Knowee
Questions
Features
Study Tools

You are given an array ๐ดA of size ๐‘N.You can rearrange the elements of ๐ดA as you want. After that, construct an array ๐ตB of size ๐‘N as:๐ต1=๐ด1B 1โ€‹ =A 1โ€‹ ;๐ต๐‘–=๐ต๐‘–โˆ’1B iโ€‹ =B iโˆ’1โ€‹ && ๐ด๐‘–A iโ€‹ for all 2โ‰ค๐‘–โ‰ค๐‘2โ‰คiโ‰คN, where && denotes the bitwise AND operator.Find the lexicographically largest possible array ๐ตB.For two arrays ๐‘‹X and ๐‘ŒY, both of size ๐‘N, the array ๐‘‹X is said to be lexicographically larger than array ๐‘ŒY, if, in the first position where ๐‘‹X and ๐‘ŒY differ, ๐‘‹๐‘–>๐‘Œ๐‘–X iโ€‹ >Y iโ€‹ .Input FormatThe first line of input will contain a single integer ๐‘‡T, denoting the number of test cases.Each test case consists of multiple lines of input.The first line of each test case contains ๐‘N, the size of the array ๐ดA.The second line of each test case contains ๐‘N space-separated integers ๐ด1,๐ด2,โ€ฆ,๐ด๐‘A 1โ€‹ ,A 2โ€‹ ,โ€ฆ,A Nโ€‹ .Output FormatFor each test case, output on a new line, ๐‘N space separated integers denoting the lexicographically largest array ๐ตB that can be formed by any rearrangement of ๐ดA.Constraints1โ‰ค๐‘‡โ‰ค2โ‹…1041โ‰คTโ‰ค2โ‹…10 4 1โ‰ค๐‘โ‰ค2โ‹…1051โ‰คNโ‰ค2โ‹…10 5 1โ‰ค๐ด๐‘–โ‰ค1091โ‰คA iโ€‹ โ‰ค10 9 The sum of ๐‘N over all test cases does not exceed 2โ‹…1052โ‹…10 5 .

Question

You are given an array ๐ดA of size ๐‘N.You can rearrange the elements of ๐ดA as you want. After that, construct an array ๐ตB of size ๐‘N as:๐ต1=๐ด1B 1โ€‹ =A 1โ€‹ ;๐ต๐‘–=๐ต๐‘–โˆ’1B iโ€‹ =B iโˆ’1โ€‹ && ๐ด๐‘–A iโ€‹ for all 2โ‰ค๐‘–โ‰ค๐‘2โ‰คiโ‰คN, where && denotes the bitwise AND operator.Find the lexicographically largest possible array ๐ตB.For two arrays ๐‘‹X and ๐‘ŒY, both of size ๐‘N, the array ๐‘‹X is said to be lexicographically larger than array ๐‘ŒY, if, in the first position where ๐‘‹X and ๐‘ŒY differ, ๐‘‹๐‘–>๐‘Œ๐‘–X iโ€‹ >Y iโ€‹ .Input FormatThe first line of input will contain a single integer ๐‘‡T, denoting the number of test cases.Each test case consists of multiple lines of input.The first line of each test case contains ๐‘N, the size of the array ๐ดA.The second line of each test case contains ๐‘N space-separated integers ๐ด1,๐ด2,โ€ฆ,๐ด๐‘A 1โ€‹ ,A 2โ€‹ ,โ€ฆ,A Nโ€‹ .Output FormatFor each test case, output on a new line, ๐‘N space separated integers denoting the lexicographically largest array ๐ตB that can be formed by any rearrangement of ๐ดA.Constraints1โ‰ค๐‘‡โ‰ค2โ‹…1041โ‰คTโ‰ค2โ‹…10 4 1โ‰ค๐‘โ‰ค2โ‹…1051โ‰คNโ‰ค2โ‹…10 5 1โ‰ค๐ด๐‘–โ‰ค1091โ‰คA iโ€‹ โ‰ค10 9 The sum of ๐‘N over all test cases does not exceed 2โ‹…1052โ‹…10 5 .

...expand
๐Ÿง Not the exact question you are looking for?Go ask a question

Solution

Para resolver este problema, sigamos los siguientes pasos:

  1. Leer el nรบmero de casos de prueba, T.
  2. 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:

  1. Leer el nรบmero de casos de prueba, T:

    T = int(input())
    
  2. Para cada caso de prueba:

    for _ in range(T):
        N = int(input())
        A = list(map(int, input().split()))
    
  3. Ordenar el array A en orden descendente:

        A.sort(reverse=True)
    
  4. Construir el array B:

        B = [A[0]]
        for i in range(1, N):
            B.append(B[-1] & A[i])
    
  5. 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.

