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Ilshat is a software engineer working on efficient data structures. One day he invented a new data structure. This data structure can store a set of non-negative n - bit integers, where n is a power of two. That is, n = 2b for some non-negative integer b.
The data structure is initially empty. A program using the data structure has to follow the following rules:
add_element(x). If the program tries to add an element that is already present in the data structure, nothing happens.
check_element(x)to check whether the element x is present in the data structure. This function may be used multiple times.
When Ilshat first implemented this data structure, he made a bug in the function
compile_set(). The bug reorders the binary digits of each element in the set in the same manner. Ilshat wants you to find the exact reordering of digits caused by the bug.
Formally, consider a sequence p = [p0, ..., pn-1] in which every number from 0 to n - 1 appears exactly once. We call such a sequence a permutation. Consider an element of the set, whose digits in binary are a0, ..., an-1 (with a0 being the most significant bit). When the function
compile_set() is called, this element is replaced by the element ap0, ap1, ..., apn-1.
The same permutation p is used to reorder the digits of every element. Any permutation is possible, including the possibility that pi = i for each 0 ≤ i ≤ n - 1.
For example, suppose that n = 4, p = [2, 1, 3, 0], and you have inserted into the set integers whose binary representations are
0111. Calling the function
compile_set changes these elements to
Your task is to write a program that finds the permutation p by interacting with the data structure. It should (in the following order):
compile_setto trigger the bug,
Note that your program may call the function compile_set only once.
In addition, there is a limit on the number of times your program calls the library functions. Namely, it may
add_elementat most w times (w is for "writes"),
check_elementat most r times (r is for "reads").
You should implement one function (method):
int restore_permutation(int n, int w, int r)
n: the number of bits in the binary representation of each element of the set (and also the length of p).
w: the maximum number of
add_elementoperations your program can perform.
r: the maximum number of
check_elementoperations your program can perform.
In order to interact with the data structure, your program should use the following three functions (methods):
void add_element(string x)
xto the set.
x: a string of '
0' and '
1' characters giving the binary representation of an integer that should be added to the set. The length of
xmust be n.
add_element()after this call. Your program cannot call
check_element()before this call.
boolean check_element(string x)
xis in the modified set.
x: a string of '
0' and '
1' characters giving the binary representation of the element that should be checked. The length of
xmust be n.
xis in the modified set, and
Note that if your program violates any of the above restrictions, its grading outcome will be "Wrong Answer".
For all the strings, the first character gives the most significant bit of the corresponding integer.
The grader fixes the permutation p before the function
restore_permutation is called.
Please use the provided template files for details of implementation in your programming language.
The grader makes the following function call:
restore_permutation(4, 16, 16). We have n = 4 and the program can do at most 16 "writes" and 16 "reads".
The program makes the following function calls:
Only one permutation is consistent with these values returned by
check_element(): the permutation p = [2, 1, 3, 0]. Thus,
restore_permutation should return
[2, 1, 3, 0].
n = 8, w = 256, r = 256, pi ≠ i for at most 2 indices i (0 ≤ i ≤ n - 1)
n = 32, w = 320, r = 1024
n = 32, w = 1024, r = 320
n = 128, w = 1792, r = 1792
n = 128, w = 896, r = 896
The sample grader reads the input in the following format:
C++17, C++14, C++20, C++14 (Clang), C++17 (Clang), C++20 (Clang)