2019年08月05日 03:31

Sechi

edited: 2019年08月23日 10:49

function validCommutativity(table){
 const n = table.length;
 for(let i=0; i<n; i++)
 for(let j=i+1; j<n; j++)
 if(table[i][j] !== table[j][i])
 return false
 return true
}
function validAssociative(table){
 const n = table.length;
 for(let i=0; i<n; i++)
 for(let j=0; j<n; j++)
 for(let k=0; k<n; k++)
 if(table[table[i][j]][k] !== table[i][table[j][k]])
 return false
 return true
}
const foo = [
 [0, 0, 0, 0, 0],
 [0, 1, 1, 1, 1],
 [0, 1, 2, 2, 2],
 [0, 1, 2, 3, 3],
 [0, 1, 2, 3, 4],
]
console.log(validCommutativity(foo));
console.log(validAssociative(foo));

package d238_commutative_associated;
public class CommutativeLaw {
 int op1(int a, int b) {
 return a*b;
 }
 public static void main(String[] args) {
 CommutativeLaw cl = new CommutativeLaw();
 int n=10;
 boolean result=true;
 int i, j;
 for(i=0; i<n; i++) {
 for(j=0; j<n; j++)
 if(cl.op1(i, j)!=cl.op1(j, i)) {
 result=false;
 break; //별 의미 없음.
 }
 }
 System.out.println(result);
 }
}

package d238_commutative_associated;
public class AssociatedLaw {
 int op2(int a, int b) {
 return a*b;
 }
 public static void main(String[] args) {
 AssociatedLaw al = new AssociatedLaw();
 int n=10;
 boolean result=true;
 int i, j, k;
 for(i=0; i<n; i++)
 for(j=0; j<n; j++)
 for (k=0; k<n; k++) {
 if( al.op2( al.op2(i, j), k) != al.op2(i, al.op2(j, k) ) ) {
 result=false;
 break; //별 의미 없음.
 }
 }
 System.out.println(result);
 }
}

a = [0:n]
b = [0:n]
c = [a,b]
for i in a:
 for j in b:
 if c[i][j] = c[j][i]: True
 else: False

흠 두번째는 좀 더 고민해봐야겠어요

dart

예외처리 포함

안 닫혀 있으면 그냥 false 리턴

typedef Matrix = List<List<int>>;
// avoid redundancy
bool isCommutative(Matrix matrix, int n) {
 for (int i = 0; i < n; i++) {
 for (int j = i + 1; j < n; j++) {
 if (matrix[i][j] != matrix[j][i]) {
 return false;
 }
 }
 }
 return true;
}
bool isAssociative(Matrix matrix, int n) {
 try {
 for (int i = 0; i < n; i++) {
 for (int j = 0; j < n; j++) {
 for (int k = 0; k < n; k++) {
 if (matrix[matrix[i][j]][k] != matrix[i][matrix[j][k]]) {
 return false;
 }
 }
 }
 } 
 } on RangeError catch(e) {
 return false; // not closed for the operator
 }
 return true;
}
void main() {
 List<Matrix> testSet = [
 [], // empty
 [[1], [2, 3]], // non-matrix
 [[1, 2, 3], [4, 5, 6]], // non-square matrix
 [[0]], // *
 [[0, 0],[0, 1]], // *
 [[0, 1, 2],[1, 2, 3], [4, 5, 6]], // +
 [[0, -1, -2],[1, 0, -1], [2, 1, 0]], // -
 [[0, 0, 0],[0, 1, 2], [0, 2, 4]] // *
 ];
 print("Commutative, Associative:");
 for (Matrix matrix in testSet) { 
 int n = matrix.length;
 if (matrix.isEmpty ||!matrix.fold(true, 
 (lengthFixed, row) => lengthFixed && row.length == n)) {
 print('$matrix => Invalid: Square matrix is needed');
 } else {
 print('$matrix => ${isCommutative(matrix, n)}, ${isAssociative(matrix, n)}');
 }
 } 
}

실행결과

Commutative, Associative:
[] => Invalid: Square matrix is needed
[[1], [2, 3]] => Invalid: Square matrix is needed
[[1, 2, 3], [4, 5, 6]] => Invalid: Square matrix is needed
[[0]] => true, true
[[0, 0], [0, 1]] => true, true
[[0, 1, 2], [1, 2, 3], [4, 5, 6]] => false, false
[[0, -1, -2], [1, 0, -1], [2, 1, 0]] => false, false
[[0, 0, 0], [0, 1, 2], [0, 2, 4]] => true, false

python 3.8
# 문제 1의 해
A = [[1,2,3], [4,5,6]]
B = [[5,6], [7,8], [9,0]]
def matrix_product(M1, M2):
 rows = len(M1)
 cols = len(M2[0])
 mids = len(M1[0])
 R = [[0 for _ in range(cols)] for _ in range(rows)]
 if cols == rows:
 for i in range(cols):
 for j in range(rows):
 for m in range(mids):
 R[i][j] += M1[i][m]*M2[m][j]
 for i in range(len(R)):
 for j in range(len(R[0])):
 print(f"{R[i][j]:>3}", end=" ")
 print()
 return R
 else:
 return "can not product"
def are_matrices_equal(M1, M2):
 if len(M1) != len(M2) or len(M1[0]) != len(M2[0]):
 return False
 for i in range(len(M1)):
 for j in range(len(M1[0])):
 if M1[i][j] != M2[i][j]:
 return False
 return True
if matrix_product(A, B) == "곱셈불가" or \
 not are_matrices_equal(matrix_product(A, B), matrix_product(B, A)):
 print("교환법칙 불만족")
else:
 print("교환법칙 만족")
# 문제 2의 해
A = [[1,2], [3,4]]
B = [[5,6], [7,8]]
C = [[9,0], [1,2]]
# (A*B)*C = A*(B*C) ??
T1 = matrix_product(A, B)
Q1 = matrix_product(T1, C)
T2 = matrix_product(B, C)
Q2 = matrix_product(A, T2)
if are_matrices_equal(Q1, Q2):
 print("결합법칙 성립")
else:
 print("결합법칙 불성립")