This problem has been solved

Similar Questions

You are given an array ๐ดA of size ๐‘N.You can rearrange the elements of ๐ดA as you want. After that, construct an array ๐ตB of size ๐‘N as:๐ต1=๐ด1B 1โ€‹ =A 1โ€‹ ;๐ต๐‘–=๐ต๐‘–โˆ’1B iโ€‹ =B iโˆ’1โ€‹ && ๐ด๐‘–A iโ€‹ for all 2โ‰ค๐‘–โ‰ค๐‘2โ‰คiโ‰คN, where && denotes the bitwise AND operator.Find the lexicographically largest possible array ๐ตB.For two arrays ๐‘‹X and ๐‘ŒY, both of size ๐‘N, the array ๐‘‹X is said to be lexicographically larger than array ๐‘ŒY, if, in the first position where ๐‘‹X and ๐‘ŒY differ, ๐‘‹๐‘–>๐‘Œ๐‘–X iโ€‹ >Y iโ€‹ .Input FormatThe first line of input will contain a single integer ๐‘‡T, denoting the number of test cases.Each test case consists of multiple lines of input.The first line of each test case contains ๐‘N, the size of the array ๐ดA.The second line of each test case contains ๐‘N space-separated integers ๐ด1,๐ด2,โ€ฆ,๐ด๐‘A 1โ€‹ ,A 2โ€‹ ,โ€ฆ,A Nโ€‹ .Output FormatFor each test case, output on a new line, ๐‘N space separated integers denoting the lexicographically largest array ๐ตB that can be formed by any rearrangement of ๐ดA.Constraints1โ‰ค๐‘‡โ‰ค2โ‹…1041โ‰คTโ‰ค2โ‹…10 4 1โ‰ค๐‘โ‰ค2โ‹…1051โ‰คNโ‰ค2โ‹…10 5 1โ‰ค๐ด๐‘–โ‰ค1091โ‰คA iโ€‹ โ‰ค10 9 The sum of ๐‘N over all test cases does not exceed 2โ‹…1052โ‹…10 5 .

You are given an array ๐ดA of size ๐‘N.You can rearrange the elements of ๐ดA as you want. After that, construct an array ๐ตB of size ๐‘N as:๐ต1=๐ด1B 1โ€‹ =A 1โ€‹ ;๐ต๐‘–=๐ต๐‘–โˆ’1โŠ•๐ด๐‘–B iโ€‹ =B iโˆ’1โ€‹ โŠ•A iโ€‹ for all 2โ‰ค๐‘–โ‰ค๐‘2โ‰คiโ‰คN, where โŠ•โŠ• denotes the bitwise XOR operator.Find a rearrangement of ๐ดA such that ๐ต๐‘–โ‰ 0B iโ€‹ ๎€ =0 for all 1โ‰ค๐‘–โ‰ค๐‘1โ‰คiโ‰คN.Input FormatThe first line of input will contain a single integer ๐‘‡T, denoting the number of test cases.Each test case consists of multiple lines of input.The first line of each test case contains ๐‘N, the size of the array ๐ดA.The second line of each test case contains ๐‘N space-separated integers : ๐ด1,๐ด2,โ€ฆ,๐ด๐‘A 1โ€‹ ,A 2โ€‹ ,โ€ฆ,A Nโ€‹ .Output FormatFor each test case, output on a new line, ๐‘N space-separated integers denoting the rearrangement of ๐ดA satisfying the conditions.In case no such rearrangement exists, print โˆ’1โˆ’1 instead.Constraints1โ‰ค๐‘‡โ‰ค2โ‹…1041โ‰คTโ‰ค2โ‹…10 4 1โ‰ค๐‘โ‰ค2โ‹…1051โ‰คNโ‰ค2โ‹…10 5 1โ‰ค๐ด๐‘–โ‰ค1091โ‰คA iโ€‹ โ‰ค10 9 The sum of ๐‘N 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 ๐ดA in a valid way.Test case 22 : A possible rearrangement of array ๐ดA is [1,2,4,3,5][1,2,4,3,5] and the corresponding array ๐ตB is [1,3,7,4,1][1,3,7,4,1]. Here ๐ต๐‘–โ‰ 0B iโ€‹ ๎€ =0 for all 1โ‰ค๐‘–โ‰ค๐‘1โ‰คiโ‰คN.

