Set of real numbers: Difference between revisions
Added example for C
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* Define ''[http://www.wolframalpha.com/input/?i=%7Csin%28pi+x2%29%7C%3E1%2F2%2C+0+%3C+x+%3C+10 A]'' = {''x'' | 0 < ''x'' < 10 and |sin(π ''x''²)| > 1/2 }, ''[http://www.wolframalpha.com/input/?i=%7Csin%28pi+x%29%7C%3E1%2F2%2C+0+%3C+x+%3C+10 B]'' = {''x'' | 0 < ''x'' < 10 and |sin(π ''x'')| > 1/2}, calculate the length of the real axis covered by the set ''A'' − ''B''. Note that
|sin(π ''x'')| > 1/2 is the same as ''n'' + 1/6 < ''x'' < ''n'' + 5/6 for all integers ''n''; your program does not need to derive this by itself.
=={{header|C}}==
Providing an implementation of lambdas would be better, but this should do for now.
<lang C>#include <math.h>
#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>
struct RealSet {
bool(*contains)(struct RealSet*, struct RealSet*, double);
struct RealSet *left;
struct RealSet *right;
double low, high;
};
typedef enum {
CLOSED,
LEFT_OPEN,
RIGHT_OPEN,
BOTH_OPEN,
} RangeType;
double length(struct RealSet *self) {
const double interval = 0.00001;
double p = self->low;
int count = 0;
if (isinf(self->low) || isinf(self->high)) return -1.0;
if (self->high <= self->low) return 0.0;
do {
if (self->contains(self, NULL, p)) count++;
p += interval;
} while (p < self->high);
return count * interval;
}
bool empty(struct RealSet *self) {
if (self->low == self->high) {
return !self->contains(self, NULL, self->low);
}
return length(self) == 0.0;
}
static bool contains_closed(struct RealSet *self, struct RealSet *_, double d) {
return self->low <= d && d <= self->high;
}
static bool contains_left_open(struct RealSet *self, struct RealSet *_, double d) {
return self->low < d && d <= self->high;
}
static bool contains_right_open(struct RealSet *self, struct RealSet *_, double d) {
return self->low <= d && d < self->high;
}
static bool contains_both_open(struct RealSet *self, struct RealSet *_, double d) {
return self->low < d && d < self->high;
}
static bool contains_intersect(struct RealSet *self, struct RealSet *_, double d) {
return self->left->contains(self->left, NULL, d) && self->right->contains(self->right, NULL, d);
}
static bool contains_union(struct RealSet *self, struct RealSet *_, double d) {
return self->left->contains(self->left, NULL, d) || self->right->contains(self->right, NULL, d);
}
static bool contains_subtract(struct RealSet *self, struct RealSet *_, double d) {
return self->left->contains(self->left, NULL, d) && !self->right->contains(self->right, NULL, d);
}
struct RealSet* makeSet(double low, double high, RangeType type) {
bool(*contains)(struct RealSet*, struct RealSet*, double);
struct RealSet *rs;
switch (type) {
case CLOSED:
contains = contains_closed;
break;
case LEFT_OPEN:
contains = contains_left_open;
break;
case RIGHT_OPEN:
contains = contains_right_open;
break;
case BOTH_OPEN:
contains = contains_both_open;
break;
default:
return NULL;
}
rs = malloc(sizeof(struct RealSet));
rs->contains = contains;
rs->left = NULL;
rs->right = NULL;
rs->low = low;
rs->high = high;
return rs;
}
struct RealSet* makeIntersect(struct RealSet *left, struct RealSet *right) {
struct RealSet *rs = malloc(sizeof(struct RealSet));
rs->contains = contains_intersect;
rs->left = left;
rs->right = right;
rs->low = fmin(left->low, right->low);
rs->high = fmin(left->high, right->high);
return rs;
}
struct RealSet* makeUnion(struct RealSet *left, struct RealSet *right) {
struct RealSet *rs = malloc(sizeof(struct RealSet));
rs->contains = contains_union;
rs->left = left;
rs->right = right;
rs->low = fmin(left->low, right->low);
rs->high = fmin(left->high, right->high);
return rs;
}
struct RealSet* makeSubtract(struct RealSet *left, struct RealSet *right) {
struct RealSet *rs = malloc(sizeof(struct RealSet));
rs->contains = contains_subtract;
rs->left = left;
rs->right = right;
rs->low = left->low;
rs->high = left->high;
return rs;
}
int main() {
struct RealSet *a = makeSet(0.0, 1.0, LEFT_OPEN);
struct RealSet *b = makeSet(0.0, 2.0, RIGHT_OPEN);
struct RealSet *c = makeSet(1.0, 2.0, LEFT_OPEN);
struct RealSet *d = makeSet(0.0, 3.0, RIGHT_OPEN);
struct RealSet *e = makeSet(0.0, 1.0, BOTH_OPEN);
struct RealSet *f = makeSet(0.0, 1.0, CLOSED);
struct RealSet *g = makeSet(0.0, 0.0, CLOSED);
int i;
for (i = 0; i < 3; ++i) {
struct RealSet *t;
t = makeUnion(a, b);
printf("(0, 1] union [0, 2) contains %d is %d\n", i, t->contains(t, NULL, i));
free(t);
t = makeIntersect(b, c);
printf("[0, 2) intersect (1, 2] contains %d is %d\n", i, t->contains(t, NULL, i));
free(t);
t = makeSubtract(d, e);
printf("[0, 3) - (0, 1) contains %d is %d\n", i, t->contains(t, NULL, i));
free(t);
t = makeSubtract(d, f);
printf("[0, 3) - [0, 1] contains %d is %d\n", i, t->contains(t, NULL, i));
free(t);
printf("\n");
}
printf("[0, 0] is empty %d\n", empty(g));
free(a);
free(b);
free(c);
free(d);
free(e);
free(f);
free(g);
return 0;
}</lang>
{{out}}
<pre>(0, 1] union [0, 2) contains 0 is 1
[0, 2) intersect (1, 2] contains 0 is 0
[0, 3) - (0, 1) contains 0 is 1
[0, 3) - [0, 1] contains 0 is 0
(0, 1] union [0, 2) contains 1 is 1
[0, 2) intersect (1, 2] contains 1 is 0
[0, 3) - (0, 1) contains 1 is 1
[0, 3) - [0, 1] contains 1 is 0
(0, 1] union [0, 2) contains 2 is 0
[0, 2) intersect (1, 2] contains 2 is 0
[0, 3) - (0, 1) contains 2 is 1
[0, 3) - [0, 1] contains 2 is 1
[0, 0] is empty 0</pre>
=={{header|C++}}==
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