如何在下面实现这些图形函数以确保我覆盖了所有具有给定约束的测试用例？

Question

I've recently gotten into discrete math and graphs. I'm trying to implement a few functions related to graphs.

But I'm not sure if I'm covering every test case that could possibly be thrown at my program.

How to cover all cases?

• Input constraints:
  1. Graph is connected
  2. Graph is undirected
  3. Graph is unweighted
  4. Graph has at least 3 vertices and upmost 100 vertices
  5. No self loops and no parallel edges
  6. A testcase must complete within 1 second of time
  7. Graph input is a 0/1 matrix

1.c file:

#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include "graphprofile.h"

int main(int argc, char const *argv[]) {
    int tc, n, i, j, ans, ret;
    clock_t t;

    int **g;
    scanf("%d", &tc);
    while(tc--) {
        t=clock();
        printf("New testcase begin...\n");
        scanf("%d", &n);
        g = (int**) malloc(n * sizeof(int*));
        for (i = 0; i < n; i++) {
            g[i] = (int*) malloc(n * sizeof(int));
            for (j = 0; j < n; j++) {
                scanf("%d", &g[i][j]);
            }
        }

        //AvgDegreeTest
        scanf("%d", &ans);
        ret = avgDegree(g, n);
        if(ret == ans) {
            printf("AvgDegreeTest passed.\n");
        } else {
            printf("AvgDegreeTest ***FAILED***! ");
            printf("(Expected: %d, Returned: %d)\n", ans, ret);
        }

        //IsRegularTest
        scanf("%d", &ans);
        ret = isRegular(g, n);
        if(ret == ans) {
            printf("IsRegularTest passed.\n");
        } else {
            printf("IsRegularTest ***FAILED***! ");
            printf("(Expected: %d, Returned: %d)\n", ans, ret);
        }

        //IsCompleteTest
        scanf("%d", &ans);
        ret = isComplete(g, n);
        if(ret == ans) {
            printf("IsCompleteTest passed.\n");
        } else {
            printf("IsCompleteTest ***FAILED***! ");
            printf("(Expected: %d, Returned: %d)\n", ans, ret);
        }

        //IsCycleTest
        scanf("%d", &ans);
        ret = isCycleGraph(g, n);
        if(ret == ans) {
            printf("IsCycleTest passed.\n");
        } else {
            printf("IsCycleTest ***FAILED***! ");
            printf("(Expected: %d, Returned: %d)\n", ans, ret);
        }

        //IsPathTest
        scanf("%d", &ans);
        ret = isPathGraph(g, n);
        if(ret == ans) {
            printf("IsPathTest passed.\n");
        } else {
            printf("IsPathTest ***FAILED***! ");
            printf("(Expected: %d, Returned: %d)\n", ans, ret);
        }

        //HasEulerCktTest
        scanf("%d", &ans);
        ret = hasEulerCkt(g, n);
        if(ret == ans) {
            printf("HasEulerCktTest passed.\n");
        } else {
            printf("HasEulerCktTest ***FAILED***! ");
            printf("(Expected: %d, Returned: %d)\n", ans, ret);
        }

        //HasEulerPathTest
        scanf("%d", &ans);
        ret = hasEulerPath(g, n);
        if(ret == ans) {
            printf("HasEulerPathTest passed.\n");
        } else {
            printf("HasEulerPathTest ***FAILED***! ");
            printf("(Expected: %d, Returned: %d)\n", ans, ret);
        }

        //OresTheoremTest
        scanf("%d", &ans);
        ret = satifiesOresTheorem(g, n);
        if(ret == ans) {
            printf("OresTheoremTest passed.\n");
        } else {
            printf("OresTheoremTest ***FAILED***! ");
            printf("(Expected: %d, Returned: %d)\n", ans, ret);
        }

        for (i = 0; i < n; i++) {
            free(g[i]);
        }
        free(g);
        t= clock() -t;
        double time_taken = ((double)t)/CLOCKS_PER_SEC; // in seconds 
    printf("Testcase %d took %f seconds to execute \n",tc,time_taken); 
        printf("\n%d testcase left.\n\n", tc);
    }
    return 0;
}

graphprofile.h file:

// 1. What is average degree of a vertex in the graph?
int avgDegree(int **g, int n);

