#include <stdio.h>

// Algoritmo de Euclides para verificar se dois números são coprimos
int coPrimos(int num1, int num2) {
    int resto;
    while (num2 != 0) {
        resto = num1 % num2;
        num1 = num2;
        num2 = resto;
    }
    return (num1 == 1); // Retorna 1 se forem coprimos, 0 caso contrário
}

// Verifica as condições do Teorema Chinês
int condicoes(int *vetor, int nEq) {
    int num1, num2;

    // Condição 1: verificar se A e MOD são coprimos
    for (int i = 0; i < nEq; i++) {
        num1 = vetor[i * 3 + 1];
        num2 = vetor[i * 3 + 2];
        if (!coPrimos(num1, num2)) {
            return 0;
        }
    }

    // Condição 2: verificar se os MODs são coprimos par a par
    for (int i = 0; i < nEq; i++) {
        for (int j = i + 1; j < nEq; j++) {
            num1 = vetor[i * 3 + 2];
            num2 = vetor[j * 3 + 2];
            if (!coPrimos(num1, num2)) {
                return 0;
            }
        }
    }

    return 1; // Retorna 1 se todas as condições forem atendidas
}

// Resolve o sistema pelo Teorema Chinês dos Restos
int teoremaChines(int *vetor, int nEq) {
    int x = 0;
    int produto = 1;

    // Calcula o produto de todos os MODs
    for (int i = 0; i < nEq; i++) {
        produto *= vetor[i * 3 + 2];
    }

    // Aplica a fórmula da solução geral
    for (int i = 0; i < nEq; i++) {
        int a = vetor[i * 3];        // Coeficiente do sistema
        int b = vetor[i * 3 + 1];    // Valor de A
        int mod = vetor[i * 3 + 2];  // Valor do módulo
        int n = produto / mod;

        // Calcula o inverso modular de n módulo mod
        int inverso = 0;
        for (int j = 1; j < mod; j++) {
            if ((n * j) % mod == 1) {
                inverso = j;
                break;
            }
        }

        // Soma parcial para o valor de X
        x += a * b * n * inverso;
    }

    // Ajusta X para o menor valor positivo
    x %= produto;
    if (x < 0) {
        x += produto;
    }

    return x;
}

int main() {
    int nEq;

    printf("Digite a quantidade de equações que o seu sistema possuirá. Deve ser maior que 1.\n");
    scanf("%d", &nEq);

    if (nEq < 2) {
        printf("O número de equações deve ser maior que 1.\n");
        return 1;
    }

    int vetor[nEq * 3];
    printf("Realize os inputs na seguinte ordem: coeficiente de X, valor de A e valor do módulo.\n");

    // Preenchimento do vetor com as equações
    for (int i = 0; i < nEq * 3; i++) {
        printf("Input número %d: ", i + 1);
        scanf("%d", &vetor[i]);
    }

    // Checa as condições antes de aplicar o Teorema Chinês
    if (!condicoes(vetor, nEq)) {
        printf("Insira equações que obedeçam às condições do Teorema Chinês.\n");
        return 1;
    }

    int resposta = teoremaChines(vetor, nEq);
    printf("O valor de X é: %d\n", resposta);

    return 0;
}
 
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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

  1. Library Functions:

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

  1. 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
}