meetforever/GRPO_CL huggingface dataset:
user: Jack, naïve fellow that he is, has fallen into the clutches of a dastardly and sophisticated multi-level marketing scheme.

It all started when a mysterious stranger pushed upon young Jack a bag of ordinary beans, promising that if only he could amass the right quantities of each kind of bean, he could grow a mighty beanstalk and climb it to the unimaginable wealth at its top.

This all sounds very sensible to Jack... But there is one catch. He must acquire the extra beans from other farmers, who as one might expect are not too keen to give away the fruits (nor the seeds) of their labour. Each time Jack comes to ask for a bean, they will give him exactly one from their farm, but since he is not a paying customer the exact species may vary between farmers and between visits.

There is another option, but it is expensive. Jack can give up some of his cows to the mysterious stranger in exchange for one additional bean per cow. Of course, this is a drastic measure. We would like to help Jack keep as many of his cows as possible, while still achieving his goals.

How many cows will Jack need to budget for to have $100\% $ certainty of success?

-----Input-----
 - One line containing an integer $B$, ($1 \le B \le 20$), the number of types of beans available.
 - One line containing $B$ integers, $V_1 \ldots V_ B$, ($0 \le V_1 \ldots V_ B \le 100$), the number of each kind of bean required.
 - One line containing $T$ ($1 \le T \le 100$), the number of other farms in Jack’s small village.
 - $T$ more lines, each beginning with an integer $M$ ($1 \le M \le B$) giving the number of kinds of bean this farmer grows. This is followed by $M$ more distinct integers $T_1 \ldots T_ M$ ($1 \le T_1 \ldots T_ M \le B$), each corresponding to one kind of bean.

-----Output-----
 - One line containing one integer: the number of cows Jack must bring with him in order to be $100\% $ sure of ending the day with enough beans to grow a magical beanstalk.

-----Examples-----
Sample Input 1:
1
5
1
1 1
Sample Output 1:
0

Sample Input 2:
3
5 5 5
2
2 1 2
2 2 3
Sample Output 2:
10
user: Everybody is into cloud computing these days, so quite a few different business models are being experimented with. You are trying a very simple one: you sell time on your machines in one of two batches called slots. A customer can buy one second of CPU time or $Q$ seconds for some integer $Q$.

Each time slot a customer purchases must be completed on a single machine, but you get to decide how to allocate the purchased time slots between machines.

After coming back from a long vacation, you see that all of your machines are idle and a variety of orders have come in. To keep customers happy, you must decide how to distribute these requests between machines in a way that minimizes the time when the purchased time slots are finally all completed.

What is the smallest amount of time in which you can complete all of the purchased time slots?

-----Input-----
The input consists of a single line containing four integers $Q$ ($2 \leq Q \leq 1000$), which is the time needed to complete the longer batches, $M$ ($1 \leq M \leq 1000000$), which is the number of machines owned by your company, $S$ ($0 \leq S \leq 1000000$), which is the number of 1-second time slots purchased, and $L$ ($0 \leq L \leq 1000000$), which is the number of $Q$-second time slots purchased.

-----Output-----
Display the smallest amount of time in which you can complete all of the purchased time slots.

-----Examples-----
Sample Input 1:
2 4 3 6
Sample Output 1:
4

Sample Input 2:
3 4 3 5
Sample Output 2:
6
user: You are playing hide-and-go-seek in a forest with Belle. The forest has one tree at each of the positive integer lattice points. That is, there is a tree at every point $(x,y)$ where $x$ and $y$ are both positive integers. You may consider each tree as a point. A logging company has cut down all of the trees in some axis-aligned rectangle, including those on the boundary of the rectangle.

You are standing at $(0,0)$ and Belle is standing at $(x_ b,y_ b)$. You can see Belle if and only if there is no tree blocking your line of sight to Belle. If there is a tree at $(x_ b,y_ b)$, Belle will make it easier for you to find her by standing on the side of the tree facing your location.

For example, suppose that Belle is standing at $(2,6)$. If the trees in the rectangle with corners at $(1,1)$ and $(5,4)$ are cut down (blue rectangle in figure), then you can see Belle. However, if the rectangle was at $(3,5)$ and $(5,7)$ (red rectangle in figure), then the tree at $(1,3)$ would be in the way.

Given the rectangle and Belle’s location, can you see her?

-----Input-----
The first line of input contains two integer $x_ b$ and $y_ b$ ($1 \leq x_ b,y_ b \leq 10^{12}$), which are the coordinates that Belle is standing on.