Make My Array EqualYou are given an array ๐ดA of length ๐‘N.Determine if it is possible to make all the elements of ๐ดA equal by performing the following operation any number of times (possibly, zero):Choose two distinct indices ๐‘–i and ๐‘—j (1โ‰ค๐‘–,๐‘—โ‰ค๐‘1โ‰คi,jโ‰คN, ๐‘–โ‰ ๐‘—i๎€ =j); andUpdate the value at index ๐‘–i by setting ๐ด๐‘–A iโ€‹ to ๐ด๐‘–+๐ด๐‘—A iโ€‹ +A jโ€‹ .For example, if ๐ด=[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 ๐ด5A 5โ€‹ with ๐ด5+๐ด3=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 ๐‘‡T, 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 ๐‘N โ€” the length of array.The second line of each test case contains ๐‘N space-separated integers ๐ด1,๐ด2,โ€ฆ,๐ด๐‘A 1โ€‹ ,A 2โ€‹ ,โ€ฆ,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).Constraints1โ‰ค๐‘‡โ‰ค1051โ‰คTโ‰ค10 5 1โ‰ค๐‘โ‰ค2โ‹…1051โ‰คNโ‰ค2โ‹…10 5 0โ‰ค๐ด๐‘–โ‰ค1090โ‰คA iโ€‹ โ‰ค10 9 The sum of ๐‘N over all test cases won't exceed 2โ‹…1052โ‹…10 5 .Sample 1:InputOutput331 1 121 231 0 0YESNOYES

You are given an array ๐ดA containing ๐‘N integers.Consider the following process:Let ๐‘†=0S=0 initially.For each ๐‘–i from 11 to ๐‘N in order, update ๐‘†S to either (๐‘†+๐ด๐‘–)(S+A iโ€‹ ) or (๐‘†ร—๐ด๐‘–)(Sร—A iโ€‹ ).That is, either add ๐ด๐‘–A iโ€‹ to ๐‘†S or multiply ๐‘†S by ๐ด๐‘–A iโ€‹ .Before performing the process, you're allowed to freely rearrange the elements of ๐ดA as you like.If you choose the rearrangement of ๐ดA and the sequence of operations optimally, what's the maximum possible value of ๐‘†S 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 ๐‘‡T, 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 ๐‘N โ€” the number of elements in the array.The second line contains ๐‘N space-separated integers ๐ด1,๐ด2,โ€ฆ,๐ด๐‘A 1โ€‹ ,A 2โ€‹ ,โ€ฆ,A Nโ€‹ - the elements of the array.Output FormatFor each test case, output on a new line the maximum possible value of ๐‘†S, modulo 109+710 9 +7.Constraints1โ‰ค๐‘‡โ‰ค1031โ‰คTโ‰ค10 3 1โ‰ค๐‘โ‰ค2โ‹…1051โ‰คNโ‰ค2โ‹…10 5 1โ‰ค๐ด๐‘–โ‰ค1091โ‰คA iโ€‹ โ‰ค10 9 The sum of ๐‘N 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 ๐ด=[2,2,5,4]A=[2,2,5,4]. Then,Add ๐ด1=2A 1โ€‹ =2 to ๐‘†S. Now, ๐‘†=2S=2.Add ๐ด2=2A 2โ€‹ =2 to ๐‘†S. Now, ๐‘†=4S=4.Multiply ๐‘†S by ๐ด3=5A 3โ€‹ =5. Now, ๐‘†=20S=20.Multiply ๐‘†S by ๐ด4=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 ๐ดA of size ๐‘N. He wants to make a permutationโ€ โ€  using this array.Find whether there exists an array ๐ตB consisting of ๐‘N non-negative integers, such that the array ๐ถC constructed as ๐ถ๐‘–=๐ด๐‘–+๐ต๐‘–C iโ€‹ =A iโ€‹ +B iโ€‹ is a permutation.โ€ โ€  A permutation of size ๐‘N is an array of ๐‘N 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 ๐‘‡T, denoting the number of test cases.Each test case consists of multiple lines of input.The first line of each test case consists of ๐‘N - the size of the array ๐ดAThe next line contains ๐‘N space-separated integers - ๐ด1,๐ด2,โ€ฆ,๐ด๐‘A 1โ€‹ ,A 2โ€‹ ,โ€ฆ,A Nโ€‹ - the elements of array ๐ดA.Output FormatFor each test case, output YES if there exists an array ๐ตB such that array ๐ถC constructed as ๐ถ๐‘–=๐ด๐‘–+๐ต๐‘–C 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).Constraints1โ‰ค๐‘‡โ‰ค1001โ‰คTโ‰ค1001โ‰ค๐‘โ‰ค1001โ‰คNโ‰ค1001โ‰ค๐ด๐‘–โ‰ค๐‘1โ‰คA iโ€‹ โ‰คNSample 1:InputOutput454 1 3 2 152 4 3 4 21161 1 1 1 6 6YESNOYESNOExplanation:Test case 11 : Consider ๐ต=[0,4,0,0,0]B=[0,4,0,0,0]. The corresponding array ๐ถC becomes [4,5,3,2,1][4,5,3,2,1], which is a permutation. Some other possible values of ๐ตB for which ๐ถC 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 ๐ตB exists.

1/2

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.