Trab 2

bootstrap.min.css

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        <h3 class="text-muted" style="text-align: center;">Trabalho 2 de Algoritmos 2</h3>
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        <h1 style="text-align: center;">Relatório</h1>
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<p>Bernardo Ferrari - GRR20150030</br>
&Eacute;rico Pizzato T&aacute;vora - GRR20157643<br />

<p>Para realizarmos o Trabalho Pr&aacute;tico 2, de Algoritmos 2, nos reunimos para discutir qual seria a melhor forma de implementar o programa proposto. Programa este que deveria conter os seguintes algoritmos de ordena&ccedil;&atilde;o: SelectSort, BubbleSort, QuickSort recursivo e QuickSort iterativo. O objetivo final era simular um jogo da mega sena, e comparar sorts diferentes para ver como a complexidade varia entre diferentes tipos e diferentes implenta&ccedil;&otilde;es (como iterativa e recursiva)</p>

<p>Ap&oacute;s implementarmos cada uma das fun&ccedil;&otilde;es e o programa, aperfei&ccedil;oamos o programa em cada detalhe. No nosso vetor principal, em vez de usarmos aloca&ccedil;&atilde;o est&aacute;tica e nos preocupar com o tamanho m&aacute;ximo dele - as vezes o usu&aacute;rio quer s&oacute; 60 n&uacute;meros -, optamos pela aloca&ccedil;&atilde;o din&acirc;mica. Assim, nos casos pequenos ele ocupa pouca mem&oacute;ria, e em casos como no teste de 10 mil vetores, ele pode ocupar muita. Outra sacada inteligente foi, muitas vezes, usar o scanf como uma das condi&ccedil;&otilde;es do while; foi pedido para checar consist&ecirc;ncia dos dados, ent&atilde;o essa foi o nosso jeito de implementar. Detalhe: a especifica&ccedil;&atilde;o est&aacute; mais preocupada com o fato do usu&aacute;rio digitar um n&uacute;mero inv&aacute;lido que com o fato do usu&aacute;rio digitar um n&uacute;mero ou n&atilde;o. Pensando nisso, nosso programa funciona perfeito quando o usu&aacute;rio digitar um n&uacute;mero. Se ele digitar uma string, isso quebra o scanf - poderiamos ter resolvido com fgets e outros meios mais sofisticados, mas sentimos que esse n&atilde;o era o foco do projeto, iria levar mais tempo, e s&oacute; aumentar o n&uacute;mero de linhas.</p>

<p>Nosso jeito de ver quantos n&uacute;meros a pessoa acertou foi bem simples. N&oacute;s pesquisamos no vetor se o valor que a pessoa inseriu est&aacute; dentro; se estiver, colocamos 1 em um vetor auxiliar. Se n&atilde;o, 0. Ap&oacute;s isso nosso programa compara o auxiliar com o que a pessoa digitou e imprime os valores que batem com 1 - ou seja, que est&atilde;o presentes. Usamos busca sequencial, pois o vetor inicial n&atilde;o est&aacute; ordenado, e ordenar ele n&atilde;o teria nenhum benef&iacute;cio para o estado atual do programa. Ent&atilde;o foi mais barato, computacionalmente falando, usar uma pesquisa sequencial.</p>

<p>No final de tudo, n&oacute;s ordenamos o vetor de n&uacute;meros, para deixar o log mais bonito e mostrar que nossas fun&ccedil;&otilde;es est&atilde;o funcionando perfeitamente. Escolhemos o bubble sort para essa ordena&ccedil;&atilde;o, pois mesmo sendo criticado durante as aulas e conversas com amigos, percebemos ao rodar no teste dos 10 mil vetores, que ele n&atilde;o &eacute; t&atilde;o ruim assim no pior caso, comparado com outros algoritimos.</p>

<p>Quanto a parte de ordenar 10 mil vetores, pode ser que exista algum problema em nosso programa com rela&ccedil;&atilde;o ao tempo. Os n&uacute;meros s&atilde;o muito pequenos e muito pr&oacute;ximos. Chegamos a conclus&atilde;o de, caso realmente haja um problema, existem duas grandes possiblidades. 1) O c&aacute;lculo de tempo est&aacute; sendo feito incorretamente - estamos contando a hora em que come&ccedil;a a opera&ccedil;&atilde;o, a hora em que termina, e fazendo uma conta para ver quanto tempo passou entre elas. Ou 2) Alguma opera&ccedil;&atilde;o no meio do caminho, pode ser at&eacute; na hora de conseguir os valores aleat&oacute;rios para colocar no vetor, est&aacute; sendo muito pesada e n&atilde;o est&aacute; permitindo que os algoritmos demonstrem o seu potencial. De qualquer forma, testamos algoritmos que foram dados em aula mas n&atilde;o foram exigidos no trabalho, e todos funcionaram da mesma forma, perfeitamente.</p>