The second line of input contains four integers $x_1$, $y_1$, $x_2$ and $y_2$ ($1 \leq x_1 \leq x_2 \leq 10^{12}$ and $1 \leq y_1 \leq y_2 \leq 10^{12}$), which specify two opposite corners of the rectangle at $(x_1, y_1)$ and $(x_2, y_2)$.

-----Output-----
If you can see Belle, display Yes.

Otherwise, display No and the coordinates of the closest tree that is blocking your view.

-----Examples-----
Sample Input 1:
2 6
1 1 5 4
Sample Output 1:
Yes

Sample Input 2:
2 6
3 5 5 7
Sample Output 2:
No
1 3
user: A multinational company is asking you to help them genetically modify an apple. In order for the apples to grow faster, to get more of them, to make them bigger and make them look nicer and more symmetrical, the apple’s DNA requires an insertion of a certain swine gene.

The apple’s DNA is represented by a series of characters from the set $\{ A, C, G, T\} $. The required swine gene is also comprised of charaters from this set. The apple’s DNA should be injected with some characters into some places, so that the resulting sequence contains a swine gene somewhere (in successive locations). To make things a bit more complicated, inserting each of the characters $A, C, G, T$ has its own cost.

Help this multinational company in achieving their goal with the lowest possible total cost. As a reward, you get a ton of their apples.

-----Input-----
The first line of input contains a sequence of $N$ ($1 \le N \le 10000$) characters which represent the apple’s DNA.

The second line of input contains a sequence of $M$ ($1 \le M \le 5000$) characters which represent the swine gene that we want to insert into the apple’s DNA.

Both the sequences are comprised only of characters from the set $\{ A, C, G, T\} $.

The third line of input contains four integers from the interval $[0, 1000]$: the cost of inserting one character $A, C, G, T$, in that order.

-----Output-----
The first and only line of output must contain the minimal total cost.

-----Examples-----
Sample Input 1:
GTA
CAT
5 7 1 3
Sample Output 1:
10

Sample Input 2:
TATA
CACA
3 0 3 0
Sample Output 2:
3
user: To save money, Santa Claus has started hiring other animals besides reindeer to pull his sleigh via short term ‘gig’ contracts. As a result, the actual animals that show up to pull his sleigh for any given trip can vary greatly in size.

Last week he had $2$ buffalo, $37$ voles and a schnauzer. Unfortunately, both buffalo were hitched on the left side and the entire sleigh flipped over in mid-flight due to the weight imbalance.

To prevent such accidents in the future, Santa needs to divide the animals for a given trip into two groups such that the sum of the weights of all animals in one group equals the sum of the weights of all animals in the other. To make the hitching process efficient, Santa is seeking an integer target weight $t$ such that all animals that are lighter than $t$ go in one group and those heavier than $t$ go into the other. If there are multiple such $t$, he wants the smallest one. There’s one small wrinkle: what should be done if there some animals have weight exactly equal to $t$? Santa solves the problem this way: if there are an even number of such animals, he divides them equally among the two groups (thus distributing the weight evenly). But if there are an odd number of such animals, then one of those animals is sent to work with the elves to make toys (it is not put in either group), and the remaining (now an even number) are divided evenly among the two groups.

-----Input-----
Input describes a list of animals’ weights. The first line contains an integer $m$ ($2 \le m \le 10^5$), indicating the number of animals. The next $m$ lines each have a positive integer. These are the weights of the animals (in ounces). Animals weighing more than $20000$ ounces are too big to pull the sleigh so no given weight exceeds this maximum.

-----Output-----
Output the smallest integer target weight $t$, as described above. It’s guaranteed that it is possible to find such an integer.

-----Examples-----
Sample Input 1:
4
3
6
1
2
Sample Output 1:
4

Sample Input 2:
4
11
8
3
10
Sample Output 2:
10
user: A group of friends snuck away from their school campus, but now they must return from the main campus gate to their dorm while remaining undetected by the many teachers who patrol the campus. Fortunately, they have an invisibility cloak, but it is only large enough to cover two people at a time. They will take turns as individuals or pairs traveling across campus under the cloak (and by necessity, returning the cloak to the gate if others remain). Each student has a maximum pace at which he or she is able to travel, yet if a pair of students are walking under the cloak together, they will have to travel at the pace of the slower of the two. Their goal is to have everyone back at the dorm as quickly as possible.

