# Exercici 13  matru simètrica

# Trencament de recorregut


# variables

# m : matriu en estudi
# i : index per a recorrer les files
# j : index per a recorrer les columnes

# funcions

escriuMatriu <- function (m){
  cat("\n")
  for (i in 1 : nrow(m)){
    cat(m[i, ])
    cat("\n")
  }
  cat("\n")
}

esSimetrica <- function(m){
  nf <- nrow(m)
  nc <- ncol(m)
  if (nf != nc){
    return (FALSE)
  }else{
    for (i in 2 : nf){
      for (j in 1 : (i - 1)){
        if (m[i, j] != m[j, i]) {
	  return (FALSE)
	}
      }
    }
    return (TRUE)
  }
}

# programa principal

m <- matrix(c(1, 2, 3, 4, 5, 6, 7, 8, 9), nrow = 3, ncol = 3)
escriuMatriu(m)
cat("Es simetrica? : ", esSimetrica(m), "\n")

m <- matrix(c(1, 2, 3, 4, 5, 6), nrow = 2, ncol = 3)
escriuMatriu(m)
cat("Es simetrica? : ", esSimetrica(m), "\n")

m <- matrix(c(1, 2, 3, 2, 2, 4, 3, 4, 3), nrow = 3, ncol = 3)
escriuMatriu(m)
cat("Es simetrica? : ", esSimetrica(m), "\n")