<p>Para utilizar o programa, &eacute; s&oacute; seguir as op&ccedil;&otilde;es apresentadas. N&atilde;o fizemos tudo na linha de comando pois achamos que ficar fazendo perguntas &eacute; mais amig&aacute;vel para o usu&aacute;rio final e se aproxima mais de uma situa&ccedil;&atilde;o real.</p>

<p>O resultado obtido foi, al&eacute;m do programa proposto, um conhecimento mais profundo e a utiliza&ccedil;&atilde;o pr&aacute;tica dos diferentes tipos de fun&ccedil;&otilde;es de busca e ordena&ccedil;&atilde;o ensinados em aula e sobre complexidade computacional.</p>
        </p>
        <p><a class="btn btn-lg btn-success" href="source.c.txt" role="button">Código Fonte .c.txt</a></p>
        <p><a class="btn btn-lg btn-success" href="source.c" role="button">Código Fonte .c</a></p>
      </div>
      <div class="row marketing">
        <div class="col-lg-6">
          <h4>Log 1</h4>
          <p>Bem vindo! Deseja jogar na mega quadra ou comparar a efici&ecirc;ncia? Digite 1 para mega, 0 para efici&ecirc;ncia: 1</p>

<p>Qual o tamanho m&aacute;ximo? 60<br />
Qual o valor m&aacute;ximo? 60</p>

<p>Imprimindo o vetor: 46 1 11 53 3 50 20 13 28 41 22 40 28 51 49 27 16 40 50 12 32 52 52 28 1 41 41 13 25 1 55 25 13 35 45 15 44 57 16 54 20 10 60 46 59 2 49 14 29 28 10 11 37 4 45 49 31 12 13 32 </p>

<p>Digite os valores da quadra:<br />
1&deg; valor: -234<br />
Por favor, n&uacute;mero tem que ser v&aacute;lido: 23<br />
2&deg; valor: 69<br />
Por favor, n&uacute;mero tem que ser v&aacute;lido: 61<br />
Por favor, n&uacute;mero tem que ser v&aacute;lido: 63<br />
Por favor, n&uacute;mero tem que ser v&aacute;lido: 59<br />
3&deg; valor: -1 <br />
Por favor, n&uacute;mero tem que ser v&aacute;lido: 98<br />
Por favor, n&uacute;mero tem que ser v&aacute;lido: 50<br />
4&deg; valor: 11<br />
Portanto, foram inseridos os n&uacute;meros: 23 59 50 11 </p>

<p>Foram sorteados os n&uacute;meros: 59 50 11 <br />
Voc&ecirc; n&atilde;o ganhou mas acertou 3</p>

<p>Ordenando o vetor..<br />
Imprimindo o vetor: 1 1 1 2 3 4 10 10 11 11 12 12 13 13 13 13 14 15 16 16 20 20 22 25 25 27 28 28 28 28 29 31 32 32 35 37 40 40 41 41 41 44 45 45 46 46 49 49 49 50 50 51 52 52 53 54 55 57 59 60 </p>

<p>
Quer jogar de novo? Digite 1 para SIM, 0 para N&Atilde;O: 1<br />
Bem vindo! Deseja jogar na mega quadra ou comparar a efici&ecirc;ncia? Digite 1 para mega, 0 para efici&ecirc;ncia: 1</p>

<p>Qual o tamanho m&aacute;ximo? 30<br />
Qual o valor m&aacute;ximo? 90</p>

<p>Imprimindo o vetor: 66 21 71 60 43 53 11 9 70 31 72 72 71 40 75 67 21 12 24 10 58 37 65 83 82 32 59 8 18 18 </p>

<p>Digite os valores da quadra:<br />
1&deg; valor: 9<br />
2&deg; valor: 70<br />
3&deg; valor: 31<br />
4&deg; valor: 72<br />
Portanto, foram inseridos os n&uacute;meros: 9 70 31 72 </p>

<p>Foram sorteados os n&uacute;meros: 9 70 31 72 <br />
Voc&ecirc; ganhou!!!!!!</p>

<p>Ordenando o vetor..<br />
Imprimindo o vetor: 8 9 10 11 12 18 18 21 21 24 31 32 37 40 43 53 58 59 60 65 66 67 70 71 71 72 72 75 82 83 </p>

