離散判斷一個代數系統是不是羣

#include <iostream>
#include <stdio.h>
#include <stdlib.h>
#define TRUE 1
#define FALSE 0

using namespace std;

typedef char ElemType;
typedef int Status;

typedef struct AlgSysNode{
	ElemType *elem;			//元素數組首地址 
	ElemType **table;		//運算表首地址 
	int length;				//元素個數 
}AlgSysNode,*AlgSystem;

//創建代數系統 
void createAlgSystem(AlgSystem &G,int n){
	int i,j;
	G = (AlgSystem)malloc(n*sizeof(AlgSysNode));
	if(!G) return;
	G->elem = (ElemType *)malloc(n*sizeof(ElemType));
	if(!G->elem) return;
	for(i=0;i<n;i++){
		printf("第%d個元素是：",i+1);
		cin>>G->elem[i];
	}
	G->table = (ElemType **)malloc(n*sizeof(ElemType*));
	if(!G->table) return;
	for(i=0;i<n;i++){
		G->table[i] = (ElemType *)malloc(n*sizeof(ElemType));
		for(j=0;j<n;j++){
			printf("運算表中第%d行第%d個是：",i+1,j+1);
			cin>>G->table[i][j];
		}
	}
	G->length = n;
	return;
}

//定位元素 
int LocateVex(AlgSystem G,ElemType e){
	int i;
	for(i=0;i<G->length;i++){
		if(G->elem[i] == e) return i;
	}
	return -1;
}

//封閉性 
Status IsClosed(AlgSystem G){
	int i,j;
	for(i=0;i<G->length;i++){
		for(j=0;j<G->length;j++){
			if(LocateVex(G,G->table[i][j])==-1) return FALSE;
		}
	}
	return TRUE;
}

//結合性 
Status IsCombined(AlgSystem G){
	int i,j,k,m,n;
	for(i=0;i<G->length;i++){
		for(j=0;j<G->length;j++){
			for(k=0;k<G->length;k++){
				m = LocateVex(G,G->table[i][j]);
				n = LocateVex(G,G->table[j][k]);
				if(G->table[m][k] != G->table[i][n]){
					return FALSE;
				}
			}
		}
	}
	return TRUE;
}

//有幺元
Status IsExist_e(AlgSystem G,ElemType &e){
	int i,j,k;
	for(i=0;i<G->length;i++){
		for(j=0;j<G->length;j++){
			if(G->table[i][j] != G->elem[j]) break;
		}
		if(j == G->length){
			for(k=0;k<G->length;k++){
				if(G->table[k][i] != G->elem[k]) break;
			}
			if(k == G->length){
				e =  G->elem[i];
				return TRUE;
			}
		}
	}
	return FALSE;
}

//逆元 
Status IsExistInverse_e(AlgSystem G,ElemType e){
	int i,j;
	for(i=0;i<G->length;i++){
		for(j=0;j<G->length;j++){
			if(G->table[i][j] == e) break;
		}
		if(j == G->length) return FALSE;
	}
	return TRUE;
}



Status IsGroup(AlgSystem G){
	ElemType e;
	return IsClosed(G) && IsCombined(G) && IsExist_e(G,e) && IsExistInverse_e(G,e);
}


int main(){
	int n = 0;
	AlgSystem G;
	printf("代數系統中元素的個數：");
	scanf("%d",&n);
	createAlgSystem(G,n);
	if(IsGroup(G)){
		printf("該代數系統是羣");
	}else{
		printf("該代數系統不是羣") ;
	}
	return 0;
}

測試結果：