago, # |
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in 456-A laptops if we give following input it should return poor alex according to the problem statement but according to your solution and the solution that is accepted it is printing happy alex. input I gave- 2 1 2 2 3

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4 years ago, # |
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Can anyone show the proof of finding the diameter of two merged components in DIV 1C?

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    3 years ago, # ^ |
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    To get the minimum diameter after merging, one should always merge two components from the middle node of their respective diameter paths which explains $$$\left \lceil{\frac{Diameter_u}{2}}\right \rceil + \left \lceil{\frac{Diameter_v}{2}}\right \rceil + 1$$$. Then we should check if any individual component's diameter is greater than it or not.

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23 months ago, # |
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for problem E — civilization do we need to connect the centroid of 2 components which are to be merged , so that our new diameter would be minimum as possible.

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12 months ago, # |
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[Sorry for necroposting]

lol Overkilled the Div. 1 C with small to large merging + $$$O(n)$$$ memory binary lifting from https://codeforces.me/blog/entry/74847.

I've got the observation that the new diameter can be obtained by connecting two middle points of two trees, also got the observation that the new diameter is whether to connect the two trees' diameter pair, or the old diameter pair of both trees.

Didn't know that the diameter will always be sum of ceil of both. So I coded the online merging lca-able tree sets that maintains the diameter pair.

231305622

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10 months ago, # |
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Is it possible to use recursion/memoization for 456C — Boredom / 455A — Boredom? No matter what I do I am getting stack overflows on larger test cases. I figure most DP problems should be able to be solved with both Top-down as well as bottom-up approaches but I am also new to CF so this may be be wrong on my part.

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8 months ago, # |
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Sorry for necroposting, don't want to create a separate post for this.

Don't understand why I am getting WA 249969116. It's almost identical to the tutorial. I think most probably it is some stupid bug, but I'm not able to figure it out even after spending a good time on it. I wonder if the reason is the pointer implementation as opposed to the 2D table one.

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4 months ago, # |
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why in problem 456C f(i) = max(f(i - 1), f(i - 2) + cnt[i]·i), 2 ≤ i ≤ n;

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