You are given an array ๐ดA of size ๐N.You can rearrange the elements of ๐ดA as you want. After that, construct an array ๐ตB of size ๐N as:๐ต1=๐ด1B 1โ =A 1โ ;๐ต๐=๐ต๐โ1B iโ =B iโ1โ && ๐ด๐A iโ for all 2โค๐โค๐2โคiโคN, where && denotes the bitwise AND operator.Find the lexicographically largest possible array ๐ตB.For two arrays ๐X and ๐Y, both of size ๐N, the array ๐X is said to be lexicographically larger than array ๐Y, if, in the first position where ๐X and ๐Y differ, ๐๐>๐๐X iโ >Y iโ .Input FormatThe first line of input will contain a single integer ๐T, denoting the number of test cases.Each test case consists of multiple lines of input.The first line of each test case contains ๐N, the size of the array ๐ดA.The second line of each test case contains ๐N space-separated integers ๐ด1,๐ด2,โฆ,๐ด๐A 1โ ,A 2โ ,โฆ,A Nโ .Output FormatFor each test case, output on a new line, ๐N space separated integers denoting the lexicographically largest array ๐ตB that can be formed by any rearrangement of ๐ดA.Constraints1โค๐โค2โ 1041โคTโค2โ 10 4 1โค๐โค2โ 1051โคNโค2โ 10 5 1โค๐ด๐โค1091โคA iโ โค10 9 The sum of ๐N over all test cases does not exceed 2โ 1052โ 10 5 .
Question
You are given an array ๐ดA of size ๐N.You can rearrange the elements of ๐ดA as you want. After that, construct an array ๐ตB of size ๐N as:๐ต1=๐ด1B 1โ =A 1โ ;๐ต๐=๐ต๐โ1B iโ =B iโ1โ && ๐ด๐A iโ for all 2โค๐โค๐2โคiโคN, where && denotes the bitwise AND operator.Find the lexicographically largest possible array ๐ตB.For two arrays ๐X and ๐Y, both of size ๐N, the array ๐X is said to be lexicographically larger than array ๐Y, if, in the first position where ๐X and ๐Y differ, ๐๐>๐๐X iโ >Y iโ .Input FormatThe first line of input will contain a single integer ๐T, denoting the number of test cases.Each test case consists of multiple lines of input.The first line of each test case contains ๐N, the size of the array ๐ดA.The second line of each test case contains ๐N space-separated integers ๐ด1,๐ด2,โฆ,๐ด๐A 1โ ,A 2โ ,โฆ,A Nโ .Output FormatFor each test case, output on a new line, ๐N space separated integers denoting the lexicographically largest array ๐ตB that can be formed by any rearrangement of ๐ดA.Constraints1โค๐โค2โ 1041โคTโค2โ 10 4 1โค๐โค2โ 1051โคNโค2โ 10 5 1โค๐ด๐โค1091โคA iโ โค10 9 The sum of ๐N over all test cases does not exceed 2โ 1052โ 10 5 .
Solution
Para resolver este problema, sigamos los siguientes pasos:
- Leer el nรบmero de casos de prueba, T.
- Para cada caso de prueba:
- Leer el tamaรฑo del array, N.
- Leer el array A de tamaรฑo N.
- Ordenar el array A en orden descendente.
- Construir el array B usando el primer elemento de A como el primer elemento de B y luego aplicar la operaciรณn AND bit a bit con los siguientes elementos de A.
- Imprimir el array B resultante.
Implementaciรณn paso a paso:
-
Leer el nรบmero de casos de prueba, T:
T = int(input()) -
Para cada caso de prueba:
for _ in range(T): N = int(input()) A = list(map(int, input().split())) -
Ordenar el array A en orden descendente:
A.sort(reverse=True) -
Construir el array B:
B = [A[0]] for i in range(1, N): B.append(B[-1] & A[i]) -
Imprimir el array B resultante:
print(" ".join(map(str, B)))
Cรณdigo completo:
T = int(input())
for _ in range(T):
N = int(input())
A = list(map(int, input().split()))
A.sort(reverse=True)
B = [A[0]]
for i in range(1, N):
B.append(B[-1] & A[i])
print(" ".join(map(str, B)))
Este cรณdigo lee los datos de entrada, procesa cada caso de prueba segรบn los pasos descritos y finalmente imprime el array B lexicogrรกficamente mรกs grande posible para cada caso de prueba.
