text stringlengths 0 801 |
|---|
* the first line contains two integers $n$ and $m$ ($0 \le n, m \le 2 \cdot 10^5$; $2 \le n + m + 1 \le 2 \cdot 10^5$) — the number of programmers and the number of testers Monocarp wants to hire, respectively; * the second line contains $n + m + 1$ integers $a_1, a_2, \dots, a_{n+m+1}$ ($1 \le a_i \le 10^9$), whe... |
Additional constraint on the input: the sum of $(n + m + 1)$ over all test cases doesn't exceed $2 \cdot 10^5$. |
For each test case, print $n + m + 1$ integers, where the $i$-th integer should be equal to the skill of the team if everyone except the $i$-th candidate comes to interview. |
Let's consider the third test |
This is an interactive problem. |
The Department of Supernatural Phenomena at the Oxenfurt Academy has opened the Library of Magic, which contains the works of the greatest sorcerers of Redania — $n$ ($3 \leq n \leq 10^{18}$) types of books, numbered from $1$ to $n$. Each book's type number is indicated on its spine. Moreover, each type of book is stor... |
One night, you wake up to a strange noise and see a creature leaving the building through a window. Three thick tomes of different colors were sticking out of the mysterious thief's backpack. Before you start searching for them, you decide to compute the numbers $a$, $b$, and $c$ written on the spines of these books. A... |
So, you have an unordered set of tomes, which includes one tome with each of the pairwise distinct numbers $a$, $b$, and $c$, and two tomes for all numbers from $1$ to $n$, except for $a$, $b$, and $c$. You want to find these values $a$, $b$, and $c$. |
Since you are not working in a simple library, but in the Library of Magic, you can only use one spell in the form of a query to check the presence of books in their place: |
* "xor l r" — Bitwise XOR query with parameters $l$ and $r$. Let $k$ be the number of such tomes in the library whose numbers are greater than or equal to $l$ and less than or equal to $r$. You will receive the result of the computation $v_1 \oplus v_2 \oplus ... \oplus v_k$, where $v_1 ... v_k$ are the numbers on th... |
Since your magical abilities as a librarian are severely limited, you can make no more than $150$ queries. |
The first line of input contains an integer $t$ ($1 \le t \le 300$) — the number of test cases. |
The first line of each test case contains a single integer $n$ ($3 \leq n \leq 10^{18}$) — the number of types of tomes. |
In the first test case, the books in the library afte |
You are given a positive integer $x$. Find any array of integers $a_0, a_1, \ldots, a_{n-1}$ for which the following holds: |
* $1 \le n \le 32$, * $a_i$ is $1$, $0$, or $-1$ for all $0 \le i \le n - 1$, * $x = \displaystyle{\sum_{i=0}^{n - 1}{a_i \cdot 2^i}}$, * There does not exist an index $0 \le i \le n - 2$ such that both $a_{i} \neq 0$ and $a_{i + 1} \neq 0$. |
It can be proven that under the constraints of the problem, a valid array always exists. |
Each test contains multiple test cases. The first line of input contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases. The description of the test cases follows. |
The only line of each test case contains a single positive integer $x$ ($1 \le x < 2^{30}$). |
For each test case, output two lines. |
On the first line, output an integer $n$ ($1 \le n \le 32$) — the length of the array $a_0, a_1, \ldots, a_{n-1}$. |
On the second line, output the array $a_0, a_1, \ldots, a_{n-1}$. |
If there are multiple valid arrays, you can output any of them. |
In the first test case, one valid array is $[1]$, since $(1) \cdot 2^0 = 1$. |
In the second test case, one possible valid array is $[0,-1,0,0,1]$, since $(0) \cdot 2^0 + (-1) \cdot 2^1 + (0) \cdot 2^2 + (0) \cdot 2^3 + (1) \cdot 2^4 = -2 + 16 = 14$. |
Timur is in a car traveling on the number line from point $0$ to point $n$. The car starts moving from point $0$ at minute $0$. |