As an example, assume that there are four people in the group, with person A able to make the trip in $1$ minute, person B able to travel in $2$ minutes, person C able to travel in $7$ minutes, and person D able to travel in $10$ minutes. It is possible to get everyone to the dorm in $17$ minutes with the following plan:


– A and B go from the gate to the dorm together

(taking $2$ minutes)

– A returns with the cloak to the gate

(taking $1$ minute)

– C and D go from the gate to the dorm together

(taking $10$ minutes)

– B returns with the cloak to the gate

(taking $2$ minutes)

– A and B go from the gate to the dorm together

(taking $2$ minutes)

-----Input-----
The input is a single line beginning with an integer, $2 \leq N \leq 15$. Following that are $N$ positive integers that respectively represent the minimum time in which each person is able to cross the campus if alone; these times are measured in minutes, with each being at most $5000$. (It is a very large campus!)

-----Output-----
Output the minimum possible time it takes to get the entire group from the gate to the dorm.

-----Examples-----
Sample Input 1:
2 15 5
Sample Output 1:
15

Sample Input 2:
4 1 2 7 10
Sample Output 2:
17
user: In geometry, ellipses are defined by two focal points $f_1, f_2$ and a length $D$. The ellipse consists of all points $p$ such that $\mathop {\mathrm{distance}}(f_1, p) + \mathop {\mathrm{distance}}(f_2, p) = D$.

When one normally thinks of ellipses, it is in the context of the Euclidean 2D plane, with the Euclidean distance as a distance measure.

This problem explores a different kind of ellipse. The space we will work in is the space of words of length $n$ using an alphabet of $q$ different symbols, often denoted as $F_ q^n$. As you can probably see, for given values of $q$ and $n$, there are $q^n$ different words (points) in the space $F_ q^n$.

For a distance measure, we use the Hamming distance. The Hamming distance between two words $x, y \in F_ q^n$ is simply the number of positions where the symbols that make up the words $x$ and $y$ differ. For example, the Hamming distance between words 01201 and 21210 is 3 because there are 3 positions where the words have different symbols. The Hamming distance between any two words in $F_ q^n$ will always be an integer between $0$ and $n$, inclusive.

Within the space $F_ q^n$, we now define the Hamming ellipse as the set of all points $p$ such that $\mathop {\mathrm{hammingdistance}}(f_1, p) + \mathop {\mathrm{hammingdistance}}(f_2, p) = D$. Given values $q$ and $n$, focal points $f_1$ and $f_2$ and distance $D$, we ask you to determine the number of points $p \in F_ q^n$ that lie on this Hamming ellipse.

-----Input-----
The first line contains three integers $q$ ($2 \le q \le 10$), $n$ ($1 \le n \le 100$) and $D$ ($1 \le D \le 2 n$).

The second and third lines specify the two focal points $f_1$ and $f_2$, each formatted as a string of length $n$ using digits $\{ 0, 1 \ldots q - 1\} $.

-----Output-----
Output one line containing a single integer, denoting the number of points on the ellipse.

The input is chosen such that the answer is less than $2^{63}$.

-----Examples-----
Sample Input 1:
3 5 9
01201
21210
Sample Output 1:
24

Sample Input 2:
4 6 5
123031
231222
Sample Output 2:
0
user: You are part of an elite hacking group who has just invented a new type of malware, called the hoppers. Hoppers can operate in any high-security computer networks; however, they can only propagate themselves in a very limited way.

A computer network is a set of hosts $V$ ($|V| = N$) and direct links $E$ ($|E| = M$). Each direct link connects two different hosts, allowing them to communicate in both directions. If a host $u$ is infected with a hopper, then it will propagate itself to all hosts $W$ where $W$ is the set of hosts which are connected to any neighbor of $u$. Formally, $W = \{ w \mid \{ (u,v),(v,w)\} \subseteq E \} $. The newly-infected host $w$ can now proceed to infect other hosts in the same manner.

You are trying to infect all hosts in a particular high-security network by compromising a single host. Of course, a compromised host will be infected with a hopper. Though it may be an impossible mission, you realize that you can trick the administrator into installing new direct links between hosts by submitting IT requests.

Too many requests may arouse suspicion. Find the minimum number of IT requests you have to submit to ensure that there exists a single host such that if it is infected with a hopper, then it will propagate to the entire network.

