added more spikes about divide-and-conquer binary opeartions, changed over to using "done" list, changed cache encoding

This commit is contained in:
Zander Thannhauser 2025-06-15 10:17:02 -05:00
parent d3ae35ceb5
commit cb1738376d
12 changed files with 1816 additions and 161 deletions

2
.gitignore vendored
View file

@ -3,3 +3,5 @@ simplifications.bin
.simplifier-*.bin
.direnv/
typescript

410
main.c
View file

@ -182,7 +182,8 @@ static void parse_args(int argc, char* const* argv)
#define N (65536)
enum kind {
ek_undef,
ek_unreachable,
ek_0,
ek_1,
ek_W,
@ -215,11 +216,10 @@ struct expr {
enum kind kind;
uint16_t cond, left, right;
int cost;
} lookup[N];
// truthtable -> cost
int costs[N] = {};
static void print(uint16_t truthtable, int depth)
{
#define LITERAL_ESCAPE "\e[38;2;200;200;100m"
@ -243,10 +243,12 @@ static void print(uint16_t truthtable, int depth)
switch (e->kind)
{
case ek_undef:
case ek_unreachable:
{
assert(!"NOPE");
break;
}
case ek_0:
{
printf(print_with_color ? LITERAL_ESCAPE "0" RESET_ESCAPE : "0");
@ -364,34 +366,46 @@ static void print(uint16_t truthtable, int depth)
void calculate_simplifications(void)
{
// heap of truthtables; key = cost
uint16_t todo[N];
int todo_n = 0;
// truthtable -> index in 'todo'
int reverse[N];
// init:
for (int i = 0; i < N; i++)
// init 'lookup':
{
lookup[i].kind = ek_undef;
reverse[i] = -1;
costs[i] = INT_MAX;
for (int i = 0; i < N; i++)
{
lookup[i].kind = ek_unreachable;
lookup[i].cost = INT_MAX;
}
}
// heap of truthtables; key = cost
struct {
uint16_t data[N];
int n;
// truthtable -> index in 'todo'
int reverse[N];
} todo;
// init 'todo':
{
todo.n = 0;
for (int i = 0; i < N; i++)
{
todo.reverse[i] = -1;
}
}
uint16_t pop(void)
{
assert(todo_n > 0);
assert(todo.n > 0);
uint16_t retval = todo[0];
uint16_t retval = todo.data[0];
reverse[retval] = -1;
todo.reverse[retval] = -1;
uint16_t moving = todo[todo_n-- - 1];
uint16_t moving = todo.data[todo.n-- - 1];
int cost = costs[moving];
int cost = lookup[moving].cost;
int index = 0;
@ -402,25 +416,25 @@ void calculate_simplifications(void)
uint16_t smallest = moving;
if (left < todo_n && costs[todo[left]] < cost)
smallest = todo[left];
if (left < todo.n && lookup[todo.data[left]].cost < cost)
smallest = todo.data[left];
if (right < todo_n && costs[todo[right]] < costs[smallest])
smallest = todo[right];
if (right < todo.n && lookup[todo.data[right]].cost < lookup[smallest].cost)
smallest = todo.data[right];
if (smallest == moving)
{
todo[index] = moving;
todo.data[index] = moving;
reverse[moving] = index;
todo.reverse[moving] = index;
}
else
{
int new = reverse[smallest];
int new = todo.reverse[smallest];
todo[index] = smallest;
todo.data[index] = smallest;
reverse[smallest] = index;
todo.reverse[smallest] = index;
index = new;
@ -433,73 +447,166 @@ void calculate_simplifications(void)
void append(uint16_t truthtable, int cost)
{
assert(reverse[truthtable] == -1);
assert(todo.reverse[truthtable] == -1);
int index = todo_n++, new_index;
int index = todo.n++, new_index;
while (index > 0 && costs[todo[new_index = (index - 1) / 2]] > cost)
while (index > 0 && lookup[todo.data[new_index = (index - 1) / 2]].cost > cost)
{
todo[index] = todo[new_index];
todo.data[index] = todo.data[new_index];
reverse[todo[new_index]] = index;
todo.reverse[todo.data[new_index]] = index;
index = new_index;
}
todo[index] = truthtable;
reverse[truthtable] = index;
costs[truthtable] = cost;
todo.data[index] = truthtable;
todo.reverse[truthtable] = index;
lookup[truthtable].cost = cost;
}
void update(uint16_t truthtable, int cost)
{
assert(reverse[truthtable] != -1);
assert(todo.reverse[truthtable] != -1);
assert(cost < costs[truthtable]);
assert(cost < lookup[truthtable].cost);
int index = reverse[truthtable], new_index;
int index =todo. reverse[truthtable], new_index;
while (index > 0 && costs[todo[new_index = (index - 1) / 2]] > cost)
while (index > 0 && lookup[todo.data[new_index = (index - 1) / 2]].cost > cost)
{
todo[index] = todo[new_index];
todo.data[index] = todo.data[new_index];
reverse[todo[new_index]] = index;
todo.reverse[todo.data[new_index]] = index;
index = new_index;
}
todo[index] = truthtable;
reverse[truthtable] = index;
todo.data[index] = truthtable;
todo.reverse[truthtable] = index;
costs[truthtable] = cost;
lookup[truthtable].cost = cost;
}
// create a list of the "done" truthtables
struct {
int headtails[N], next[N], head;
// for debugging:
bool in[N];
} done = {};
// init 'done':
{
done.head = -1;
for (int i = 0; i < N; i++)
{
done.headtails[i] = -1;
done.in[i] = false;
}
}
void insert(int index)
{
assert(!done.in[index]);
int head = index & 1 ? index & ~(index & -index) : index, prevhead = -1;
while (done.headtails[head] == -1 || index < done.headtails[head])
{
done.headtails[head] = index;
prevhead = head, head = head & ~(head & -head);
}
if (done.headtails[head] < index)
{
if (prevhead == -1)
{
assert(done.headtails[head] == head);
done.next[head] = index;
}
else
{
int tophalftail = done.headtails[prevhead - 1];
assert(tophalftail != -1);
done.next[tophalftail] = index;
}
}
else
{
done.head = index;
}
int n = ~index & M;
int tail = index & 1 ? index : index | (n & -n), prevtail = -1;
while (done.headtails[tail] == -1 || done.headtails[tail] < index)
{
done.headtails[tail] = index;
prevtail = tail, tail = tail | (n = ~tail & M, n & -n);
}
if (index < done.headtails[tail])
{
if (prevtail == -1)
{
assert(done.headtails[tail] == tail);
assert(done.in[tail]);
done.next[index] = tail;
}
else
{
int bottomhalfhead = done.headtails[prevtail + 1];
assert(bottomhalfhead != -1);
done.next[index] = bottomhalfhead;
}
}
else
{
done.next[index] = -1;
}
done.in[index] = true;
}
append(W, 0), lookup[W].kind = ek_W;
append(X, 0), lookup[X].kind = ek_X;
append(Y, 0), lookup[Y].kind = ek_Y;
append(Z, 0), lookup[Z].kind = ek_Z;
append(0, 1), lookup[0].kind = ek_0;
append(M, 1), lookup[M].kind = ek_1;
while (todo_n)
for (int iterations = 1; todo.n && iterations <= N; iterations++)
{
uint16_t truthtable = pop();
int cost = costs[truthtable];
insert(truthtable);
int cost = lookup[truthtable].cost;
if (verbose)
{
int left = N - todo_n;
