#include <stdio.h>

// Ao rodar o código, inserir em ordem no STDIN
// 1 LINHA - QUANTIDADE DE EQUAÇÕES (MAX 4)
// 2 LINHA - VALORES DO RESTO E DO MODULO DA EQUACÃO 1 RESPECTIVAMENTE (EX: 8 7)
// 3 LINHA - VALORES DO RESTO E DO MODULO DA EQUACÃO 2 (CASO EXISTA) RESPECTIVAMENTE (EX: 5 7)
// 4 LINHA - VALORES DO RESTO E DO MODULO DA EQUACÃO 3 (CASO EXISTA) RESPECTIVAMENTE (EX: 5 9)
// 5 LINHA - VALORES DO RESTO E DO MODULO DA EQUACÃO 4 (CASO EXISTA) RESPECTIVAMENTE (EX: 6 7)



// calcula o inverso mod de 'a' mod 'm'
int inverso_modular(int a, int m) {
    int m_original = m, x0 = 0, x1 = 1, q, t;
    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 + m_original : x1;
}

// resolve o sistema de congruencias
long long resolver_congruencias(int restos[], int modulos[], int n, long long *produto_total) {
    *produto_total = 1;
    long long resultado = 0;

    // calcula o produto total dos mod
    for (int i = 0; i < n; i++) {
        *produto_total *= modulos[i];
    }

    // aplica o TCR
    for (int i = 0; i < n; i++) {
        long long Mi = *produto_total / modulos[i];
        int inverso = inverso_modular(Mi % modulos[i], modulos[i]);
        resultado += (long long)restos[i] * Mi * inverso;
        resultado %= *produto_total;
    }

    return (resultado < 0) ? resultado + *produto_total : resultado;
}

int main() {
    int n, restos[4], modulos[4];
    long long produto_total;

    scanf("%d", &n); // Le o numero de equacoes

    for (int i = 0; i < n; i++) {
        scanf("%d %d", &restos[i], &modulos[i]); // Le restos e modulos
    }

    // calcula a solucao e imprime
    long long resultado = resolver_congruencias(restos, modulos, n, &produto_total);
    printf("Solucao: x =(congruente) %lld (mod %lld)\n", resultado, produto_total);

    return 0;
}
by

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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
}