<p>
Quer jogar de novo? Digite 1 para SIM, 0 para N&Atilde;O: 1<br />
Bem vindo! Deseja jogar na mega quadra ou comparar a efici&ecirc;ncia? Digite 1 para mega, 0 para efici&ecirc;ncia: 1</p>

<p>Qual o tamanho m&aacute;ximo? 30<br />
Qual o valor m&aacute;ximo? 9999</p>

<p>Imprimindo o vetor: 7369 1605 5546 3510 1230 7862 4383 656 9977 2176 5048 1706 649 2056 9980 7821 4387 9069 6989 4564 2265 7949 564 2871 4416 7209 2131 9271 9095 9888 </p>

<p>Digite os valores da quadra:<br />
1&deg; valor: 1<br />
2&deg; valor: 2<br />
3&deg; valor: 3<br />
4&deg; valor: 4<br />
Portanto, foram inseridos os n&uacute;meros: 1 2 3 4 </p>

<p>Sem nada<br />
voc&ecirc; errou tudo</p>

<p>Ordenando o vetor..<br />
Imprimindo o vetor: 564 649 656 1230 1605 1706 2056 2131 2176 2265 2871 3510 4383 4387 4416 4564 5048 5546 6989 7209 7369 7821 7862 7949 9069 9095 9271 9888 9977 9980 </p>

<p>
Quer jogar de novo? Digite 1 para SIM, 0 para N&Atilde;O: 0</p>
        </div>

        <div class="col-lg-6">


          <h4>Log 2</h4>
          <p>Bem vindo! Deseja jogar na mega quadra ou comparar a efici&ecirc;ncia? Digite 1 para mega, 0 para efici&ecirc;ncia: 0<br />
Vamos checar os tempos de execu&ccedil;&atilde;o para 10000 vetores:<br />
SelectSort: 0.930036<br />
BubbleSort: 0.923228<br />
Quick (recur): 0.907137<br />
Quick (iter): 0.906473</p>

<p>
Quer jogar de novo? Digite 1 para SIM, 0 para N&Atilde;O: 1<br />
Bem vindo! Deseja jogar na mega quadra ou comparar a efici&ecirc;ncia? Digite 1 para mega, 0 para efici&ecirc;ncia: 1</p>

<p>Qual o tamanho m&aacute;ximo? 10<br />
Qual o valor m&aacute;ximo? 50</p>

<p>Imprimindo o vetor: 29 4 37 24 38 5 34 39 29 23 </p>

<p>Digite os valores da quadra:<br />
1&deg; valor: 1 <br />
2&deg; valor: 2<br />
3&deg; valor: 7<br />
4&deg; valor: 9<br />
Portanto, foram inseridos os n&uacute;meros: 1 2 7 9 </p>

<p>Sem nada<br />
voc&ecirc; errou tudo</p>

<p>Ordenando o vetor..<br />
Imprimindo o vetor: 4 5 23 24 29 29 34 37 38 39 </p>

<p>
Quer jogar de novo? Digite 1 para SIM, 0 para N&Atilde;O: 0</p>
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source.c

#include <stdio.h>
#include <stdlib.h>
#include <time.h>
// Bernardo Ferrari GRR20150030
// Érico Pizzato Távora GRR20157643
#define DEZMIL 10000

int randint(int max_n){
    return rand() % max_n + 1;
}

int pesqBin(int vetor[], int Elem, int N){
    int meio, esq, dir;
    esq=1;
    dir=N;//direita recebe tamanho do vetor (ultimo elemento)
    do{//enquanto elemento diferente do elemento do meio do vetor e esquerda menor que direita
        meio=(esq+dir)/2;//acha elemento do meio
        if(Elem > vetor[meio])//se elemento maior que vetor de meio
        esq = meio+1;      //esquerda vira meio+1 (elemento a direita do meio)
        else                  //caso contrario direita vira meio-1 (elemento a esquerda do meio)
        dir = meio-1;
    }while(Elem != vetor[meio] && esq <= dir);
    if(Elem == vetor[meio])//se elemento igual ao elemento que esta no meio
    return(meio);      //retorna meio (sua posicao)
    else                   //caso contrario retorna 0
    return 0;
}

void troca(int vetor[], int x, int y){ //funcao para troca de dois valores
    int aux;
    aux=vetor[x]; //guarda vetor de x
    vetor[x]=vetor[y]; //troca vetor de x por vetor de y
    vetor[y]=aux; // troca vetor de y pelo antigo valor de vetor de x
}

