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#include "AppHdr.h"
#include "random-var.h"
#include "random.h"
random_var::random_var(int c)
: start(c), end(c+1)
{
weights.push_back(1);
init();
}
random_var::random_var(int s, int e, weight_func w)
: start(s), end(e)
{
init_weights(w);
init();
}
random_var::random_var(int s, int e, vector<int> ws)
: start(s), end(e), weights(ws)
{
ASSERT(weights.size() == static_cast<unsigned int>(end - start));
init();
}
const random_var& random_var::operator=(const random_var& other)
{
start = other.start;
end = other.end;
total = other.total;
weights = other.weights;
return *this;
}
int random_var::weight(int val) const
{
if (val < start || val >= end)
return 0;
return weights[val - start];
}
void random_var::init_weights(weight_func w)
{
ASSERT(weights.empty());
for (int v = start; v < end; ++v)
weights.push_back(w ? (*w)(v) : 1);
}
void random_var::init()
{
int64_t sum = 0;
for (int v = start; v < end; ++v)
sum += weight(v);
if (sum <= (int64_t) INT_MAX)
total = (int) sum;
else
{
// The total is too big: rescale all entries by 256.
ASSERT(sum <= 256 * (int64_t) INT_MAX);
total = 0;
const int length = weights.size();
int first_nonzero = -1;
int last_nonzero = -1;
for (int i = 0; i < length; ++i)
{
weights[i] /= 256;
total += weights[i];
if (first_nonzero < 0 && weights[i] > 0)
first_nonzero = i;
if (weights[i] > 0)
last_nonzero = i;
}
ASSERT(first_nonzero >= 0 && last_nonzero >= 0);
// Weights that rounded to zero should be dropped.
weights.erase(weights.begin() + last_nonzero + 1, weights.end());
weights.erase(weights.begin(), weights.begin() + first_nonzero);
start += first_nonzero;
end -= (length - last_nonzero - 1);
}
ASSERT(total > 0);
ASSERT(weight(start) > 0);
ASSERT(weight(end - 1) > 0);
}
int random_var::roll2val(int r) const
{
ASSERT(0 <= r);
ASSERT(r < total);
int v = start;
int w = weight(v);
while (r >= w)
{
v++;
w += weight(v);
}
return v;
}
int random_var::roll() const
{
return roll2val(random2(total));
}
int random_var::max() const
{
return end - 1;
}
int random_var::min() const
{
return start;
}
double random_var::expected() const
{
double ev = 0;
for (int i = start; i < end; ++i)
ev += i * weight(i) / (double)total;
return ev;
}
//////////////////////////////////
random_var constant(int n)
{
return random_var(n);
}
random_var operator+(const random_var& x, const random_var& y)
{
const int start = x.min() + y.min();
const int end = x.max() + y.max() + 1;
vector<int> weights(end - start, 0);
for (int vx = x.min(); vx <= x.max(); ++vx)
for (int vy = y.min(); vy <= y.max(); ++vy)
weights[vx + vy - start] += x.weight(vx) * y.weight(vy);
return random_var(start, end, weights);
}
random_var negate(const random_var& x)
{
const int start = -x.max();
const int end = -x.min() + 1;
vector<int> weights(end - start, 0);
for (int v = x.min(); v <= x.max(); ++v)
weights[-v - start] = x.weight(v);
return random_var(start, end, weights);
}
random_var operator-(const random_var& x, const random_var& y)
{
return x + ::negate(y);
}
const random_var& operator+=(random_var& x, const random_var& y)
{
x = x + y;
return x;
}
const random_var& operator-=(random_var& x, const random_var& y)
{
x = x - y;
return x;
}
random_var operator/(const random_var& x, int d)
{
const int start = x.min() / d;
const int end = x.max() / d + 1;
vector<int> weights(end - start, 0);
for (int v = x.min(); v <= x.max(); ++v)
weights[v / d - start] += x.weight(v);
return random_var(start, end, weights);
}
random_var operator*(const random_var& x, int d)
{
const int start = x.min() * d;
const int end = x.max() * d + 1;
vector<int> weights(end - start, 0);
for (int v = x.min(); v <= x.max(); ++v)
weights[v * d - start] = x.weight(v);
return random_var(start, end, weights);
}
random_var div_rand_round(const random_var& x, int d)
{
const int start = x.min() / d;
const int end = (x.max() + d - 1) / d + 1;
vector<int> weights(end - start, 0);
for (int v = x.min(); v <= x.max(); ++v)
{
int rem = v % d;
weights[v / d - start] += x.weight(v) * (d - rem);
if (rem > 0)
weights[v / d + 1 - start] += x.weight(v) * rem;
}
return random_var(start, end, weights);
}
random_var rv::max(const random_var& x, const random_var& y)
{
const int start = ::max(x.min(), y.min());
const int end = ::max(x.max(), y.max()) + 1;
vector<int> weights(end - start, 0);
for (int vx = x.min(); vx <= x.max(); ++vx)
for (int vy = y.min(); vy <= y.max(); ++vy)
weights[::max(vx, vy) - start] += x.weight(vx) * y.weight(vy);
return random_var(start, end, weights);
}
random_var rv::min(const random_var& x, const random_var& y)
{
const int start = ::min(x.min(), y.min());
const int end = ::min(x.max(), y.max()) + 1;
vector<int> weights(end - start, 0);
for (int vx = x.min(); vx <= x.max(); ++vx)
for (int vy = y.min(); vy <= y.max(); ++vy)
weights[::min(vx, vy) - start] += x.weight(vx) * y.weight(vy);
return random_var(start, end, weights);
}
random_var rv::roll_dice(int d, int n)
{
if (n <= 0)
return constant(0);
random_var x = constant(0);
for (int i = 0; i < d; ++i)
x += random_var(1, n+1);
return x;
}
random_var rv::random2(int n)
{
return random_var(0, max(n, 1));
}
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