 #include <stdio.h>

// Questão 09 – Desenvolver um código que calcule sistemas de congruência linear de até 4 equações utilizando o teorema chinês do resto

// Calculo do mdc 
int mdc(int a, int b) {
    while (b != 0) {
        int temp = b;
        b = a % b;
        a = temp;
    }
    return a;
}

int mod_inverso(int a, int m) {
    int m0 = m, t, q;
    int x0 = 0, x1 = 1;
    
    if (mdc(a, m) != 1) // Verifica se a e m são coprimos
        return -1;
    
    while (a > 1) {
        q = a / m;
        t = m;
        m = a % m;
        a = t;
        t = x0;
        x0 = x1 - q * x0;
        x1 = t;
    }
    
    return (x1 < 0) ? x1 + m0 : x1;
}

// FUnção teo chines
int teorema_chines_do_resto(int a[], int m[], int n) {
    int M = 1, i, x = 0;
    
    for (i = 0; i < n; i++) {
        if (i > 0 && mdc(m[i], m[i-1]) != 1) { // Verifica se os módulos são coprimos
            printf("Erro: Os módulos devem ser coprimos entre si!\n"); 
            return -1;
        }
        M *= m[i];
    }
    
    for (i = 0; i < n; i++) {
        int Mi = M / m[i];
        int inverso = mod_inverso(Mi, m[i]);
        if (inverso == -1) {
            printf("Erro: Não existe inverso modular para %d mod %d!\n", Mi, m[i]);
            return -1;
        }
        x = (x + a[i] * Mi * inverso) % M;
    }
    
    return (x + M) % M; // Garantir que x seja positivo
}

int main() {
    int n, i;
    printf("Número de equações (máximo 4): \n");
    scanf("%d", &n);
    
    if (n < 1 || n > 4) {
        printf("Número de equações inválido!\n");
        return 1;
    }
    
    int a[n], m[n];
    
    printf("Coeficientes 'a' e os módulos 'm' (a1 m1 a2 m2 ... an mn):\n");
    for (i = 0; i < n; i++) {
        scanf("%d %d", &a[i], &m[i]);
    }
    
    int resultado = teorema_chines_do_resto(a, m, n);
    if (resultado != -1)
        printf("Solução mínima (menor x possível) x = %d\n", resultado);
    
    return 0;
}

created 5 months ago by MARIIANA SIQUEIRA NERIS

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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
}