if (print_with_color)
{
printf("\e[2K");
}
printf("%i of %i (%.2f%%): [%i] ", left, N, (100.0 * left / N), cost);
printf("%i of %i (%.2f%%): [%i] ",
iterations, N, (100.0 * iterations / N), cost);
print(truthtable, 0), puts("");
@ -516,9 +623,9 @@ void calculate_simplifications(void)
int not_cost = cost + 1;
if (not_cost < costs[not_truthtable])
if (not_cost < lookup[not_truthtable].cost)
{
if (reverse[not_truthtable] == -1)
if (todo.reverse[not_truthtable] == -1)
{
append(not_truthtable, not_cost);
}
@ -534,44 +641,41 @@ void calculate_simplifications(void)
#define BINARY_OPERATOR(ekind, function) \
{ \
for (int i = 0; i < N; i++) \
for (int i = done.head; i != -1; i = done.next[i]) \
{ \
if (costs[i] != INT_MAX) \
{ \
uint16_t bin_truthtable = function(truthtable, i) & M; \
\
int bin_cost = 1 + cost + lookup[i].cost; \
\
if (bin_cost < lookup[bin_truthtable].cost) \
{ \
uint16_t bin_truthtable = function(truthtable, i) & M; \
if (todo.reverse[bin_truthtable] == -1) \
append(bin_truthtable, bin_cost); \
else \
update(bin_truthtable, bin_cost); \
\
int bin_cost = 1 + cost + costs[i]; \
\
if (bin_cost < costs[bin_truthtable]) \
{ \
if (reverse[bin_truthtable] == -1) \
append(bin_truthtable, bin_cost); \
else \
update(bin_truthtable, bin_cost); \
\
lookup[bin_truthtable].kind = ekind; \
lookup[bin_truthtable].left = truthtable; \
lookup[bin_truthtable].right = i; \
} \
lookup[bin_truthtable].kind = ekind; \
lookup[bin_truthtable].left = truthtable; \
lookup[bin_truthtable].right = i; \
} \
\
} \
\
{ \
uint16_t bin_truthtable = function(i, truthtable) & M; \
\
int bin_cost = 1 + cost + lookup[i].cost; \
\
if (bin_cost < lookup[bin_truthtable].cost) \
{ \
uint16_t bin_truthtable = function(i, truthtable) & M; \
if (todo.reverse[bin_truthtable] == -1) \
append(bin_truthtable, bin_cost); \
else \
update(bin_truthtable, bin_cost); \
\
int bin_cost = 1 + cost + costs[i]; \
\
if (bin_cost < costs[bin_truthtable]) \
{ \
if (reverse[bin_truthtable] == -1) \
append(bin_truthtable, bin_cost); \
else \
update(bin_truthtable, bin_cost); \
\
lookup[bin_truthtable].kind = ekind; \
lookup[bin_truthtable].left = i; \
lookup[bin_truthtable].right = truthtable; \
} \
lookup[bin_truthtable].kind = ekind; \
lookup[bin_truthtable].left = i; \
lookup[bin_truthtable].right = truthtable; \
} \
} \
} \
@ -654,44 +758,38 @@ void calculate_simplifications(void)
if (use_operators.ternary)
{
for (int i = 0; i < N; i++)
for (int i = done.head; i != -1; i = done.next[i])
{
if (costs[i] != INT_MAX)
for (int j = done.head; j != -1; j = done.next[j])
{
for (int j = 0; j < N; j++)
{
if (costs[j] != INT_MAX)
{
int ternary_cost = 1 + cost + costs[i] + costs[j];
int ternary_cost = 1 + cost + lookup[i].cost + lookup[j].cost;
#define TERNARY(C, T, F) \
#define TERNARY(C, T, F) \
{ \
uint16_t ternary_truthtable = \
((C) & (T)) | (~(C) & (F)); \
\
if (ternary_cost < lookup[ternary_truthtable].cost) \
{ \
if (todo.reverse[ternary_truthtable] == -1) \
{ \
uint16_t ternary_truthtable = \
((C) & (T)) | (~(C) & (F)); \
\
if (ternary_cost < costs[ternary_truthtable]) \
{ \
if (reverse[ternary_truthtable] == -1) \
{ \
append(ternary_truthtable, ternary_cost); \
} \
else \
{ \
update(ternary_truthtable, ternary_cost); \
} \
\
lookup[ternary_truthtable].kind = ek_ternary; \
lookup[ternary_truthtable].cond = (C); \
lookup[ternary_truthtable].left = (T); \
lookup[ternary_truthtable].right = (F); \
} \
append(ternary_truthtable, ternary_cost); \
} \
else \
{ \
update(ternary_truthtable, ternary_cost); \
} \
\
lookup[ternary_truthtable].kind = ek_ternary; \
lookup[ternary_truthtable].cond = (C); \
lookup[ternary_truthtable].left = (T); \
lookup[ternary_truthtable].right = (F); \
} \
} \
TERNARY(truthtable, i, j);
TERNARY(i, truthtable, j);
TERNARY(i, j, truthtable);
}
}
TERNARY(truthtable, i, j);
TERNARY(i, truthtable, j);
TERNARY(i, j, truthtable);
}
}
}
@ -705,7 +803,7 @@ void calculate_simplifications(void)
void get_simplifications(void)
{
char path[PATH_MAX] = ".simplifier-cache";
char path[PATH_MAX] = ".simplifier-cache-2";
if (use_operators.not)
strcat(path, "-not");
@ -766,12 +864,6 @@ void get_simplifications(void)
printf("%s: read() to cache failed: %m\n", argv0);
exit(1);
}
if (read(fd, costs, sizeof(costs)) < (ssize_t) sizeof(costs))
{
printf("%s: read() to cache failed: %m\n", argv0);
exit(1);
}
}
else if (fd < 0 && errno == ENOENT)
{
@ -806,12 +898,6 @@ void get_simplifications(void)
printf("%s: write() to cache failed: %m\n", argv0);
exit(1);
}
if (write(fd, costs, sizeof(costs)) < (ssize_t) sizeof(costs))
{
printf("%s: write() to cache failed: %m\n", argv0);
exit(1);
}
}
else
{
@ -1326,7 +1412,7 @@ int main(int argc, char* const* argv)
{
for (int i = 0; i < N; i++)
{
int cost = costs[i];
int cost = lookup[i].cost;
if (cost != INT_MAX)
{
@ -1340,48 +1426,52 @@ int main(int argc, char* const* argv)
// printf("truthtable = 0b%016b\n", truthtable);
if (costs[truthtable] == INT_MAX)
if (lookup[truthtable].kind == ek_unreachable)
{
puts("unreachable");
}
else
{
printf("%2i: ", costs[truthtable]), print(truthtable, 0), puts("");
printf("%2i: ", lookup[truthtable].cost), print(truthtable, 0), puts("");
}
}
else
{
int max_cost = 0;
for (int i = 0; i < N; i++)
// Let's humble-brag just a little.
{
int cost = costs[i];
int max_cost = 0;
if (cost != INT_MAX && max_cost < cost)
for (int i = 0; i < N; i++)
{
max_cost = cost;
int cost = lookup[i].cost;
if (cost != INT_MAX && max_cost < cost)
{
max_cost = cost;
}
}
puts("");
printf("I can simplify any tree down to %i operators or less.\n",
max_cost);
puts("");
}
// we subtract 4 from the cost because
puts("");
printf("I can simplify any tree down to %i operators or less.\n",
max_cost);
puts("");
for (char* line; (line = readline(">>> ")); free(line))
{
add_history(line);
uint16_t truthtable = evaluate(line);
// printf("truthtable = 0b%016b\n", truthtable);
if (costs[truthtable] == INT_MAX)
if (lookup[truthtable].kind == ek_unreachable)
{
puts("unreachable");
}
else
{
printf("%2i: ", costs[truthtable]), print(truthtable, 0), puts("");
printf("%2i: ", lookup[truthtable].cost), print(truthtable, 0), puts("");
}
}
}

