sequence | C++ для приматов

Условия задачи

Даны действительные числа [latex]a_{1}[/latex], [latex]a_{2}[/latex], [latex]\ldots[/latex], [latex]a_{2n}[/latex]. Получить [latex]a_{1}[/latex], [latex]a_{2n}[/latex], [latex]a_{2}[/latex], [latex]a_{2n-1}[/latex], [latex]a_{3}[/latex], [latex]\ldots[/latex], [latex]a_{n}[/latex], [latex]a_{n+1}[/latex].

Данную задачу можно найти здесь.

Входные данные

Последовательность действительных чисел [latex]a_{1}[/latex], [latex]a_{2}[/latex], [latex]\ldots[/latex], [latex]a_{2n}[/latex].

Выходные данные

Последовательность действительных чисел [latex]a_{1}[/latex], [latex]a_{2n}[/latex], [latex]a_{2}[/latex], [latex]a_{2n-1}[/latex], [latex]a_{3}[/latex], [latex]\ldots[/latex], [latex]a_{n}[/latex], [latex]a_{n+1}[/latex] .

Тесты

№	Входные данные	Выходные данные
1	1 2 3 4 5 6	1 6 2 5 3 4
2	0 0 0 0 0 1	0 1 0 0 0 0
3	3 12 42 -6 15 0 0 0 501 20 20 20	3 20 12 20 42 20 -6 501 15 0 0 0
4	42 0 17 -2.6 -54 41888 0.25 13 1.3333 -284.73	42 -284.73 0 1.3333 17 13 -2.6 0.25 -54 41888
5	0 1 -1 0 1 -1 97 113 -7.777 0 48 -69	0 -69 1 48 -1 0 0 -7.777 1 113 -1 97

Код

#include <iostream>
#include <vector>
using namespace std;
 
int main() {
    vector <double> sequence, result_sequence;
    double term_of_sequence;
    while (cin >> term_of_sequence){
        sequence.push_back(term_of_sequence);
    }
    for (int i = 0; i < sequence.size() / 2; i++){
        result_sequence.push_back(sequence[i]);
        result_sequence.push_back(sequence[sequence.size() - 1 - i]);
    }
    for (int i = 0; i < result_sequence.size(); i++){
        cout << result_sequence[i] << " ";
    }
    return 0;
}

#include <iostream>

#include <vector>

using namespace std;

int main() {

vector <double> sequence, result_sequence;

double term_of_sequence;

while (cin >> term_of_sequence){

sequence.push_back(term_of_sequence);

}

for (int i = 0; i < sequence.size() / 2; i++){

result_sequence.push_back(sequence[i]);

result_sequence.push_back(sequence[sequence.size() - 1 - i]);

}

for (int i = 0; i < result_sequence.size(); i++){

cout << result_sequence[i] << " ";

}

return 0;

}

Код на ideone можно найти здесь.

Ход решения

Считываем все числа из входного потока и записываем их в вектор исходной последовательности sequence. Результатом работы нашей программы должна быть новая последовательность действительных чисел result_sequence, которая задаётся по следующему правилу: первый член новой последовательности совпадает с первым членом исходной, второй член новой последовательности является последним членом исходной, третий – второй член исходной и так далее до исчерпания чисел. Иными словами, новая последовательность из [latex]2n[/latex] чисел на нечётных номерах имеет члены исходной последовательности (от первого и до [latex]n[/latex]-го включительно), чётным же номерам новой последовательности соответствуют члены исходной с номерами от [latex]n+1[/latex] до [latex]2n[/latex] включительно, записанные в обратном порядке.

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There is a sequence of real numbers [latex]a_1, a_2, \ldots[/latex](read to the end of the input stream). You need to get the sequence of numbers [latex]b_1, \ldots, b_{10}[/latex], where [latex]b_i[/latex] is the sum of those members of input sequence, that belong left-open interval [latex](i — 1, i](i = 1, \ldots, 10)[/latex]. If the interval doesn’t contain any members of the sequence, the corresponding [latex]b_i[/latex] will be set equal to zero.

Input

The sequence of real numbers [latex]a_1, a_2, \ldots[/latex].

Output

Output the sequence [latex]b_1, \ldots, b_{10}[/latex], that satisfies specified conditions.

Tests

№	Input sequence	Output sequence
1	1 2 3 4 5 6 7 8 9 10	1 2 3 4 5 6 7 8 9 10
2	1 1 1 1 1 1 1	7 0 0 0 0 0 0 0 0 0
3	2.1 2.5 2.7	0 0 7.3 0 0 0 0 0 0 0
4	11 12 13 14 15	0 0 0 0 0 0 0 0 0 0
5	2 12 85 0.6	0.6 2 0 0 0 0 0 0 0 0
6	2.02 42 1.998 3 7.43 3.33 3.03 5.56 5 5.5	0 1.998 5.02 6.36 5 11.06 0 7.43 0 0

Algorithm

The proposed task we can solve in two different ways: using class vector and like a problem with stream processing of data.