-----Input-----
The first line contains two integers $N$ and $M$, where $3 \le N \le 5 \cdot 10^5$ and $2 \le M \le 5 \cdot 10^5$. The next $M$ lines contain two integers $u$ and $v$ ($1 \le u, v \le N$), representing a direct link between hosts $u$ and $v$. There is at most one direct link between any pair of hosts, and no host is directly linked to itself.

-----Output-----
The output contains an integer in a line representing the minimum number of IT requests you must send.

-----Explanation-----
In the first example, there are $N = 3$ hosts and $M = 2$ direct links $\{ (1,2),(2,3)\} $. In this network, there is no way to spread the hopper to all hosts by compromising only a single host, e.g., if we compromise host $1$, then only hosts $1$ and $3$ are infected, etc. We need to submit one IT request to connect $(1,3)$ to achieve our goal. By doing so, if we compromise host $1$, all hosts $1$, $2$, and $3$ are infected. $1 \rightarrow 3 \rightarrow 2$ (thus, host $2$ is infected). $1 \rightarrow 2 \rightarrow 3$ (thus, host $3$ is infected).

-----Examples-----
Sample Input 1:
3 2
1 2
2 3
Sample Output 1:
1

Sample Input 2:
5 10
1 2
2 3
3 4
4 5
5 1
1 3
2 4
3 5
4 1
5 2
Sample Output 2:
0
user: Mirko has an array of $N$ different words that he wants to encrypt using a substitution cypher.

We encrypt the text using a substitution cypher by first choosing a key – a permutation of the English alphabet. Then we replace all occurrences of letter ‘a’ with the first letter of the key, all occurrences of letter ‘b’ with the second letter of the key, and so on until letter ‘z’.

Besides the words, Mirko has an array $A$ consisting of numbers from $1$ to $N$ given in a certain order (in other words, array $A$ is a permutation of numbers from $1$ to $N$). Mirko wants to pick a key such that the array of words after encrypting and lexicographic sorting corresponds to array $A$. More precisely, he wants the word initially located at $A_ i$ to be at location $i$ after encryption and sorting.

Let’s recall that the lexicographic word order is the order in which the words appear in the dictionary. If we are comparing two words, going from left to right, we search for the first position in both words where the letters differ and, based on that, we determine which word is lexicographically smaller. If word $X$ is the beginning of the word $Y$, then word $X$ is lexicographically smaller than word $Y$.

Mirko is currently not in the mood for encrypting, so he kindly asks you to do it for him.

-----Input-----
The first line of input contains the integer $N$ ($2 \leq N \leq 100$). Each of the following $N$ lines contains a single word that consists of at most $100$ lowercase letters of the English alphabet. The words will be mutually distinct. The last line contains $N$ integers – the elements of array $A$.

-----Output-----
In the case when a solution doesn’t exist, output “NE”. Otherwise, output “DA” in the first line, and in the second line output a word consisting of $26$ different letters of the English alphabet – the key for the substitution cipher. If multiple solutions exist, output any.

-----Examples-----
Sample Input 1:
2
ab
bc
2 1
Sample Output 1:
DA
bacdefghijklmnopqrstuvwxyz

Sample Input 2:
3
abc
bcd
add
1 2 3
Sample Output 2:
NE
user: Morse Code is an assignment of sequences of dots and dashes to alphabet characters. You are to create a Morse-like code that yields the shortest total length to a given message, and return that total length.

A dot symbol has length $1$. A dash symbol has length $3$. The gap between symbols within a character encoding has length $1$. The gap between character encodings has length $3$. Spaces, punctuation, and alphabetic case are ignored, so the text:The quick brown dog jumps over the lazy fox.

is encoded as though it were justTHEQUICKBROWNDOGJUMPSOVERTHELAZYFOX

For example, with input ICPC, the answer is $17$: Encode the C’s with a single dot, the I with a dash, and the P with two dots, for an encoding of— $\bullet $ $\bullet \bullet $ $\bullet $

which has length$(3)+3+(1)+3+(1+1+1)+3+(1) = 17$. 

-----Input-----
The single line of input contains a string $s$ ($1 \le |s| \le 32000$) of upper-case or lower-case letters, spaces, commas, periods, exclamation points, and/or question marks. Everything but the letters should be ignored. The line will contain at least one letter.

-----Output-----
Output a single integer, which is the length of $s$ when encoded with an optimal reassignment of the sequences of Morse Code.