int mediana(int vetor[], int esq, int dir){//funcao para achar a mediana do primeiro, ultimo e valor do meio do vetor
    int meio=(esq+dir)/2;
    if (dir == esq - 1) return esq;  // only two elements, already sorted by median3()
    if(vetor[dir] < vetor[esq])//se vetor de direita(dir) menor que vetor de esquerda(esq)
    troca(vetor, esq, dir);  //troca esquerda(esq) e direita(dir)
    if(vetor[meio] < vetor[esq]) //se vetor de meio menor que vetor de esquerda(esq)
    troca(vetor, meio, esq);   //troca meio e esquerda(esq)
    if(vetor[dir] < vetor[meio])  //se vetor de direita menor que vetor de meio
    troca(vetor, dir, meio);    //troca direita(dir) e meio
    return meio;//retorna meio
}

int particao(int vetor[], int esq, int dir) {//faz a particao recebendo o vetor, a primeira e a ultima posicao do mesmo
    int pivo, i, j, t, med;
    med=mediana(vetor, esq, dir); //acha mediana
    pivo = vetor[med];//atribui a mediana como pivo
    i = esq; j = dir+1;

    while(1){
        do ++i; while(vetor[i] <= pivo && i <= dir ); //aumenta i enquanto vetor de i for menor ou igual ao pivo e menor que direita
        do --j; while(vetor[j] > pivo );//diminui i enquanto vetor de j for maior que o pivo
        if(i >= j ) break; //sai do loop quando esquerda esteja a direita de direita, ou na mesma posicao(ou seja, esq>=dir, ou i>=j)
        t = vetor[i]; vetor[i] = vetor[j]; vetor[j] = t;//faz troca entre vetor de i e vetor de j
    }
    t = vetor[esq]; vetor[esq] = vetor[j]; vetor[j] = t;//faz troca entre vetor de esquerda e vetor de j
    return j;//retorna j
}

void quickSortR(int vetor[], int esq, int dir) //quicksort na versao recursiva
{
    int j;

    if( esq < dir ) {// se esquerda menor que direita (verifica se esta a esquerda mesmo)
        j = particao(vetor, esq, dir);//j recebe a particao feita com a mediana
        quickSortR(vetor, esq, j-1);//faz quicksort de um dos lados
        quickSortR(vetor, j+1, dir);//faz quicksort do outro lado
    }

}

void quickSortI(int *vetor, int esq, int dir) {//versao iterativa do quicksort
    int pivo, i[dir], j[dir], x=0, aux ;
    
    i[0]=esq;
    j[0]=dir;
    
    while (x>=0) {
        esq=i[x];
        dir=j[x];
        
        if (esq<dir) { //checa se esquerda realmente esta a esquerda de direita
            pivo = vetor[esq];
         
            while (esq<dir) {
                while (vetor[dir]>=pivo && esq<dir)
                	dir--;
                //fica no while enquanto vetor de direita maior ou igual ao pivo e esquerda menor que direita, diminuindo dir
                if (esq<dir)
                	vetor[esq++] = vetor[dir];
                //se esquerda esta a esquerda de direita, vetor de esq+1 recebe vetor de dir
                while (vetor[esq]<=pivo && esq<dir)
                	esq++;
                //fica no while enquanto vetor de esquerda menor ou igual ao pivo e esquerda menor que direita, aumentando esq
                if (esq<dir)
                	vetor[dir--]=vetor[esq];
                //se esquerda esta a esquerda de direita, vetor de dir-1 recebe vetor de esq
            }
            vetor[esq] = pivo;
            i[x+1] = esq+1;
            j[x+1] = j[x];
            j[x++] = esq;
            
            if (j[x]-i[x] > j[x-1] - i[x-1]) {
                aux = i[x];
                i[x] = i[x-1];
                i[x-1] = aux;
                aux = j[x];
                j[x] = j[x-1];
                j[x-1] = aux;
            }
        }
        else
            x--;     
    }
}


void bubblesort(int *vetor, int n){
    int i, j, aux;
    for (i = n-1; i >= 1; i--) //enquanto i menor que tamanho do vetor i recebe i+1
    for (j = 0; j<i; j++)
    if (vetor[j] > vetor[j+1])
    {
        aux = vetor[j];
        vetor[j] = vetor[j+1];
        vetor[j+1] = aux;
    }
}