View file

@ -23,5 +23,6 @@ run: /tmp/4-variable-simplifier
$< $(args)
# nix --extra-experimental-features nix-command --extra-experimental-features flakes develop --command 'make'
# nix --extra-experimental-features nix-command \
# --extra-experimental-features flakes develop --command 'make'

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@ -0,0 +1,100 @@
#include <stdbool.h>
#include <assert.h>
#include <assert.h>
#include <stdio.h>
#define N(array) (sizeof(array) / sizeof(*array))
// 0 1 2 3 4 5 6 7 8 9
int a[10] = { 2, 4, 5, 7, 9, 11, 15, 17, 17, 19};
int b[10] = {10, 11, 11, 14, 14, 19, 20, 23, 26, 29};
int c[20] = {
15, 17, 19, 21, 22, 25, 26, 26, 27, 32,
33, 33, 36, 39, 42, 44, 48, 49, 49, 49
};
// [ 0] [ 1] [ 2] [ 3] [ 4] [ 5] [ 6] [ 7] [ 8] [ 9]
// 2 4 5 7 9 11 15 17 17 19
// --------------------------------------------------
// [ 0] 10 | 12 14 (15) (17) (19) (21) (25) (27) (27) 29
// [ 1] 11 | 13 (15) 16 28 20 (22) (26) 28 28 30
// [ 2] 11 | 13 (15) 16 18 20 (22) (26) 28 28 30
// [ 3] 14 | 16 18 (19) (21) 23 (25) 29 31 31 (33)
// [ 4] 14 | 16 18 (19) (21) 23 (25) 29 31 31 (33)
// [ 5] 19 |(21) 23 24 (26) 28 30 34 (36) (36) 38
// [ 6] 20 |(22) 24 (25) (27) 29 31 38 40 40 (42)
// [ 7] 23 |(25) (27) 28 30 (32) 34 38 40 40 (42)
// [ 8] 26 | 28 30 31 (33) 35 37 41 43 43 45
// [ 9] 29 | 31 (33) 34 (36) 38 40 (44) 46 46 (48)
int main()
{
puts("hello, world!");
for (int ci = 0; ci < 20; ci++)
{
bool found[10][10] = {};
int goal = c[ci];
bool again = true;
while (again)
{
again = false;
int ai = 0, bi = 9;
while (ai < 10 && bi >= 0)
{
int sum = found[ai][bi] ? 0 : a[ai] + b[bi];
if (sum < goal)
{
ai++;
}
else if (sum > goal)
{
bi--;
}
else
{
assert(a[ai] + b[bi] == c[ci]);
printf("a[%2i] + b[%2i] == c[%2i] "
"(%2i + %2i == %2i)\n",
ai, bi, ci, a[ai], b[bi], c[ci]);
found[ai][bi] = true;
again = true;
bi--;
}
}
}
}
return 0;
}