Class vector:
Initialize a vector, that will store all the elements of the input sequence (push them to the vector to the end of the input stream). Further, sort it ascending for easy follow-up work. For the each element of initial sequence check whether it belongs to the current interval. If it is true, it will be added to the corresponding element of resulting sequence, or zero will be added otherwise. Output the resulting sequence.
Stream processing:
While we are reading the input stream, we can determine which element of the resulting sequence it belongs, by using rounding to smallest integral value that is not less that our and substracting one (we need to remember that we can’t go beyond the bounds of the array, therefore we use a separate check). Perform the output of the result.

Code (class Vector)

#include <vector>
#include <iostream>
#include <algorithm>
using namespace std;

const unsigned int RESULTING_SEQUENCE_SIZE = 10;

int main() {
	double currentMember;
	vector <double> inputSequence;
    double resultingSequence[RESULTING_SEQUENCE_SIZE]{0};
    // Adds a new element to the vector to the end of the input stream
    while (cin >> currentMember) {
    	inputSequence.push_back(currentMember);
    } 
    sort(inputSequence.begin(), inputSequence.end()); // Sort ascending initial sequence
    for (int i = 0; i < RESULTING_SEQUENCE_SIZE; i++) {
    	// Accumulate the sum of suitable elements to the corresponding member of the result sequence
    	for (auto currentMember : inputSequence) {
    		resultingSequence[i] += (i < currentMember && currentMember <= i + 1 ? currentMember : 0);
    	}
    }
    // Output the sequence
    for (auto currentMember : resultingSequence) {
    	cout << currentMember << " ";
    } 
	return 0;
}

#include <vector>

#include <iostream>

#include <algorithm>

using namespace std;

const unsigned int RESULTING_SEQUENCE_SIZE = 10;

int main() {

double currentMember;

vector <double> inputSequence;

double resultingSequence[RESULTING_SEQUENCE_SIZE]{0};

// Adds a new element to the vector to the end of the input stream

while (cin >> currentMember) {

inputSequence.push_back(currentMember);

}

sort(inputSequence.begin(), inputSequence.end()); // Sort ascending initial sequence

for (int i = 0; i < RESULTING_SEQUENCE_SIZE; i++) {

// Accumulate the sum of suitable elements to the corresponding member of the result sequence

for (auto currentMember : inputSequence) {

resultingSequence[i] += (i < currentMember && currentMember <= i + 1 ? currentMember : 0);

}

// Output the sequence

for (auto currentMember : resultingSequence) {

cout << currentMember << " ";

}

return 0;

}

Code (stream processing)

#include <cmath>
#include <iostream>
using namespace std;

const unsigned int RESULTING_SEQUENCE_SIZE = 10;

int main() {
	double currentMember;
	double resultingSequence[RESULTING_SEQUENCE_SIZE]{0}; 
    // Process until the end of the input stream
    while (cin >> currentMember) {
    	// Accumulate the sum of suitable elements to the corresponding member of the resulting sequence
    	if (1 <= ceil(currentMember) && ceil(currentMember) <= RESULTING_SEQUENCE_SIZE) {
    		resultingSequence[(int)ceil(currentMember) - 1] += currentMember; 
    	} 
    } 
    // Output the sequence
    for (auto currentMember : resultingSequence) {
    	cout << currentMember << " ";
    } 
	return 0;
}

#include <cmath>

#include <iostream>

using namespace std;

const unsigned int RESULTING_SEQUENCE_SIZE = 10;

int main() {

double currentMember;

double resultingSequence[RESULTING_SEQUENCE_SIZE]{0};

// Process until the end of the input stream

while (cin >> currentMember) {

// Accumulate the sum of suitable elements to the corresponding member of the resulting sequence

if (1 <= ceil(currentMember) && ceil(currentMember) <= RESULTING_SEQUENCE_SIZE) {

resultingSequence[(int)ceil(currentMember) - 1] += currentMember;

}

// Output the sequence

for (auto currentMember : resultingSequence) {

cout << currentMember << " ";

}

return 0;

}

C++ для приматов

Начальный курс программирования для студентов направления "Прикладная математика" Одесского национального университета имени И.И.Мечникова

Tag Archives: sequence

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Input

Output

Tests

Algorithm

Code (class Vector)

Code (stream processing)

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