void selection_sort(int num[], int tam)
{
    int i, j, min, aux;
    for (i = 0; i < (tam-1); i++){ //enquanto i menor que tamanho do vetor min recebe i e i recebe i+1
        min = i;
        for (j = (i+1); j < tam; j++){ //enquanto j menor ou igual que tamanho do vetor min recebe j e j recebe j++
            if(num[j] < num[min]) //se vetor de j for menor que vetor de min, min recebe j
            min = j; //troca vetor de min com vetor de i
        }
        if (i != min) {
            aux = num[i];
            num[i] = num[min];
            num[min] = aux;
        }
    }
}

void imprimevetor(int * vetor, int tam){
    int i;
    printf("\nImprimindo o vetor: ");
    for (i = 0; i < tam; i++){
        printf("%d ",vetor[i]);
    }
    printf("\n");
}
void geravetor(int * vetor, int tam, int max){
    int i;
    for (i = 0; i < tam; i++){
        vetor[i] = randint(max);
    }
}

int main(){
    int max,i,loto[4], aux[4], soma, j, achou, tam, menor, passos;
    time_t t;
    int * vetor;
    srand((unsigned) time(&t));

    do{
        printf("Bem vindo! Deseja jogar na mega quadra ou comparar a eficiência? Digite 1 para mega, 0 para eficiência: ");
        scanf("%d",&passos);

        if (passos == 1){
            printf("\nQual o tamanho máximo? "); // Número de valores que a loteria terá.
            scanf("%d",&tam);
            vetor = (int *) malloc(sizeof(int) * (tam + 1)); // Essa forma de alocar a memória é útil, pois nesse caso o vetor tende a ser pequeno, mas no caso de 10 mil é o oposto.

            printf("Qual o valor máximo? "); // Valor máximo da loteria a ser sorteado.
            scanf("%d",&max);

            geravetor(vetor,tam,max);
            imprimevetor(vetor, tam);
            printf("\n");

            printf("Digite os valores da quadra:\n");
            for (i = 0; i < 4; i++){
                printf("%d° valor: ",i+1);
                while(scanf("%d",&menor) && (menor > max || menor < 0)){ //Essa parte irá checar a consistência dos dados. Se é maior que 0 e menor que o tamanho máximo.
                    printf("Por favor, número tem que ser válido: ");
                }
                loto[i] = menor;
            }

            printf("Portanto, foram inseridos os números: ");
            for (i = 0; i < 4; i++){
                printf("%d ", loto[i]); // Irá mostrar os números inseridos pelo usuário, que agora estão guardados em um vetor.
            }
            printf("\n");

            soma = 0;
            for (i = 0; i < 4; i++){
                achou = 0;
                for (j = 0; j < tam; j++){
                    if (loto[i] == vetor[j]){ //Irá procurar pelos números em que o usuário acertou. Busca sequencial, nesse caso é mais barata que ordenar e fazer busca binária.
                        achou = 1;
                        soma++;
                        break;
                    }
                }
                if (achou == 1){
                    aux[i] = 1; // 1 significa que o usuário acertou
                }
                else{
                    aux[i] = 0; // 0 significa que o usuário errou
                }
            }

            if (soma == 0)
            printf("\nSem nada\n");
            else{
                printf("\nForam sorteados os números: ");
                for (i = 0; i < 4; i++){
                    if (aux[i])
                    printf("%d ", loto[i]); // Aqui checa se o usuário acertou ou errou e imprime os números que ele acertou.
                }
                printf("\n");
            }
            if (soma == 4){
                printf("Você ganhou!!!!!!");
            }
            else if (soma > 0){
                printf("Você não ganhou mas acertou %d",soma);
            }
            else{
                printf("você errou tudo");
            }
            printf("\n\n");
            printf("Ordenando o vetor..");
            bubblesort(vetor,tam);
            imprimevetor(vetor, tam);
        }
        else{
            printf("Vamos checar os tempos de execução para 10000 vetores:\n");
            vetor = (int *) malloc(sizeof(int) * (DEZMIL + 1));

            clock_t start, end;
            double cpu_time_used;

            start = clock(); // Conta a hora no início
            for(j = 0; j < DEZMIL; j++){ //Faz 10 mil iterações. É possível mudar o conteúdo do DEZMIL, para ver como os algoritmos se comportam.
                for (i = 0; i < DEZMIL; i++){
                    vetor[i] = randint(DEZMIL); // Coloca um valor aleatório
                }
                selection_sort(vetor,tam); // Chama a ordenação
            }
            end = clock(); // Termina o relógio

            cpu_time_used = ((double) (end - start)) / CLOCKS_PER_SEC; // Guarda o intervalo de tempo em uma variável
            printf("SelectSort: %f\n",cpu_time_used); // Imprime