94
spikes/kattis-add.c Normal file
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@ -0,0 +1,94 @@
#include <stdbool.h>
#include <assert.h>
#include <assert.h>
#include <stdio.h>
#define N(array) (sizeof(array) / sizeof(*array))
// 0 1 2 3 4 5 6 7 8 9
int a[10] = { 2, 4, 5, 7, 9, 11, 15, 17, 17, 19};
int b[10] = {10, 11, 11, 14, 14, 19, 20, 23, 26, 29};
int c[20] = {
15, 17, 19, 21, 22, 25, 26, 26, 27, 32,
33, 33, 36, 39, 42, 44, 48, 49, 49, 49
};
// [ 0] [ 1] [ 2] [ 3] [ 4] [ 5] [ 6] [ 7] [ 8] [ 9]
// 2 4 5 7 9 11 15 17 17 19
// --------------------------------------------------
// [ 0] 10 | 12 14 15 (17) 19 21 25 27 27 29
// [ 1] 11 | 13 15 16 28 20 22 26 28 28 30
// [ 2] 11 | 13 (15) 16 18 20 22 26 28 28 30
// [ 3] 14 | 16 18 19 21 23 25 29 31 31 33
// [ 4] 14 | 16 18 (19) 21 23 25 29 31 31 33
// [ 5] 19 |(21) 23 24 (26) 28 30 34 36 36 38
// [ 6] 20 |(22) 24 25 27 29 31 38 40 40 (42)
// [ 7] 23 |(25) (27) 28 30 32 34 38 40 40 (42)
// [ 8] 26 | 28 30 31 33 35 37 41 43 43 45
// [ 9] 29 | 31 (33) 34 (36) 38 40 (44) 46 46 (48)
int main()
{
puts("hello, world!");
for (int ci = 0; ci < 20; ci++)
{
int goal = c[ci];
int ai = 0, bi = 9;
while (1)
{
int sum = a[ai] + b[bi];
if (sum < goal)
{
ai++;
if (ai == 10)
break;
}
else if (sum > goal)
{
if (bi == 0)
break;
bi--;
}
else
{
assert(a[ai] + b[bi] == c[ci]);
printf("a[%2i] + b[%2i] == c[%2i] "
"(%2i + %2i == %2i)\n",
ai, bi, ci, a[ai], b[bi], c[ci]);
break;
}
}
}
return 0;
}

85
spikes/kattis-subtract.c Normal file
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@ -0,0 +1,85 @@
#include <limits.h>
#include <stdio.h>
#include <stdbool.h>
#include <assert.h>
// in this one, 'a' is fixed and we're trying to find a 'b' and 'c' to
// satisify the equation: `a + b = c`
// which we're re-writing as:
// `a = c - b`
int a = 7;
/*int a = 11;*/
// 0 1 2 3 4 5 6 7 8 9
int b[10] = {10, 11, 11, 14, 14, 19, 20, 23, 26, 29};
int c[20] = {
15, 17, 19, 21, 22, 25, 26, 26, 27, 32,
33, 33, 36, 39, 42, 44, 48, 49, 49, 49
};
int main()
{
puts("hello, world!");
bool found[10][20] = {};
int passes = 0;
bool again = true;
while (again)
{
passes++;
again = false;
int bi = 0, ci = 0;
while (bi < 10 && ci < 20)
{
int diff = found[bi][ci] ? INT_MIN : c[ci] - b[bi];
if (a < diff)
{
bi++;
}
else if (diff < a)
{
ci++;
}
else
{
assert(a + b[bi] == c[ci]);
printf("a + b[%2i] == c[%2i] "
"(%2i + %2i == %2i)\n",
bi, ci, a, b[bi], c[ci]);
found[bi][ci] = true;
again = true;
// From now on, this cell will be seen as "too low"
// so we'll take that path like it's too high.
bi++;
}
}
}
printf("passes = %i\n", passes);
return 0;
}

172
spikes/linear-add.c Normal file
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@ -0,0 +1,172 @@
#include <stdbool.h>
#include <assert.h>
#include <assert.h>
#include <stdio.h>
#define N(array) (sizeof(array) / sizeof(*array))
// 0 1 2 3 4 5 6 7 8 9
int a[10] = { 2, 4, 5, 7, 9, 11, 15, 17, 17, 19};
int b[10] = {10, 11, 11, 14, 14, 19, 20, 23, 26, 29};
int c[20] = {
15, 17, 19, 21, 22, 25, 26, 26, 27, 32,
33, 33, 36, 39, 42, 44, 48, 49, 49, 49
};
// [ 0] [ 1] [ 2] [ 3] [ 4] [ 5] [ 6] [ 7] [ 8] [ 9]
// 2 4 5 7 9 11 15 17 17 19
// --------------------------------------------------
// [ 0] 10 | 12 14 (15) (17) (19) (21) (25) (27) (27) 29
// [ 1] 11 | 13 (15) 16 28 20 (22) (26) 28 28 30
// [ 2] 11 | 13 (15) 16 18 20 (22) (26) 28 28 30
// [ 3] 14 | 16 18 (19) (21) 23 (25) 29 31 31 (33)
// [ 4] 14 | 16 18 (19) (21) 23 (25) 29 31 31 (33)
// [ 5] 19 |(21) 23 24 (26) 28 30 34 (36) (36) 38
// [ 6] 20 |(22) 24 (25) (27) 29 31 38 40 40 (42)
// [ 7] 23 |(25) (27) 28 30 (32) 34 38 40 40 (42)
// [ 8] 26 | 28 30 31 (33) 35 37 41 43 43 45
// [ 9] 29 | 31 (33) 34 (36) 38 40 (44) 46 46 (48)
int sums[10 * 10];
bool queued[10 * 10];
struct {
int data[10 * 10];
int n;
} heap;
void append(int e)
{
int index = heap.n++, new_index;
while (index > 0 && sums[heap.data[new_index = (index - 1) / 2]] > sums[e])
{
heap.data[index] = heap.data[new_index];
index = new_index;
}
heap.data[index] = e;
}
int pop(void)
{
assert(heap.n > 0);
int retval = heap.data[0];
heap.data[0] = heap.data[heap.n-- - 1];
int index = 0;
again:
{
int left = index * 2 + 1;
int right = index * 2 + 2;
int smallest = index;
if (left < heap.n && sums[heap.data[left]] < sums[heap.data[index]])
smallest = left;
if (right < heap.n && sums[heap.data[right]] < sums[heap.data[smallest]])
smallest = right;
if (smallest != index)
{
int tmp = heap.data[index];
heap.data[index] = heap.data[smallest];
heap.data[smallest] = tmp;
index = smallest;
goto again;
}
}
return retval;
}
int main()
{
puts("hello, world!");
int ci = 0;
sums[0] = a[0] + b[0];
queued[0] = true;
append(0);
while (heap.n && ci < 20)
{
int sum = sums[heap.data[0]], ce = c[ci];
// printf("sum = %i, ce = %i\n", sum, ce);
if (sum < ce)
{
next_sum: ;
int xy = pop();
if (xy % 10 + 1 < 10 && !queued[xy + 1])
{
int nxy = xy + 1;
sums[nxy] = a[nxy % 10] + b[nxy / 10];
queued[nxy] = true;
append(nxy);
}
if (xy + 10 < 100 && !queued[xy + 10])
{
int nxy = xy + 10;
sums[nxy] = a[nxy % 10] + b[nxy / 10];
queued[nxy] = true;
append(nxy);
}
}
else if (sum > ce)
{
ci++;
}
else
{
int xy = heap.data[0];
int ai = xy % 10, bi = xy / 10;
assert(a[ai] + b[bi] == c[ci]);
printf("a[%2i] + b[%2i] == c[%2i] (%2i + %2i == %2i)\n",
ai, bi, ci, a[ai], b[bi], c[ci]);
goto next_sum;
}
}
return 0;
}

