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| 1 | +/* rat.zc */ |
| 2 | + |
| 3 | +import "std/string.zc" |
| 4 | + |
| 5 | +fn gcd(x: i64, y: i64) -> i64 { |
| 6 | + while y { |
| 7 | + let t = y; |
| 8 | + y = x % y; |
| 9 | + x = t; |
| 10 | + } |
| 11 | + return labs(x); |
| 12 | +} |
| 13 | + |
| 14 | +@derive(Copy) |
| 15 | +struct Rat { |
| 16 | + num: i64; |
| 17 | + den: i64; |
| 18 | +} |
| 19 | + |
| 20 | +impl Rat { |
| 21 | + // Creates a new Rat struct in canonical form |
| 22 | + // i.e. n and d have no common factors and d > 0. |
| 23 | + // The Rat struct should not be created directly |
| 24 | + // unless you're certain it's already in such a form. |
| 25 | + fn new(n: i64, d: i64 = 1) -> Self { |
| 26 | + assert(d != 0, "Denominator must be non-zero."); |
| 27 | + if n == 0 { |
| 28 | + d = 1; |
| 29 | + } else if d < 0 { |
| 30 | + n = -n; |
| 31 | + d = -d; |
| 32 | + } |
| 33 | + if labs(n) != 1 && d > 1 { |
| 34 | + let g = gcd(n, d); |
| 35 | + if g > 1 { |
| 36 | + n /= g; |
| 37 | + d /= g; |
| 38 | + } |
| 39 | + } |
| 40 | + return Rat{num: n, den: d}; |
| 41 | + } |
| 42 | + |
| 43 | + fn neg(self) -> Rat { |
| 44 | + return Rat{num: -self.num, den: self.den}; |
| 45 | + } |
| 46 | + |
| 47 | + fn add(self, other: Rat) -> Rat { |
| 48 | + return Rat::new( |
| 49 | + self.num * other.den + self.den * other.num, |
| 50 | + self.den * other.den |
| 51 | + ); |
| 52 | + } |
| 53 | + |
| 54 | + fn sub(self, other: Rat) -> Rat { |
| 55 | + return *self + (-other); |
| 56 | + } |
| 57 | + |
| 58 | + fn mul(self, other: Rat) -> Rat { |
| 59 | + return Rat::new( |
| 60 | + self.num * other.num, |
| 61 | + self.den * other.den |
| 62 | + ); |
| 63 | + } |
| 64 | + |
| 65 | + fn div(self, other: Rat) -> Rat { |
| 66 | + return Rat::new( |
| 67 | + self.num * other.den, |
| 68 | + self.den * other.num |
| 69 | + ); |
| 70 | + } |
| 71 | + |
| 72 | + fn trunc(self) -> Rat { |
| 73 | + return Rat{num: self.num / self.den, den: 1}; |
| 74 | + } |
| 75 | + |
| 76 | + fn ceil(self) -> Rat { |
| 77 | + if self.den == 1 return self.clone(); |
| 78 | + return self.num >= 0 ? self.trunc().inc() : self.trunc(); |
| 79 | + } |
| 80 | + |
| 81 | + fn floor(self) -> Rat { |
| 82 | + if self.den == 1 return self.clone(); |
| 83 | + return self.num >= 0 ? self.trunc() : self.trunc().dec(); |
| 84 | + } |
| 85 | + |
| 86 | + fn round(self) -> Rat { |
| 87 | + if self.num >= 0 { return (*self + Rat{num: 1, den: 2}).trunc(); } |
| 88 | + return (*self - Rat{num: 1, den: 2}).trunc(); |
| 89 | + } |
| 90 | + |
| 91 | + fn frac(self) -> Rat { |
| 92 | + return *self - self.trunc(); |
| 93 | + } |
| 94 | + |
| 95 | + fn idiv(self, other: Rat) -> Rat { |
| 96 | + return (*self / other).trunc(); |
| 97 | + } |
| 98 | + |
| 99 | + fn rem(self, other: Rat) -> Rat { |
| 100 | + return *self - self.idiv(other) * other; |
| 101 | + } |
| 102 | + |
| 103 | + fn pow(self, exp: int) -> Rat { |
| 104 | + let r = Rat{num: self.num ** abs(exp), den: self.den ** abs(exp)}; |
| 105 | + return exp >= 0 ? r : r.inv(); |
| 106 | + } |
| 107 | + |
| 108 | + fn inv(self) -> Rat { |
| 109 | + return Rat::new(self.den, self.num); |
