エジプト式分数

ある分数を，分子が 1 の分数の和で表す
1/3 でも，1/4 + 1/12 のようにすること

EgyptianFraction = function(numerator, denominator) {
  EF = function(numerator, denominator) {
    denominator2 = 1
    repeat {
      denominator2 = denominator2 + 1
      if (denominator < numerator * denominator2)
        break
    }
    answer <<- c(answer, denominator2)
    numerator2 = numerator * denominator2 - denominator
    denominator2 = denominator * denominator2
    gcd = GCD(numerator2, denominator2)
    numerator2 = numerator2/gcd
    denominator2 = denominator2/gcd
    if (numerator2 == 1)
      answer <<- c(answer, denominator2)
    else if (numerator2 != 0)
      Recall(numerator2, denominator2)
  }
  GCD = function(x, y) {
    while (y%%x != 0) {
      t = y%%x
      y = x
      x = t
    }
    x
  }
  cat("\n", numerator, "/", denominator, "== ")
  answer = NULL
  EF(numerator, denominator)
  cat(sub("^ \\+ ", "", paste(" + 1 /", answer, collapse = "")), "\n")
  check = TRUE
  if (check == TRUE) {
    library(gmp)
    left = as.bigq(numerator)/as.bigq(denominator)
    right = sum(as.bigq(1)/answer)
    print(left, initLine = FALSE)
    print(right, initLine = FALSE)
    if (left != right) {
      cat("Warning! wrong answer\n")
      cat(numerator, denominator, "\n")
    }
  }
  invisible(answer)
}
EgyptianFraction(3, 5)
EgyptianFraction(5, 7)
EgyptianFraction(1, 3)
dat = cbind(numerator = c(66, 80, 2, 235, 40, 168, 72, 146, 5, 112, 148, 95, 106, 210, 92, 31,
  137, 177, 30, 22), denominator = c(152, 416, 90, 300, 159, 340, 115, 451, 6, 254, 285, 247,
  206, 377, 228, 222, 218, 398, 94, 39))
options(scipen = 10)
for (i in 1:20) {
  EgyptianFraction(dat[i, 1], dat[i, 2])
}