37
spikes/quadrant-or-1.c Normal file
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#include <stdio.h>
#include <assert.h>
void search(
int mask,
int ai, int bi,
int findme)
{
if (mask)
{
if (findme & mask)
{
search(mask >> 1, ai, bi | mask, findme);
search(mask >> 1, ai | mask, bi, findme);
search(mask >> 1, ai | mask, bi | mask, findme);
}
else
{
search(mask >> 1, ai, bi, findme);
}
}
else
{
assert((ai | bi) == findme);
printf("0b%04b | 0b%04b == 0b%04b "
"(%2i | %2i == %2i)\n", ai, bi, findme, ai, bi, findme);
}
}
int main()
{
search(0b1000, 0, 0, 11);
return 0;
}

220
spikes/quadrant-or-2.c Normal file
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#include <stdio.h>
#include <assert.h>
#ifdef ZDEBUG
#define zprintf(fmt, ...) printf(fmt, ## __VA_ARGS__);
#else
#define zprintf(...) ;
#endif
// 0 1 2 3 4 5 6 7 8 9
int a[10] = { 2, 4, 5, 7, 9, 11, 15, 17, 17, 19};
int b[10] = {10, 11, 11, 14, 14, 19, 20, 23, 26, 29};
// [ 0] [ 1] [ 2] [ 3] [ 4] [ 5] [ 6] [ 7] [ 8] [ 9]
// 2 4 5 7 9 11 15 17 17 19
// --------------------------------------------------
// [ 0] 10 | 10 14 15 15 11 11 15 27 27 27
// [ 1] 11 | 11 15 15 15 11 11 15 27 27 27
// [ 2] 11 | 11 15 15 15 11 11 15 27 27 27
// [ 3] 14 | 14 14 15 15 15 15 15 31 31 31
// [ 4] 14 | 14 14 15 15 15 15 15 31 31 31
// [ 5] 19 | 19 (23) (23) (23) 27 27 31 19 19 19
// [ 6] 20 | 22 20 21 (23) 29 31 31 21 21 (23)
// [ 7](23)|(23) (23) (23) (23) 31 31 31 (23) (23) (23)
// [ 8] 26 | 26 30 31 31 27 27 31 27 27 27
// [ 9] 29 | 31 29 29 31 29 31 31 29 29 31
int binary(
int mask,
int *array,
int i, int n)
{
while (n > 1)
{
int m = n / 2;
if (array[i + m] & mask)
n = m;
else
i += m, n = n - m;
}
return (array[i] & mask) ? i : i + 1;
}
void search(
int mask,
int ai, int an,
int bi, int bn,
int findme,
int calldepth)
{
zprintf("%*s" "search():" "\n", calldepth++, "");
zprintf("%*s" "mask = 0b%05b" "\n", calldepth, "", mask);
zprintf("%*s" "findme = 0b%05b" "\n", calldepth, "", findme);
zprintf("%*s" "ai = %i" "\n", calldepth, "", ai);
zprintf("%*s" "an = %i" "\n", calldepth, "", an);
zprintf("%*s" "bi = %i" "\n", calldepth, "", bi);
zprintf("%*s" "bn = %i" "\n", calldepth, "", bn);
if (mask)
{
int asplit = binary(mask, a + ai, 0, an);
int bsplit = binary(mask, b + bi, 0, bn);
zprintf("%*s" "asplit = %i" "\n", calldepth, "", asplit);
zprintf("%*s" "bsplit = %i" "\n", calldepth, "", bsplit);
assert((asplit == an) || (a[ai + asplit] & mask));
assert((bsplit == bn) || (b[bi + bsplit] & mask));
if (mask & findme)
{
zprintf("%*s" "one path" "\n", calldepth, "");
// 0 ... (asplit - 1) | asplit ... (an - 1)
// --------------------- -------------------
// 0 | | |
// ... | first quadrant. | second quadrant |
// (bsplit - 1) | | |
// --- ---------------------- -------------------
// bsplit | | |
// ... | third quadrant | fourth quadrant |
// (bn - 1) | | |
// --- | | |
// ---------------------- -------------------
// second quadrant.
if (asplit < an && 0 < bsplit)
{
zprintf("%*s" "entering second quadrant." "\n", calldepth, "");
search(
mask >> 1,
ai + asplit, an - asplit,
bi, bsplit,
findme,
calldepth);
}
else
{
zprintf("%*s" "empty second quadrant." "\n", calldepth, "");
}
// third quadrant.
if (0 < asplit && bsplit < bn)
{
zprintf("%*s" "entering third quadrant." "\n", calldepth, "");
search(
mask >> 1,
ai, asplit,
bi + bsplit, bn - bsplit,
findme,
calldepth);
}
else
{
zprintf("%*s" "empty third quadrant." "\n", calldepth, "");
}
// fourth quadrant.
if (asplit < an && bsplit < bn)
{
zprintf("%*s" "entering fourth quadrant." "\n", calldepth, "");
search(
mask >> 1,
ai + asplit, an - asplit,
bi + bsplit, bn - bsplit,
findme,
calldepth);
}
else
{
zprintf("%*s" "empty fourth quadrant." "\n", calldepth, "");
}
}
else
{
zprintf("%*s" "zero path" "\n", calldepth, "");
// first quadrant.
if (0 < asplit && 0 < bsplit)
{
zprintf("%*s" "entering first quadrant." "\n", calldepth, "");
search(
mask >> 1,
ai, asplit,
bi, bsplit,
findme,
calldepth);
}
else
{
zprintf("%*s" "empty first quadrant." "\n", calldepth, "");
}
}
}
else for (int i = 0; i < an; i++)
{
for (int j = 0; j < bn; j++)
{
assert((a[ai + i] | b[bi + j]) == findme);
printf("%2i [%2i] (0b%05b) | %2i [%2i] "
"(0b%05b) == %2i (0b%05b)" "\n",
a[ai + i], ai + i, a[ai + i],
b[bi + j], bi + j, b[bi + j],
findme, findme);
}
}
calldepth--;
}
int main()
{
search(
16,
0, 10,
0, 10,
23,
0);
return 0;
}