-----Examples-----
Sample Input 1:
ICPC
Sample Output 1:
17

Sample Input 2:
A
Sample Output 2:
1
user: You are on an $n \times m$ grid where each square on the grid has a digit on it. From a given square that has digit $k$ on it, a Move consists of jumping exactly $k$ squares in one of the four cardinal directions. A move cannot go beyond the edges of the grid; it does not wrap. What is the minimum number of moves required to get from the top-left corner to the bottom-right corner?

-----Input-----
Each input will consist of a single test case. Note that your program may be run multiple times on different inputs. The first line of input contains two space-separated integers $n$ and $m$ ($1 \le n, m \le 500$), indicating the size of the grid. It is guaranteed that at least one of $n$ and $m$ is greater than $1$.

The next $n$ lines will each consist of $m$ digits, with no spaces, indicating the $n \times m$ grid. Each digit is between 0 and 9, inclusive.

The top-left corner of the grid will be the square corresponding to the first character in the first line of the test case. The bottom-right corner of the grid will be the square corresponding to the last character in the last line of the test case.

-----Output-----
Output a single integer on a line by itself representing the minimum number of moves required to get from the top-left corner of the grid to the bottom-right. If it isn’t possible, output -1.

-----Examples-----
Sample Input 1:
2 2
11
11
Sample Output 1:
2

Sample Input 2:
2 2
22
22
Sample Output 2:
-1
user: You have located a major supply line that the enemy has been using. With satellite imaging, you’ve been able to determine the current location and velocity of every vehicle along the supply line, which is for all practical purposes an infinitely long straight line. Furthermore, you know that each vehicle moves at constant velocity, and that they can pass by each other without incident along this supply line. What you need to do now is deploy an air drone with special sensors that can give you readings of the contents of the vehicles. The sensor is capable of reading everything in its range instantaneously, but power limitations allow it to do so only once. In order to minimize the required range, you want to deploy it when the vehicles are as close to each other as possible. Given knowledge of the current location and velocity of all the vehicles, what is the closest that the vehicles will get to each other?

-----Input-----
There will be a single test case in the input. This test case will begin with a line with a single integer $n$ ($1 \le n \le 100000$) representing the number of vehicles. Each of the next $n$ lines will have two integers, $x$ and $v$ ($-100000 \le x,v \le 100000$), indicating the position ($x$, in meters) and velocity ($v$, in meters/hour) of that vehicle. The sign of velocity indicates direction.

-----Output-----
Output a single number equal to the minimum distance that will cover all of the vehicles at some time, in meters. Your result should have an absolute or relative error of less than $10^{-3}$.

-----Examples-----
Sample Input 1:
2
-100 1
100 -1
Sample Output 1:
0

Sample Input 2:
3
-100 1
100 -1
101 -1
Sample Output 2:
1
user: Pixels in a digital picture can be represented with three integers in the range $0$ to $255$ that indicate the intensity of the red, green, and blue colors. To compress an image or to create an artistic effect, many photo-editing tools include a “posterize” operation which works as follows. Each color channel is examined separately; this problem focuses only on the red channel. Rather than allow all integers from $0$ to $255$ for the red channel, a posterized image allows at most $k$ integers from this range. Each pixel’s original red intensity is replaced with the nearest of the allowed integers. The photo-editing tool selects a set of $k$ integers that minimizes the sum of the squared errors introduced across all pixels in the original image. If there are $n$ pixels that have original red values $r_1, \ldots , r_ n$, and $k$ allowed integers $v_1, \ldots , v_ k$, the sum of squared errors is defined as\[ \sum _{i=1}^n \min _{1 \leq j \leq k} (r_ i - v_ j)^2. \]

Your task is to compute the minimum achievable sum of squared errors, given parameter $k$ and a description of the red intensities of an image’s pixels.

-----Input-----
The first line of the input contains two integers $d$ ($1 \leq d \leq 256$), the number of distinct red values that occur in the original image, and $k$ ($1 \leq k \leq d$), the number of distinct red values allowed in the posterized image. The remaining $d$ lines indicate the number of pixels of the image having various red values. Each such line contains two integers $r$ ($0 \leq r \leq 255$) and $p$ ($1 \leq p \leq 2^{26}$), where $r$ is a red intensity value and $p$ is the number of pixels having red intensity $r$. Those $d$ lines are given in increasing order of red value.

-----Output-----
Display the sum of the squared errors for an optimally chosen set of $k$ allowed integer values.

-----Examples-----
Sample Input 1:
2 1
50 20000
150 10000
Sample Output 1:
66670000

Sample Input 2:
2 2
50 20000
150 10000
Sample Output 2:
0