            // De agora em diante, repete o processo anterior.

            start = clock();
            for(j = 0; j < DEZMIL; j++){
                for (i = 0; i < DEZMIL; i++){
                    vetor[i] = randint(DEZMIL);
                }
                bubblesort(vetor,tam);
            }
            end = clock();

            cpu_time_used = ((double) (end - start)) / CLOCKS_PER_SEC;
            printf("BubbleSort: %f\n",cpu_time_used);

            start = clock();
            for(j = 0; j < DEZMIL; j++){
                for (i = 0; i < DEZMIL; i++){
                    vetor[i] = randint(DEZMIL);
                }
                quickSortR(vetor,0,tam);
            }
            end = clock();

            cpu_time_used = ((double) (end - start)) / CLOCKS_PER_SEC;
            printf("Quick (recur): %f\n",cpu_time_used);

            start = clock();
            for(j = 0; j < DEZMIL; j++){
                for (i = 0; i < DEZMIL; i++){
                    vetor[i] = randint(DEZMIL);
                }
                quickSortI(vetor,0,tam);
            }
            end = clock();

            cpu_time_used = ((double) (end - start)) / CLOCKS_PER_SEC;
            printf("Quick (iter): %f\n",cpu_time_used);
        }
        free(vetor); // Irá limpar a memória do vetor, que é usado em ambas as partes do programa.
        printf("\n\n");
        printf("Quer jogar de novo? Digite 1 para SIM, 0 para NÃO: ");
    } while(scanf("%d",&max) && max == 1);
}

source.c.txt

#include <stdio.h>
#include <stdlib.h>
#include <time.h>
// Bernardo Ferrari GRR20150030
// Érico Pizzato Távora GRR20157643
#define DEZMIL 10000

int randint(int max_n){
    return rand() % max_n + 1;
}

int pesqBin(int vetor[], int Elem, int N){
    int meio, esq, dir;
    esq=1;
    dir=N;//direita recebe tamanho do vetor (ultimo elemento)
    do{//enquanto elemento diferente do elemento do meio do vetor e esquerda menor que direita
        meio=(esq+dir)/2;//acha elemento do meio
        if(Elem > vetor[meio])//se elemento maior que vetor de meio
        esq = meio+1;      //esquerda vira meio+1 (elemento a direita do meio)
        else                  //caso contrario direita vira meio-1 (elemento a esquerda do meio)
        dir = meio-1;
    }while(Elem != vetor[meio] && esq <= dir);
    if(Elem == vetor[meio])//se elemento igual ao elemento que esta no meio
    return(meio);      //retorna meio (sua posicao)
    else                   //caso contrario retorna 0
    return 0;
}

void troca(int vetor[], int x, int y){ //funcao para troca de dois valores
    int aux;
    aux=vetor[x]; //guarda vetor de x
    vetor[x]=vetor[y]; //troca vetor de x por vetor de y
    vetor[y]=aux; // troca vetor de y pelo antigo valor de vetor de x
}

int mediana(int vetor[], int esq, int dir){//funcao para achar a mediana do primeiro, ultimo e valor do meio do vetor
    int meio=(esq+dir)/2;
    if (dir == esq - 1) return esq;  // only two elements, already sorted by median3()
    if(vetor[dir] < vetor[esq])//se vetor de direita(dir) menor que vetor de esquerda(esq)
    troca(vetor, esq, dir);  //troca esquerda(esq) e direita(dir)
    if(vetor[meio] < vetor[esq]) //se vetor de meio menor que vetor de esquerda(esq)
    troca(vetor, meio, esq);   //troca meio e esquerda(esq)
    if(vetor[dir] < vetor[meio])  //se vetor de direita menor que vetor de meio
    troca(vetor, dir, meio);    //troca direita(dir) e meio
    return meio;//retorna meio
}

int particao(int vetor[], int esq, int dir) {//faz a particao recebendo o vetor, a primeira e a ultima posicao do mesmo
    int pivo, i, j, t, med;
    med=mediana(vetor, esq, dir); //acha mediana
    pivo = vetor[med];//atribui a mediana como pivo
    i = esq; j = dir+1;

    while(1){
        do ++i; while(vetor[i] <= pivo && i <= dir ); //aumenta i enquanto vetor de i for menor ou igual ao pivo e menor que direita
        do --j; while(vetor[j] > pivo );//diminui i enquanto vetor de j for maior que o pivo
        if(i >= j ) break; //sai do loop quando esquerda esteja a direita de direita, ou na mesma posicao(ou seja, esq>=dir, ou i>=j)
        t = vetor[i]; vetor[i] = vetor[j]; vetor[j] = t;//faz troca entre vetor de i e vetor de j
    }
    t = vetor[esq]; vetor[esq] = vetor[j]; vetor[j] = t;//faz troca entre vetor de esquerda e vetor de j
    return j;//retorna j
}