// 2. Is the graph a regular graph?
int isRegular(int **g, int n);

// 3. Is the graph a complete graph?
int isComplete(int **g, int n);

// 4. Is the graph a cycle graph?
int isCycleGraph(int **g, int n);

// 5. Is the graph a path graph but not a cycle graph?
int isPathGraph(int **g, int n);

// 6. Does the graph has an Euler circuit?
int hasEulerCkt(int **g, int n);

// 7. Does the graph has an Euler path but not an Euler circuit?
int hasEulerPath(int **g, int n);

// 8. Does the graph satisfy the sufficient condition of the Ore's theorem?
// Sufficient condition for the graph to have a Hamilton according the Ore's theorem:
// deg(u) + deg(v) ≥ n for every pair of nonadjacent vertices u and v in the graph
int satifiesOresTheorem(int **g, int n);

my_implementation.c file:

#include <stdlib.h>
#include "graphprofile.h"
// Returns list of degrees of each vertex of the graph
int* degreeCal(int **g,int n)
{   int* degList=(int*)malloc(sizeof(int)*n);
    for(int i=0;i<n;i++)
       { degList[i]=0;
        for(int j=0;j<n;j++)
            if(g[i][j]==1)
                degList[i]++;
       }
       return degList;
}
int degSum(int** g,int n)
{
    int* degList = degreeCal(g,n);
    int sum=0;
    for(int i=0;i<n;i++)
        sum+=degList[i];
    return sum;
}
// 1. What is average degree of a vertex in the graph?
int avgDegree(int **g, int n) {
    return (degSum(g,n))/n;
}

// 2. Is the graph a regular graph?
int isRegular(int **g, int n) {
    int* degList;
    degList = degreeCal(g,n);
    int cd = degList[0];
    for(int i=1;i<n;i++)
    {
        if(cd!=degList[i])
            return 0;
    }
   return 1;

}
// Returns list of degrees of each vertex of the graph

// 3. Is the graph a complete graph?
int isComplete(int **g, int n) {
    int sum = degSum(g,n);
    int e = sum/2;
    if((n*(n-1)/2)==e)
        return 1;
    else
    {
            return 0;
    }

}

// 4. Is the graph a cycle graph?

int isCycleGraph(int **g, int n) {
    int* degList = degreeCal(g,n);
    int e = degSum(g,n)/2;
    for(int i=0;i<n;i++)
    {
        if(degList[i]!=2)
            return 0;
    }
    if(e==n)
        return 1;
    else
    {
            return 0;
    }

}

// 5. Is the graph a path graph but not a cycle graph?
int isPathGraph(int **g, int n) {
    int* degList = degreeCal(g,n);
    int one = 0;
    int e = degSum(g,n)/2;
    for(int i=0;i<n;i++)
    {
        if(degList[i]==2)
            continue;
        else if(degList[i]==1 && one<=2)
            one++;
        else
            return 0;

    }
    if(one==2 && e==n-1)
        return 1;
    else
    {
            return 0;
    }

}

// 6. Does the graph has an Euler circuit?
int hasEulerCkt(int **g, int n) {
    int* degList = degreeCal(g,n);
    for(int i=0;i<n;i++)
    {if(degList[i]%2!=0)
        return 0;
    }
    return 1;
}

// 7. Does the graph has an Euler path but not an Euler circuit?
int hasEulerPath(int **g, int n) {
    int* degList = degreeCal(g,n);
    int sum_o = 0;
    for(int i=0;i<n;i++)
    {
        if(degList[i]%2!=0)
            sum_o++;
    }
    if(sum_o==2)
        return 1;
    else
        return 0;
}

// 8. Does the graph satisfy the sufficient condition of the Ore's theorem?
// Sufficient condition for the graph to have a Hamilton according the Ore's theorem:
// deg(u) + deg(v) ≥ n for every pair of nonadjacent vertices u and v in the graph
int satifiesOresTheorem(int **g, int n) {
    int* degList = degreeCal(g,n);
    for(int i=0;i<n;i++)
        for(int j=0;j<n;j++)
            if(i!=j && g[i][j]==0)
                if(degList[i]+degList[j]<n)
                    return 0;

    return 1;
}

Sample inputs:

2

4
0 0 1 1
0 0 1 1
1 1 0 0
1 1 0 0

2 1 0 1 0 1 0 1

3
0 1 1
1 0 0
1 0 0

1 0 0 0 1 0 1 0

Answer 1

Anyway, I realised that the definitions of the types of graphs themselves prove to be enough for me to implement them in C.