Similar Questions
You are given an array ๐ดA of size ๐N.You can rearrange the elements of ๐ดA as you want. After that, construct an array ๐ตB of size ๐N as:๐ต1=๐ด1B 1โ =A 1โ ;๐ต๐=๐ต๐โ1B iโ =B iโ1โ && ๐ด๐A iโ for all 2โค๐โค๐2โคiโคN, where && denotes the bitwise AND operator.Find the lexicographically largest possible array ๐ตB.For two arrays ๐X and ๐Y, both of size ๐N, the array ๐X is said to be lexicographically larger than array ๐Y, if, in the first position where ๐X and ๐Y differ, ๐๐>๐๐X iโ >Y iโ .Input FormatThe first line of input will contain a single integer ๐T, denoting the number of test cases.Each test case consists of multiple lines of input.The first line of each test case contains ๐N, the size of the array ๐ดA.The second line of each test case contains ๐N space-separated integers ๐ด1,๐ด2,โฆ,๐ด๐A 1โ ,A 2โ ,โฆ,A Nโ .Output FormatFor each test case, output on a new line, ๐N space separated integers denoting the lexicographically largest array ๐ตB that can be formed by any rearrangement of ๐ดA.Constraints1โค๐โค2โ 1041โคTโค2โ 10 4 1โค๐โค2โ 1051โคNโค2โ 10 5 1โค๐ด๐โค1091โคA iโ โค10 9 The sum of ๐N over all test cases does not exceed 2โ 1052โ 10 5 .
You are given an array ๐ดA of size ๐N.You can rearrange the elements of ๐ดA as you want. After that, construct an array ๐ตB of size ๐N as:๐ต1=๐ด1B 1โ =A 1โ ;๐ต๐=๐ต๐โ1โ๐ด๐B iโ =B iโ1โ โA iโ for all 2โค๐โค๐2โคiโคN, where โโ denotes the bitwise XOR operator.Find a rearrangement of ๐ดA such that ๐ต๐โ 0B iโ ๎ =0 for all 1โค๐โค๐1โคiโคN.Input FormatThe first line of input will contain a single integer ๐T, denoting the number of test cases.Each test case consists of multiple lines of input.The first line of each test case contains ๐N, the size of the array ๐ดA.The second line of each test case contains ๐N space-separated integers : ๐ด1,๐ด2,โฆ,๐ด๐A 1โ ,A 2โ ,โฆ,A Nโ .Output FormatFor each test case, output on a new line, ๐N space-separated integers denoting the rearrangement of ๐ดA satisfying the conditions.In case no such rearrangement exists, print โ1โ1 instead.Constraints1โค๐โค2โ 1041โคTโค2โ 10 4 1โค๐โค2โ 1051โคNโค2โ 10 5 1โค๐ด๐โค1091โคA iโ โค10 9 The sum of ๐N over all test cases does not exceed 2โ 1052โ 10 5 .Sample 1:InputOutput431 2 351 2 3 4 531 2 211-11 2 4 3 51 2 21Explanation:Test case 11 : It can be shown that it's impossible to rearrange ๐ดA in a valid way.Test case 22 : A possible rearrangement of array ๐ดA is [1,2,4,3,5][1,2,4,3,5] and the corresponding array ๐ตB is [1,3,7,4,1][1,3,7,4,1]. Here ๐ต๐โ 0B iโ ๎ =0 for all 1โค๐โค๐1โคiโคN.
Make My Array EqualYou are given an array ๐ดA of length ๐N.Determine if it is possible to make all the elements of ๐ดA equal by performing the following operation any number of times (possibly, zero):Choose two distinct indices ๐i and ๐j (1โค๐,๐โค๐1โคi,jโคN, ๐โ ๐i๎ =j); andUpdate the value at index ๐i by setting ๐ด๐A iโ to ๐ด๐+๐ด๐A iโ +A jโ .For example, if ๐ด=[1,5,3,5,6]A=[1,5,3,5,6],Choosing ๐=5i=5 and ๐=3j=3 would result in the array [1,5,3,5,9][1,5,3,5,9], since we replace ๐ด5A 5โ with ๐ด5+๐ด3=9A 5โ +A 3โ =9.Choosing ๐=2i=2 and ๐=4j=4 would instead result in the array [1,10,3,5,6][1,10,3,5,6].Output "YES" if it is possible to make all elements of the array equal after performing several (possibly, zero) of these operations, otherwise output "NO" (without quotes).Input FormatThe first line of input will contain a single integer ๐T, denoting the number of test cases.Each test case consists of two lines of input.The first line of each test case contains a single integer ๐N โ the length of array.The second line of each test case contains ๐N space-separated integers ๐ด1,๐ด2,โฆ,๐ด๐A 1โ ,A 2โ ,โฆ,A Nโ , denoting the initial array.Output FormatFor each test case, print Yes if it is possible to make all elements of array equal using any number of operations, otherwise print No.You may print each character of the output in either uppercase or lowercase (for example, the strings YES, yEs, yes, and yeS will all be treated as identical).Constraints1โค๐โค1051โคTโค10 5 1โค๐โค2โ 1051โคNโค2โ 10 5 0โค๐ด๐โค1090โคA iโ โค10 9 The sum of ๐N over all test cases won't exceed 2โ 1052โ 10 5 .Sample 1:InputOutput331 1 121 231 0 0YESNOYES
