How to resolve the algorithm World Cup group stage step by step in the C programming language

Published on 7 June 2024 03:52 AM
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How to resolve the algorithm World Cup group stage step by step in the C programming language

Table of Contents

Problem Statement

It's World Cup season (or at least it was when this page was created)! The World Cup is an international football/soccer tournament that happens every 4 years.   Countries put their international teams together in the years between tournaments and qualify for the tournament based on their performance in other international games.   Once a team has qualified they are put into a group with 3 other teams. For the first part of the World Cup tournament the teams play in "group stage" games where each of the four teams in a group plays all three other teams once.   The results of these games determine which teams will move on to the "knockout stage" which is a standard single-elimination tournament.   The two teams from each group with the most standings points move on to the knockout stage. Each game can result in a win for one team and a loss for the other team or it can result in a draw/tie for each team.

Don't worry about tiebreakers as they can get complicated.   We are basically looking to answer the question "if a team gets x standings points, where can they expect to end up in the group standings?". Hint: there should be no possible way to end up in second place with less than two points as well as no way to end up in first with less than three.   Oddly enough, there is no way to get 8 points at all.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm World Cup group stage step by step in the C programming language

This C program simulates a simple game where players compete in different events and earn points based on their performance. The program calculates the points earned by each player for different results in multiple events and presents the final standings.

Explanation:

  1. compare Function:

    • This function is used as a comparison function for qsort. It compares two integers and returns a value based on their relative values. It is used to sort the points earned by players in descending order.
  2. results Array and next_result Function:

    • The results array is a 6-character buffer used to generate different combinations of results for the events.
    • The next_result function generates the next valid combination of results by incrementing the value represented by the base-3 string in the results array. It returns false when all possible combinations have been exhausted.
  3. games and places Arrays:

    • The games array contains all possible pairs of events (e.g., "12" represents playing event 1 against event 2).
    • The places array contains the place names (e.g., "1st", "2nd", "3rd", "4th").
  4. Main Function:

    • Initialization: It initializes a 4x10 points array to zero, which will store the points earned by each player for each possible result.

    • Generating and Processing Results:

      • It repeatedly generates the next valid combination of results using the next_result function.
      • For each combination, it calculates the points earned by each player based on the rules of the game.
      • The points are added to the corresponding cell in the points array.
    • Sorting and Output:

      • After all possible combinations have been processed, the points earned by each player are sorted in descending order using qsort.
      • The final standings are printed, showing the points earned by each player for each possible result.

Source code in the c programming language

#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>

// to supply to qsort
int compare(const void *a, const void *b) {
    int int_a = *((int *)a);
    int int_b = *((int *)b);
    return (int_a > int_b) - (int_a < int_b);
}

char results[7];
bool next_result() {
    char *ptr = results + 5;
    int num = 0;
    size_t i;

    // check if the space has been examined
    if (strcmp(results, "222222") == 0) {
        return false;
    }

    // translate the base 3 string back to a base 10 integer
    for (i = 0; results[i] != 0; i++) {
        int d = results[i] - '0';
        num = 3 * num + d;
    }

    // to the next value to process
    num++;

    // write the base 3 string (fixed width)
    while (num > 0) {
        int rem = num % 3;
        num /= 3;
        *ptr-- = rem + '0';
    }
    // zero fill the remainder
    while (ptr > results) {
        *ptr-- = '0';
    }

    return true;
}

char *games[6] = { "12", "13", "14", "23", "24", "34" };
char *places[4] = { "1st", "2nd", "3rd", "4th" };
int main() {
    int points[4][10];
    size_t i, j;

    strcpy(results, "000000");
    for (i = 0; i < 4; i++) {
        for (j = 0; j < 10; j++) {
            points[i][j] = 0;
        }
    }

    do {
        int records[] = { 0, 0, 0, 0 };

        for (i = 0; i < 6; i++) {
            switch (results[i]) {
            case '2':
                records[games[i][0] - '1'] += 3;
                break;
            case '1':
                records[games[i][0] - '1']++;
                records[games[i][1] - '1']++;
                break;
            case '0':
                records[games[i][1] - '1'] += 3;
                break;
            default:
                break;
            }
        }

        qsort(records, 4, sizeof(int), compare);
        for (i = 0; i < 4; i++) {
            points[i][records[i]]++;
        }
    } while (next_result());

    printf("POINTS       0    1    2    3    4    5    6    7    8    9\n");
    printf("-----------------------------------------------------------\n");
    for (i = 0; i < 4; i++) {
        printf("%s place", places[i]);
        for (j = 0; j < 10; j++) {
            printf("%5d", points[3 - i][j]);
        }
        printf("\n");
    }

    return 0;
}


  

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