//Profile a connected undirected unweighted graph for the following properties.
#include <stdlib.h>
#include "graphprofile.h"

// 1. What is average degree of a vertex in the graph?
int avgDegree(int **g, int n)
{
    int e = 0; 
    int result;
    for(int i = 0; i<n; i++)
    {
        for(int j = 0; j<n;j++)
        {
            if(g[i][j] == 1)
            {
                e++;
            }
        }
    }
    result = e/n;
    return result;
}

// 2. Is the graph a regular graph?
int isRegular(int **g, int n)
{
    int e1 = 0, e2 = 0;
    //checking 0th row
    for (int i = 0; i < n; i++)
    {
        if (g[0][i] == 1)
        {
            e1++;
        }
    }
    //checking 1st row and continuing if equal
    for (int i = 1; i < n; i++)
    {
        e2 = 0;
        for (int j = 0; j < n; j++)
        {
            if (g[i][j] == 1)
            {
                e2++;
            }
        }
        if (e1 == e2)
            continue;
        else
            return 0;
    }
    return 1;
}

// 3. Is the graph a complete graph?
int isComplete(int **g, int n)
{
    int e = 0;
    for(int i = 0; i<n ; i++)
    {
        e = 0;
        for(int j = 0; j>n; j++)
        {
            if(g[i][j]==1)
                e++;
        }
    }
    if(e == (n*(n-1))/2)
        return 1;
    else
        return 0;
}

// 4. Is the graph a cycle graph?
int isCycleGraph(int **g, int n)
{
    int e = 0;
    for (int i = 0; i < n; i++)
    {
        e = 0;
        for (int j = 0; j < n; j++)
        {
            if (g[i][j] == 1)
            {
                e++;
            }
        }
        if (e!= 2)
            return 0;
    }
    return 1;
}
// 5. Is the graph a path graph but not a cycle graph?
int isPathGraph(int **g, int n)
{
    int a = 0;
    int b = 0;
    for (int i = 0; i< n; i++)
    {
        a = 0;
        for (int j = 0; j < n; j++)
        {
            if (g[i][j] == 1)
                a++;
        }
        if (a > 2)
            return 0;
        else
        {
            if (a == 1)
                b++;
        }
    }
    if (b != 2)
        return 0;
    else
        return 1;

    return 0;
}

// 6. Does the graph has an Euler circuit?
int hasEulerCkt(int **g, int n)
{
    int e = 0;
    for (int i = 0; i< n; i++)
    {
        e = 0;
        for (int j = 0; j < n; j++)
        {
            if (g[i][j] == 1)
            {
                e++;
            }
        }
        if (e % 2 == 0)
            continue;
        else
            return 0;
    }
    return 1;
}

// 7. Does the graph has an Euler path but not an Euler circuit?
int hasEulerPath(int **g, int n)
{
    int a = 0;
    int b = 0;
    for (int i = 0; i < n; i++)
    {
        a = 0;
        for (int j = 0; j < n; j++)
        {
            if (g[i][j] == 1)
            {
                a++;
            }
        }
        if (a%2 == 0)
            continue;
        else
            b++;
    }
    if (b != 2)
        return 0;
    else
        return 1;
}
// 8. Does the graph satisfy the sufficient condition of the Ore's theorem?
// Sufficient condition for the graph to have a Hamilton according the Ore's theorem:
// deg(u) + deg(v) ≥ n for every pair of nonadjacent vertices u and v in the graph

//user-defined function to calculate degree
int degree(int **g, int n, int v)
{
    int e = 0;
    for (int i = 0; i < n; i++)
    {
        if (g[v][i] != 1)
            continue;
        else
            e++;
    }
    return e;
}

int satifiesOresTheorem(int **g, int n)
{
    for (int i = 0; i < n; i++)
    {
        for (int j = 0; j < n; j++)
        {
            if (g[i][j] != 0)
                continue;
            else
            {
                if ((degree(g, n, i) + degree(g, n, j)) >= n)
                    continue;
                else
                    return 0;
            }
        }
    }
    return 1;
}