| 110 | + } |
| 111 | + |
| 112 | + fn abs(self) -> Rat { |
| 113 | + return Rat{num: labs(self.num), den: self.den}; |
| 114 | + } |
| 115 | + |
| 116 | + fn inc(self) -> Rat { |
| 117 | + return Rat{num: self.num + self.den, den: self.den}; |
| 118 | + } |
| 119 | + |
| 120 | + fn dec(self) -> Rat { |
| 121 | + return Rat{num: self.num - self.den, den: self.den}; |
| 122 | + } |
| 123 | + |
| 124 | + fn sign(self) -> int { |
| 125 | + return self.num > 0 ? 1 : self.num < 0 ? -1 : 0; |
| 126 | + } |
| 127 | + |
| 128 | + fn eq(self, other: Rat) -> bool { |
| 129 | + return self.num == other.num && self.den == other.den; |
| 130 | + } |
| 131 | + |
| 132 | + fn neq(self, other: Rat) -> bool { |
| 133 | + return !self.eq(other); |
| 134 | + } |
| 135 | + |
| 136 | + fn lt(self, other: Rat) -> bool { |
| 137 | + return (*self - other).num < 0; |
| 138 | + } |
| 139 | + |
| 140 | + fn gt(self, other: Rat) -> bool { |
| 141 | + return (*self - other).num > 0; |
| 142 | + } |
| 143 | + |
| 144 | + fn le(self, other: Rat) -> bool { |
| 145 | + return (*self - other).num <= 0; |
| 146 | + } |
| 147 | + |
| 148 | + fn ge(self, other: Rat) -> bool { |
| 149 | + return (*self - other).num >= 0; |
| 150 | + } |
| 151 | + |
| 152 | + fn to_f64(self) -> f64 { |
| 153 | + return (f64)self.num / (f64)self.den; |
| 154 | + } |
| 155 | + |
| 156 | + fn to_i64(self) -> i64 { |
| 157 | + return self.trunc().num; |
| 158 | + } |
| 159 | + |
| 160 | + fn to_string(self) -> String { |
| 161 | + let s = .den > 1 ? "{self.num:ld} / {self.den:ld}" : "{self.num:ld}"; |
| 162 | + return String::from(s); |
| 163 | + } |
| 164 | + |
| 165 | + fn max(r1: Rat, r2: Rat) -> Rat { |
| 166 | + return r1 < r2 ? r2 : r1; |
| 167 | + } |
| 168 | + |
| 169 | + fn min(r1: Rat, r2: Rat) -> Rat { |
| 170 | + return r1 < r2 ? r1 : r2; |
| 171 | + } |
| 172 | +} |
| 173 | + |
| 174 | +impl Clone for Rat { |
| 175 | + fn clone(self) -> Rat { |
| 176 | + return Rat{num: self.num, den: self.den}; |
| 177 | + } |
| 178 | +} |
| 179 | + |
| 180 | +import "std/vec.zc" |
| 181 | +import "rat.zc" |
| 182 | + |
| 183 | +fn divisors(n: int) -> Vec<int> { |
| 184 | + let divs = Vec<int>::new(); |
| 185 | + if n < 1 { return divs; } |
| 186 | + let divs2 = Vec<int>::new(); |
| 187 | + let i = 1; |
| 188 | + let k = (n % 2 == 0) ? 1 : 2; |
| 189 | + while i * i <= n { |
| 190 | + if n % i == 0 { |
| 191 | + divs << i; |
| 192 | + let j = n / i; |
| 193 | + if j != i { divs2 << j; } |
| 194 | + } |
| 195 | + i += k; |
| 196 | + } |
| 197 | + if divs2.length() { |
| 198 | + divs2.reverse(); |
| 199 | + for l in 0..divs2.length() { divs << divs2[l]; } |
| 200 | + } |
| 201 | + return divs; |
| 202 | +} |
| 203 | + |
| 204 | +fn main() { |
| 205 | + println "The following numbers (less than 2^19) are perfect:"; |
| 206 | + let one: const Rat = Rat::new(1); |
| 207 | + for i in 2..(1 << 19) { |
| 208 | + let sum = Rat::new(1, i); |
| 209 | + let pd = divisors(i); |
| 210 | + for j in 1..(pd.length() - 1) { sum += Rat::new(1, pd[j]); } |
| 211 | + if sum == one { println " {i}"; } |
| 212 | + } |
| 213 | +} |
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