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#include <stdbool.h>
#include <stdio.h>
#include <assert.h>
#ifdef ZDEBUG
#define zprintf(fmt, ...) printf(fmt, ## __VA_ARGS__);
#else
#define zprintf(...) ;
#endif
#define N (256)
#define M (255)
struct sparselist {
int headtails[N], next[N], head;
bool in[N];
} b, c;
void init(struct sparselist* this)
{
this->head = -1;
for (int i = 0; i < N; i++)
{
this->headtails[i] = -1;
this->next[i] = -1;
this->in[i] = false;
}
}
void print(struct sparselist* this)
{
puts("print():");
for (int i = 0; i < N; i++)
{
if (this->headtails[i] != -1)
{
printf(" " "headtails[%3i (0b%08b)] = %i" "\n", i, i, this->headtails[i]);
}
}
printf("head = %i\n", this->head);
for (int index = this->head; index != -1; index = this->next[index])
{
printf(" " "index = %i\n", index);
}
}
void insert(struct sparselist* this, int index)
{
assert(!this->in[index]);
int head = index & 1 ? index & ~(index & -index) : index, prevhead = -1;
while (this->headtails[head] == -1 || index < this->headtails[head])
{
this->headtails[head] = index;
prevhead = head, head = head & ~(head & -head);
}
if (this->headtails[head] < index)
{
if (prevhead == -1)
{
assert(this->headtails[head] == head);
assert(this->in[head]);
this->next[head] = index;
}
else
{
int tophalftail = this->headtails[prevhead - 1];
assert(tophalftail != -1);
this->next[tophalftail] = index;
}
}
else
{
this->head = index;
}
int n = ~index & M;
int tail = index & 1 ? index : index | (n & -n), prevtail = -1;
while (this->headtails[tail] == -1 || this->headtails[tail] < index)
{
this->headtails[tail] = index;
prevtail = tail, tail = tail | (n = ~tail & M, n & -n);
}
if (index < this->headtails[tail])
{
if (prevtail == -1)
{
assert(this->headtails[tail] == tail);
assert(this->in[tail]);
this->next[index] = tail;
}
else
{
int bottomhalfhead = this->headtails[prevtail + 1];
assert(bottomhalfhead != -1);
this->next[index] = bottomhalfhead;
}
}
else
{
this->next[index] = -1;
}
this->in[index] = true;
}
int a = 17;
void search(
int mask,
int bheadindex, int btailindex,
int cheadindex, int ctailindex,
int calldepth)
{
zprintf("%*s" "quadrant_search():" "\n", calldepth++, "");
zprintf("%*s" "mask = 0b%05b" "\n", calldepth, "", mask);
zprintf("%*s" "bheadindex = %i" "\n", calldepth, "", bheadindex);
zprintf("%*s" "btailindex = %i" "\n", calldepth, "", btailindex);
zprintf("%*s" "cheadindex = %i" "\n", calldepth, "", cheadindex);
zprintf("%*s" "ctailindex = %i" "\n", calldepth, "", ctailindex);
if (mask)
{
// 0 ... (bsplit - 1) | bsplit ... (an - 1)
// --------------------- -------------------
// 0 | | |
// ... | first quadrant. | second quadrant |
// (csplit - 1) | | |
// --- ---------------------- -------------------
// csplit | | |
// ... | third quadrant | fourth quadrant |
// (cn - 1) | | |
// --- | | |
// ---------------------- -------------------
if (mask & a)
{
zprintf("%*s" "one case" "\n", calldepth, "");
// third quadrant
int q3_btailindex = btailindex & ~mask;
int q3_cheadindex = cheadindex | mask;
zprintf("%*s" "q3_btailindex = %i" "\n", calldepth, "", q3_btailindex);
zprintf("%*s" "q3_cheadindex = %i" "\n", calldepth, "", q3_cheadindex);
if (true
&& b.headtails[q3_btailindex] != -1
&& c.headtails[q3_cheadindex] != -1)
{
zprintf("%*s" "entering third quadrant." "\n", calldepth, "");
search(
mask >> 1,
bheadindex, q3_btailindex,
q3_cheadindex, ctailindex,
calldepth);
}
else
{
zprintf("%*s" "empty third quadrant." "\n", calldepth, "");
}
// fourth quadrant
int q4_bheadindex = bheadindex | mask;
int q4_cheadindex = cheadindex | mask;
if (true
&& b.headtails[q4_bheadindex] != -1
&& c.headtails[q4_cheadindex] != -1)
{
zprintf("%*s" "entering fourth quadrant." "\n", calldepth, "");
search(
mask >> 1,
q4_bheadindex, btailindex,
q4_cheadindex, ctailindex,
calldepth);
}
else
{
zprintf("%*s" "empty fourth quadrant." "\n", calldepth, "");
}
}
else
{
zprintf("%*s" "zero case" "\n", calldepth, "");
// first quadrant
int q1_btailindex = btailindex & ~mask;
int q1_ctailindex = ctailindex & ~mask;
zprintf("%*s" "q1_btailindex = %i" "\n", calldepth, "", q1_btailindex);
zprintf("%*s" "q1_ctailindex = %i" "\n", calldepth, "", q1_ctailindex);
if (true
&& b.headtails[q1_btailindex] != -1
&& c.headtails[q1_ctailindex] != -1)
{
zprintf("%*s" "entering first quadrant." "\n", calldepth, "");
search(
mask >> 1,
bheadindex, q1_btailindex,
cheadindex, q1_ctailindex,
calldepth);
}
else
{
zprintf("%*s" "empty first quadrant." "\n", calldepth, "");
}
// fourth quadrant
int q4_bheadindex = bheadindex | mask;
int q4_cheadindex = cheadindex | mask;
if (true
&& b.headtails[q4_bheadindex] != -1
&& c.headtails[q4_cheadindex] != -1)
{
zprintf("%*s" "entering fourth quadrant." "\n", calldepth, "");
search(
mask >> 1,
q4_bheadindex, btailindex,
q4_cheadindex, ctailindex,
calldepth);
}
else
{
zprintf("%*s" "empty fourth quadrant." "\n", calldepth, "");
}
}
}
else
{
assert(bheadindex == btailindex);
assert(cheadindex == ctailindex);
int be = b.headtails[bheadindex];
int ce = c.headtails[cheadindex];
if (be == bheadindex && ce == cheadindex && (a | be) == ce)
{
assert(b.in[be]);
assert(c.in[ce]);
printf("%2i (0b%05b) | %2i (0b%05b) == %2i (0b%05b)" "\n",
a, a, be, be, ce, ce);
}
}
calldepth--;
}
int main()
{
puts("hello, world!");
init(&b);
insert(&b, 10);
insert(&b, 11);
insert(&b, 14);
insert(&b, 19);
insert(&b, 20);
insert(&b, 23);
insert(&b, 26);
insert(&b, 29);
#ifdef ZDEBUG
print(&b);
#endif
init(&c);
insert(&c, 15);
insert(&c, 17);
insert(&c, 19);
insert(&c, 21);
insert(&c, 22);
insert(&c, 25);
insert(&c, 26);
insert(&c, 27);
insert(&c, 32);
insert(&c, 33);
insert(&c, 36);
insert(&c, 39);
insert(&c, 42);
insert(&c, 44);
insert(&c, 48);
insert(&c, 49);
#ifdef ZDEBUG
print(&c);
#endif
search(128, 0, 255, 0, 255, 0);
return 0;
}