void quickSortR(int vetor[], int esq, int dir) //quicksort na versao recursiva
{
    int j;

    if( esq < dir ) {// se esquerda menor que direita (verifica se esta a esquerda mesmo)
        j = particao(vetor, esq, dir);//j recebe a particao feita com a mediana
        quickSortR(vetor, esq, j-1);//faz quicksort de um dos lados
        quickSortR(vetor, j+1, dir);//faz quicksort do outro lado
    }

}

void quickSortI(int *vetor, int esq, int dir) {//versao iterativa do quicksort
    int pivo, i[dir], j[dir], x=0, aux ;
    
    i[0]=esq;
    j[0]=dir;
    
    while (x>=0) {
        esq=i[x];
        dir=j[x];
        
        if (esq<dir) { //checa se esquerda realmente esta a esquerda de direita
            pivo = vetor[esq];
         
            while (esq<dir) {
                while (vetor[dir]>=pivo && esq<dir)
                	dir--;
                //fica no while enquanto vetor de direita maior ou igual ao pivo e esquerda menor que direita, diminuindo dir
                if (esq<dir)
                	vetor[esq++] = vetor[dir];
                //se esquerda esta a esquerda de direita, vetor de esq+1 recebe vetor de dir
                while (vetor[esq]<=pivo && esq<dir)
                	esq++;
                //fica no while enquanto vetor de esquerda menor ou igual ao pivo e esquerda menor que direita, aumentando esq
                if (esq<dir)
                	vetor[dir--]=vetor[esq];
                //se esquerda esta a esquerda de direita, vetor de dir-1 recebe vetor de esq
            }
            vetor[esq] = pivo;
            i[x+1] = esq+1;
            j[x+1] = j[x];
            j[x++] = esq;
            
            if (j[x]-i[x] > j[x-1] - i[x-1]) {
                aux = i[x];
                i[x] = i[x-1];
                i[x-1] = aux;
                aux = j[x];
                j[x] = j[x-1];
                j[x-1] = aux;
            }
        }
        else
            x--;     
    }
}


void bubblesort(int *vetor, int n){
    int i, j, aux;
    for (i = n-1; i >= 1; i--) //enquanto i menor que tamanho do vetor i recebe i+1
    for (j = 0; j<i; j++)
    if (vetor[j] > vetor[j+1])
    {
        aux = vetor[j];
        vetor[j] = vetor[j+1];
        vetor[j+1] = aux;
    }
}

void selection_sort(int num[], int tam)
{
    int i, j, min, aux;
    for (i = 0; i < (tam-1); i++){ //enquanto i menor que tamanho do vetor min recebe i e i recebe i+1
        min = i;
        for (j = (i+1); j < tam; j++){ //enquanto j menor ou igual que tamanho do vetor min recebe j e j recebe j++
            if(num[j] < num[min]) //se vetor de j for menor que vetor de min, min recebe j
            min = j; //troca vetor de min com vetor de i
        }
        if (i != min) {
            aux = num[i];
            num[i] = num[min];
            num[min] = aux;
        }
    }
}

void imprimevetor(int * vetor, int tam){
    int i;
    printf("\nImprimindo o vetor: ");
    for (i = 0; i < tam; i++){
        printf("%d ",vetor[i]);
    }
    printf("\n");
}
void geravetor(int * vetor, int tam, int max){
    int i;
    for (i = 0; i < tam; i++){
        vetor[i] = randint(max);
    }
}

int main(){
    int max,i,loto[4], aux[4], soma, j, achou, tam, menor, passos;
    time_t t;
    int * vetor;
    srand((unsigned) time(&t));

    do{
        printf("Bem vindo! Deseja jogar na mega quadra ou comparar a eficiência? Digite 1 para mega, 0 para eficiência: ");
        scanf("%d",&passos);

        if (passos == 1){
            printf("\nQual o tamanho máximo? "); // Número de valores que a loteria terá.
            scanf("%d",&tam);
            vetor = (int *) malloc(sizeof(int) * (tam + 1)); // Essa forma de alocar a memória é útil, pois nesse caso o vetor tende a ser pequeno, mas no caso de 10 mil é o oposto.

