 #include <stdio.h>

// Este programa resolve um sistema de congruências usando o Teorema Chinês do Resto.
// O usuário deve fornecer o número de equações, seguido dos módulos e restos para cada equação.

// Exemplo de entrada:
// Digite o número de equações: 3
// Digite o módulo a1: 1
// Digite o resto da equação n1: 5
// Digite o módulo a2: 3
// Digite o resto da equação n2: 7
// Digite o módulo a3: 5
// Digite o resto da equação n3: 9

/*
Exemplo de input:
3
1
5
3
7
5
9
*/

// Exemplo de saída:
// O resultado é: 311

// Função para calcular o máximo divisor comum (MDC) usando o algoritmo de Euclides
int calcularMDC(int a, int b)
{
    while (b != 0)
    {
        int temp = b;
        b = a % b;
        a = temp;
    }
    return a;
}

// Função para calcular o inverso modular de a módulo m
int calcularInversoModular(int a, int modulo)
{
    a = a % modulo;
    for (int x = 1; x < modulo; x++)
    {
        if ((a * x) % modulo == 1)
        {
            return x;
        }
    }
    return -1;
}

// Função para resolver o sistema de congruências usando o Teorema Chinês do Resto
int teoremaChinesDoResto(int modulos[], int restos[], int numEquacoes)
{
    int produtoTotal = 1;

    // Calcula o produto de todos os números em 'modulos'
    for (int i = 0; i < numEquacoes; i++)
    {
        produtoTotal *= modulos[i];
    }

    int resultado = 0;

    // Calcula o resultado usando o Teorema Chinês do Resto
    for (int i = 0; i < numEquacoes; i++)
    {
        // 'produtoParcial' é o produto total dividido pelo número atual
        int produtoParcial = produtoTotal / modulos[i];

        // Adiciona ao resultado o termo correspondente
        // restos[i] é o resto da i-ésima equação
        // calcularInversoModular(produtoParcial, modulos[i]) é o inverso modular de 'produtoParcial' módulo 'modulos[i]'
        // Multiplica pelo produto parcial 'produtoParcial'
        resultado += restos[i] * calcularInversoModular(produtoParcial, modulos[i]) * produtoParcial;
    }

    // Retorna o resultado final módulo 'produtoTotal' para garantir que está no intervalo correto
    return resultado % produtoTotal;
}

int main()
{
    int modulos[4], restos[4], numEquacoes;

    //printf("Digite o número de equações (até 4): ");
    scanf("%d", &numEquacoes);
    //printf("\n");

    for (int i = 0; i < numEquacoes; i++)
    {
        //printf("Digite o valor de a%d: ", i + 1);
        scanf("%d", &restos[i]);
        //printf("Digite o valor de n%d: ", i + 1);
        scanf("%d", &modulos[i]);
    }

    printf("As equações fornecidas são:\n");
    for (int i = 0; i < numEquacoes; i++)
    {
        printf("x ≡ %d (mod %d)\n", restos[i], modulos[i]);
    }

    int resultado = teoremaChinesDoResto(modulos, restos, numEquacoes);
    printf("\nO valor de x que satisfaz todas as congruências é: %d\n", resultado);

    return 0;
}

created 3 months ago by SAMUEL NOGUEIRA CAETANO

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About C

C language is one of the most popular general-purpose programming language developed by Dennis Ritchie at Bell laboratories for UNIX operating system. The initial release of C Language was in the year 1972. Most of the desktop operating systems are written in C Language.

Key features:

Structured Programming
Popular system programming language
UNIX, MySQL and Oracle are completely written in C.
Supports variety of platforms
Efficient and also handle low-level activities.
As fast as assembly language and hence used as system development language.

Syntax help

Loops

1. If-Else:

When ever you want to perform a set of operations based on a condition if-else is used.

if(conditional-expression) {
   // code
} else {
   // code
}

You can also use if-else for nested Ifs and if-else-if ladder when multiple conditions are to be performed on a single variable.

2. Switch:

Switch is an alternative to if-else-if ladder.

switch(conditional-expression) {    
case value1:    
 // code    
 break;  // optional  
case value2:    
 // code    
 break;  // optional  
...    
    
default:     
 // code to be executed when all the above cases are not matched;    
}

3. For:

For loop is used to iterate a set of statements based on a condition.

for(Initialization; Condition; Increment/decrement){  
  // code  
}

4. While:

While is also used to iterate a set of statements based on a condition. Usually while is preferred when number of iterations are not known in advance.

while(condition) {  
 // code 
}

5. Do-While:

Do-while is also used to iterate a set of statements based on a condition. It is mostly used when you need to execute the statements atleast once.

do {
  // code 
} while (condition);

Arrays

Array is a collection of similar data which is stored in continuous memory addresses. Array values can be fetched using index. Index starts from 0 to size-1.

Syntax

One dimentional Array:

data-type array-name[size];

Two dimensional array:

data-type array-name[size][size];

Functions

Function is a sub-routine which contains set of statements. Usually functions are written when multiple calls are required to same set of statements which increases re-usuability and modularity.

Two types of functions are present in C

Library Functions:

Library functions are the in-built functions which are declared in header files like printf(),scanf(),puts(),gets() etc.,

User defined functions:

User defined functions are the ones which are written by the programmer based on the requirement.

How to declare a Function

return_type function_name(parameters);

How to call a Function

function_name (parameters)

How to define a Function

return_type function_name(parameters) {  
  //code
}