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#include <stdio.h>
#include <assert.h>
#ifdef ZDEBUG
#define zprintf(fmt, ...) printf(fmt, ## __VA_ARGS__);
#else
#define zprintf(...) ;
#endif
int a = 17;
// 0 1 2 3 4 5 6 7 8 9
int b[10] = {10, 11, 11, 14, 14, 19, 20, 23, 26, 29};
int c[20] = {
// 0 1 2 3 4 5 6 7 8 9
15, 17, 19, 21, 22, 25, 26, 26, 27, 32,
// 10 11 12 13 14 15 16 17 18 19
33, 33, 36, 39, 42, 44, 48, 49, 49, 49
};
// [ 0] [ 1] [ 2] [ 3] [ 4] [ 5] [ 6] [ 7] [ 8] [ 9]
// 10 11 11 14 14 19 20 23 26 29
// --------------------------------------------------
// [ 0] 15 | 5 4 4 1 1 12 11 8 5 2
// [ 1] 17 | 17 16 16 17 17 0 1 0 1 0
// [ 2] 19 | 17 16 16 17 17 (0) 3 0 1 2
// [ 3] 21 | 21 20 20 17 17 4 (1) 0 5 0
// [ 4] 22 | 20 20 20 16 16 4 2 0 4 2
// [ 5] 25 | 17 16 16 17 17 8 9 8 1 0
// [ 6] 26 | 16 16 16 16 16 8 10 8 0 2
// [ 7] 26 | 16 16 16 16 16 8 10 8 0 2
// [ 8] 27 |(17) (16) (16) 17 17 8 11 8 ( 1) 2
// [ 9] 32 | 32 32 32 32 32 32 32 32 32 32
// [10] 33 | 33 32 32 33 33 32 33 32 33 32
// [11] 33 | 33 32 32 33 33 32 33 32 33 32
// [12] 36 | 36 36 36 32 32 36 32 32 36 32
// [13] 39 | 37 36 36 33 33 36 35 32 37 34
// [14] 42 | 32 32 32 32 32 40 42 40 32 34
// [15] 44 | 36 36 36 32 32 44 40 40 36 32
// [16] 48 | 48 48 48 48 48 32 32 32 32 32
// [17] 49 | 49 48 48 49 49 32 33 32 33 32
// [18] 49 | 49 48 48 49 49 32 33 32 33 32
// [19] 49 | 49 48 48 49 49 32 33 32 33 32
int binary(
int mask,
int *array,
int i, int n)
{
while (n > 1)
{
int m = n / 2;
if (array[i + m] & mask)
n = m;
else
i += m, n = n - m;
}
return (array[i] & mask) ? i : i + 1;
}
void quadrant_search(
int mask,
int bi, int bn,
int ci, int cn,
int calldepth)
{
zprintf("%*s" "quadrant_search():" "\n", calldepth++, "");
zprintf("%*s" "mask = 0b%05b" "\n", calldepth, "", mask);
zprintf("%*s" "bi = %i" "\n", calldepth, "", bi);
zprintf("%*s" "bn = %i" "\n", calldepth, "", bn);
zprintf("%*s" "ci = %i" "\n", calldepth, "", ci);
zprintf("%*s" "cn = %i" "\n", calldepth, "", cn);
if (mask)
{
int bsplit = binary(mask, b + bi, 0, bn);
int csplit = binary(mask, c + ci, 0, cn);
zprintf("%*s" "bsplit = %i" "\n", calldepth, "", bsplit);
zprintf("%*s" "csplit = %i" "\n", calldepth, "", csplit);
assert((bsplit == bn) || (b[bi + bsplit] & mask));
assert((csplit == cn) || (c[ci + csplit] & mask));
// 0 ... (bsplit - 1) | bsplit ... (an - 1)
// --------------------- -------------------
// 0 | | |
// ... | first quadrant. | second quadrant |
// (csplit - 1) | | |
// --- ---------------------- -------------------
// csplit | | |
// ... | third quadrant | fourth quadrant |
// (cn - 1) | | |
// --- | | |
// ---------------------- -------------------
if (mask & a)
{
zprintf("%*s" "one case" "\n", calldepth, "");
// third quadrant
if (0 < bsplit && csplit < cn)
{
zprintf("%*s" "entering third quadrant." "\n", calldepth, "");
quadrant_search(
mask >> 1,
bi, bsplit,
ci + csplit, cn - csplit,
calldepth);
}
else
{
zprintf("%*s" "empty third quadrant." "\n", calldepth, "");
}
// fourth quadrant
if (bsplit < bn && csplit < cn)
{
zprintf("%*s" "entering fourth quadrant." "\n", calldepth, "");
quadrant_search(
mask >> 1,
bi + bsplit, bn - bsplit,
ci + csplit, cn - csplit,
calldepth);
}
else
{
zprintf("%*s" "empty fourth quadrant." "\n", calldepth, "");
}
}
else
{
zprintf("%*s" "zero case" "\n", calldepth, "");
// first quadrant
if (0 < bsplit && 0 < csplit)
{
zprintf("%*s" "entering first quadrant." "\n", calldepth, "");
quadrant_search(
mask >> 1,
bi, bsplit,
ci, csplit,
calldepth);
}
else
{
zprintf("%*s" "empty first quadrant." "\n", calldepth, "");
}
// fourth quadrant
if (bsplit < bn && csplit < cn)
{
zprintf("%*s" "entering fourth quadrant." "\n", calldepth, "");
quadrant_search(
mask >> 1,
bi + bsplit, bn - bsplit,
ci + csplit, cn - csplit,
calldepth);
}
else
{
zprintf("%*s" "empty fourth quadrant." "\n", calldepth, "");
}
}
}
else for (int i = 0; i < bn; i++)
{
for (int j = 0; j < cn; j++)
{
assert((a | b[bi + i]) == c[ci + j]);
printf("%2i (0b%05b) | %2i [%2i] "
"(0b%05b) == %2i [%2i] (0b%05b)" "\n",
a, a,
b[bi + i], bi + i, b[bi + i],
c[ci + j], ci + j, c[ci + j]);
}
}
calldepth--;
}
void brute_force_search(int bn, int cn)
{
for (int bi = 0; bi < bn; bi++)
{
for (int ci = 0; ci < cn; ci++)
{
if ((a | b[bi]) == c[ci])
{
printf("%2i (0b%05b) | %2i [%2i] "
"(0b%05b) == %2i [%2i] (0b%05b)" "\n",
a, a,
b[bi], bi, b[bi],
c[ci], ci, c[ci]);
}
}
}
}
int main()
{
puts("divide-and-conquer:");
quadrant_search(32, 0, 10, 0, 20, 0);
puts("");
puts("brute-force:");
brute_force_search(10, 20);
return 0;
}