            printf("Qual o valor máximo? "); // Valor máximo da loteria a ser sorteado.
            scanf("%d",&max);

            geravetor(vetor,tam,max);
            imprimevetor(vetor, tam);
            printf("\n");

            printf("Digite os valores da quadra:\n");
            for (i = 0; i < 4; i++){
                printf("%d° valor: ",i+1);
                while(scanf("%d",&menor) && (menor > max || menor < 0)){ //Essa parte irá checar a consistência dos dados. Se é maior que 0 e menor que o tamanho máximo.
                    printf("Por favor, número tem que ser válido: ");
                }
                loto[i] = menor;
            }

            printf("Portanto, foram inseridos os números: ");
            for (i = 0; i < 4; i++){
                printf("%d ", loto[i]); // Irá mostrar os números inseridos pelo usuário, que agora estão guardados em um vetor.
            }
            printf("\n");

            soma = 0;
            for (i = 0; i < 4; i++){
                achou = 0;
                for (j = 0; j < tam; j++){
                    if (loto[i] == vetor[j]){ //Irá procurar pelos números em que o usuário acertou. Busca sequencial, nesse caso é mais barata que ordenar e fazer busca binária.
                        achou = 1;
                        soma++;
                        break;
                    }
                }
                if (achou == 1){
                    aux[i] = 1; // 1 significa que o usuário acertou
                }
                else{
                    aux[i] = 0; // 0 significa que o usuário errou
                }
            }

            if (soma == 0)
            printf("\nSem nada\n");
            else{
                printf("\nForam sorteados os números: ");
                for (i = 0; i < 4; i++){
                    if (aux[i])
                    printf("%d ", loto[i]); // Aqui checa se o usuário acertou ou errou e imprime os números que ele acertou.
                }
                printf("\n");
            }
            if (soma == 4){
                printf("Você ganhou!!!!!!");
            }
            else if (soma > 0){
                printf("Você não ganhou mas acertou %d",soma);
            }
            else{
                printf("você errou tudo");
            }
            printf("\n\n");
            printf("Ordenando o vetor..");
            bubblesort(vetor,tam);
            imprimevetor(vetor, tam);
        }
        else{
            printf("Vamos checar os tempos de execução para 10000 vetores:\n");
            vetor = (int *) malloc(sizeof(int) * (DEZMIL + 1));

            clock_t start, end;
            double cpu_time_used;

            start = clock(); // Conta a hora no início
            for(j = 0; j < DEZMIL; j++){ //Faz 10 mil iterações. É possível mudar o conteúdo do DEZMIL, para ver como os algoritmos se comportam.
                for (i = 0; i < DEZMIL; i++){
                    vetor[i] = randint(DEZMIL); // Coloca um valor aleatório
                }
                selection_sort(vetor,tam); // Chama a ordenação
            }
            end = clock(); // Termina o relógio

            cpu_time_used = ((double) (end - start)) / CLOCKS_PER_SEC; // Guarda o intervalo de tempo em uma variável
            printf("SelectSort: %f\n",cpu_time_used); // Imprime

            // De agora em diante, repete o processo anterior.

            start = clock();
            for(j = 0; j < DEZMIL; j++){
                for (i = 0; i < DEZMIL; i++){
                    vetor[i] = randint(DEZMIL);
                }
                bubblesort(vetor,tam);
            }
            end = clock();

            cpu_time_used = ((double) (end - start)) / CLOCKS_PER_SEC;
            printf("BubbleSort: %f\n",cpu_time_used);

            start = clock();
            for(j = 0; j < DEZMIL; j++){
                for (i = 0; i < DEZMIL; i++){
                    vetor[i] = randint(DEZMIL);
                }
                quickSortR(vetor,0,tam);
            }
            end = clock();

            cpu_time_used = ((double) (end - start)) / CLOCKS_PER_SEC;
            printf("Quick (recur): %f\n",cpu_time_used);

            start = clock();
            for(j = 0; j < DEZMIL; j++){
                for (i = 0; i < DEZMIL; i++){
                    vetor[i] = randint(DEZMIL);
                }
                quickSortI(vetor,0,tam);
            }
            end = clock();

            cpu_time_used = ((double) (end - start)) / CLOCKS_PER_SEC;
            printf("Quick (iter): %f\n",cpu_time_used);
        }
        free(vetor); // Irá limpar a memória do vetor, que é usado em ambas as partes do programa.
        printf("\n\n");
        printf("Quer jogar de novo? Digite 1 para SIM, 0 para NÃO: ");
    } while(scanf("%d",&max) && max == 1);
}