# Exercici 13  matriu simetrica

# Cerca canònica


# 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")
}

esSimetricaCanonica <- function(m){
  nf <- nrow(m)
  nc <- ncol(m)
  if (nf != nc){
    return (FALSE)
  }else{
    i <- 2
    j <- 1
    while ( !(m[i,j] != m[j,i]) && i <= nf && j < nc){
      j <- j + 1
      if (j > i){
        i <- i + 1
	j <- 1
      }
    }
    return (m[i, j] == m[j, i])
  }
}

# programa principal

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

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

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