You are given an array ๐ดA containing ๐N integers.Consider the following process:Let ๐=0S=0 initially.For each ๐i from 11 to ๐N in order, update ๐S to either (๐+๐ด๐)(S+A iโ ) or (๐ร๐ด๐)(SรA iโ ).That is, either add ๐ด๐A iโ to ๐S or multiply ๐S by ๐ด๐A iโ .Before performing the process, you're allowed to freely rearrange the elements of ๐ดA as you like.If you choose the rearrangement of ๐ดA and the sequence of operations optimally, what's the maximum possible value of ๐S that you can obtain?This maximum value can be very large, so print it modulo 109+710 9 +7.Input FormatThe first line of input will contain a single integer ๐T, denoting the number of test cases.Each test case consists of two lines of input.The first line of each test case contains a single integer ๐N โ the number of elements in the array.The second line contains ๐N space-separated integers ๐ด1,๐ด2,โฆ,๐ด๐A 1โ ,A 2โ ,โฆ,A Nโ - the elements of the array.Output FormatFor each test case, output on a new line the maximum possible value of ๐S, modulo 109+710 9 +7.Constraints1โค๐โค1031โคTโค10 3 1โค๐โค2โ 1051โคNโค2โ 10 5 1โค๐ด๐โค1091โคA iโ โค10 9 The sum of ๐N over all test cases won't exceed 2โ 1052โ 10 5 .Sample 1:InputOutput244 2 5 231 2 1804Explanation:Test case 11: Choose the rearrangement ๐ด=[2,2,5,4]A=[2,2,5,4]. Then,Add ๐ด1=2A 1โ =2 to ๐S. Now, ๐=2S=2.Add ๐ด2=2A 2โ =2 to ๐S. Now, ๐=4S=4.Multiply ๐S by ๐ด3=5A 3โ =5. Now, ๐=20S=20.Multiply ๐S by ๐ด4=4A 4โ =4. Now, ๐=80S=80.This is the maximum value that can be obtained.Test case 22: Choose any rearrangement and sum up all the numbers to get 1+1+2=41+1+2=4.This is the maximum value that can be obtained.
Make PermutationChef has an array ๐ดA of size ๐N. He wants to make a permutationโ โ using this array.Find whether there exists an array ๐ตB consisting of ๐N non-negative integers, such that the array ๐ถC constructed as ๐ถ๐=๐ด๐+๐ต๐C iโ =A iโ +B iโ is a permutation.โ โ A permutation of size ๐N is an array of ๐N distinct elements in the range [1,๐][1,N]. For example, [4,2,1,3][4,2,1,3] is a permutation of size 44, while [3,2,2,1][3,2,2,1] and [1,3,4][1,3,4] are not.Input FormatThe first line of input will contain a single integer ๐T, denoting the number of test cases.Each test case consists of multiple lines of input.The first line of each test case consists of ๐N - the size of the array ๐ดAThe next line contains ๐N space-separated integers - ๐ด1,๐ด2,โฆ,๐ด๐A 1โ ,A 2โ ,โฆ,A Nโ - the elements of array ๐ดA.Output FormatFor each test case, output YES if there exists an array ๐ตB such that array ๐ถC constructed as ๐ถ๐=๐ด๐+๐ต๐C iโ =A iโ +B iโ is a permutation, otherwise output NO.You may print each character of the string in uppercase or lowercase (for example, the strings YES, yEs, yes, and yeS will all be treated as identical).Constraints1โค๐โค1001โคTโค1001โค๐โค1001โคNโค1001โค๐ด๐โค๐1โคA iโ โคNSample 1:InputOutput454 1 3 2 152 4 3 4 21161 1 1 1 6 6YESNOYESNOExplanation:Test case 11 : Consider ๐ต=[0,4,0,0,0]B=[0,4,0,0,0]. The corresponding array ๐ถC becomes [4,5,3,2,1][4,5,3,2,1], which is a permutation. Some other possible values of ๐ตB for which ๐ถC is a permutation are [1,0,1,1,1][1,0,1,1,1] and [1,3,0,0,0][1,3,0,0,0].Test case 22 : It can be proven that no valid array ๐ตB exists.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.