There are $k+1$ signs on the line at points $0, a_1, a_2, \dots, a_k$, and Timur knows that the car will arrive there at minutes $0, b_1, b_2, \dots, b_k$, respectively. The sequences $a$ and $b$ are strictly increasing with $a_k = n$. |
 |
Between any two adjacent signs, the car travels with a constant speed. Timur has $q$ queries: each query will be an integer $d$, and Timur wants you to output how many minutes it takes the car to reach point $d$, rounded down to the nearest integer. |
The first line contains a single integer $t$ ($1 \leq t \leq 10^4$) — the number of test cases. |
The first line of each test case contains three integers $n$, $k$, and $q$, ($k \leq n \leq 10^9$; $1 \leq k, q \leq 10^5$) — the final destination, the number of points Timur knows the time for, and the number of queries respectively. |
The second line of each test case contains $k$ integers $a_i$ ($1 \leq a_i \leq n$; $a_i < a_{i+1}$ for every $1 \leq i \leq k-1$; $a_k = n$). |
The third line of each test case contains $k$ integers $b_i$ ($1 \leq b_i \leq 10^9$; $b_i < b_{i+1}$ for every $1 \leq i \leq k-1$). |
Each of the following $q$ lines contains a single integer $d$ ($0 \leq d \leq n$) — the distance that Timur asks the minutes passed for. |
The sum of $k$ over all test cases doesn't exceed $10^5$, and the sum of $q$ over all test cases doesn't exceed $10^5$. |
For each query, output a single integer — the number of minutes passed until the car reaches the point $d$, rounded down. |
For the first test case, the car goes from point $0$ to point $10$ in $10$ minutes, so the speed is $1$ unit per minute and: |
* At point $0$, the time will be $0$ minutes. * At point $6$, the time will be $6$ minutes. * At point $7$, the time will be $7$ minutes. |
For the second test case, between points $0$ and $4$, the car travels at a speed of $1$ unit per minut |
Bob decided to open a bakery. On the opening day, he baked $n$ buns that he can sell. The usual price of a bun is $a$ coins, but to attract customers, Bob organized the following promotion: |
* Bob chooses some integer $k$ ($0 \le k \le \min(n, b)$). * Bob sells the first $k$ buns at a modified price. In this case, the price of the $i$-th ($1 \le i \le k$) sold bun is $(b - i + 1)$ coins. * The remaining $(n - k)$ buns are sold at $a$ coins each. |
Note that $k$ can be equal to $0$. In this case, Bob will sell all the buns at $a$ coins each. |
Help Bob determine the maximum profit he can obtain by selling all $n$ buns. |
Each test consists of multiple test cases. The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases. The description of the test cases follows. |
The only line of each test case contains three integers $n$, $a$, and $b$ ($1 \le n, a, b \le 10^9$) — the number of buns, the usual price of a bun, and the price of the first bun to be sold at a modified price. |
For each test case, output a single integer — the maximum profit that Bob can obtain. |
In the first test case, it is optimal for Bob to choose $k = 1$. Then he will sell one bun for $5$ coins, and three buns at the usual price for $4$ coins each. Then the profit will be $5 + 4 + 4 + 4 = 17$ coins. |
In the second test case, it is optimal for Bob to choose $k = 5$. Then he will sell all the buns at the modified price and obtain a profit of $9 + 8 + 7 + 6 + 5 = 35$ coins. |
In the third test case, it is optimal for Bob to choose $k = 0$. Then he will sell all the buns at the usual price and obtain a profit of $10 \cdot 10 = 100$ coins. |
Dmitry has $n$ cubes, numbered from left to right from $1$ to $n$. The cube with index $f$ is his favorite. |
Dmitry threw all the cubes on the table, and the $i$-th cube showed the value $a_i$ ($1 \le a_i \le 100$). After that, he arranged the cubes in non-increasing order of their values, from largest to smallest. If two cubes show the same value, they can go in any order. |
After sorting, Dmitry removed the first $k$ cubes. Then he became interested in whether he removed his favorite cube (note that its position could have changed after sorting). |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.