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#include <stdbool.h>
#include <assert.h>
#include <stdio.h>
#define N (256)
#define M (255)
int headtails[N], next[N], globalhead = -1;
bool in[N];
void init()
{
for (int i = 0; i < N; i++)
{
headtails[i] = -1;
next[i] = -1;
in[i] = false;
}
}
void print()
{
puts("print():");
for (int i = 0; i < N; i++)
{
if (headtails[i] != -1)
{
printf(" " "headtails[%3i (0b%08b)] = %i" "\n", i, i, headtails[i]);
}
}
printf("globalhead = %i\n", globalhead);
for (int index = globalhead; index != -1; index = next[index])
{
printf(" " "index = %i\n", index);
}
}
void insert(int index)
{
printf("insert():" "\n");
assert(!in[index]);
printf(" " "index = %i (0b%08b)" "\n", index, index);
int head = index & 1 ? index & ~(index & -index) : index, prevhead = -1;
printf(" " "head = %i (0b%08b)" "\n", head, head);
// while they're blank or we beat them:
while (headtails[head] == -1 || index < headtails[head])
{
headtails[head] = index;
printf(" " "headtails[%i] = %i" "\n", head, index);
prevhead = head, head = head & ~(head & -head);
printf(" " "head = %i (0b%08b)" "\n", head, head);
}
// there should be only two reasons why we're stopped:
// - because we hit the limits of the list
// - because we found someone who beat us.
if (headtails[head] < index)
{
printf(" " "hit someone with a better head" "\n");
printf(" " "prevhead = %i (0b%08b)" "\n", prevhead, prevhead);
if (prevhead == -1)
{
// if we got beat imeedately, connect to them.
assert(headtails[head] == head);
assert(in[head]);
next[head] = index;
printf(" " "next[%i] = %i" "\n", head, next[head]);
}
else
{
// we must be coming out of the bottom half
// and if we lost, then we know there must be elements in the
// first half that should come before us.
// and that we should connect to their tail.
// so the top-half's tail's "next" should point to us.
// and we also know that the top-half's tail comes right before
// our previous's head.
int tophalftail = headtails[prevhead - 1];
printf(" " "tophalftail = %i" "\n", tophalftail);
assert(tophalftail != -1);
next[tophalftail] = index;
printf(" " "next[%i] = %i" "\n", tophalftail, next[tophalftail]);
}
}
else
{
printf(" " "hit the lower limit of the list" "\n");
globalhead = index;
printf(" " "globalhead = %i" "\n", globalhead);
}
int n = ~index & M;
int tail = index & 1 ? index : index | (n & -n), prevtail = -1;
printf(" " "tail = %i (0b%08b)" "\n", tail, tail);
// while they're blank:
while (headtails[tail] == -1 || headtails[tail] < index)
{
headtails[tail] = index;
printf(" " "headtails[%i] = %i" "\n", tail, index);
prevtail = tail, tail = tail | (n = ~tail & M, n & -n);
printf(" " "tail = %i (0b%08b)" "\n", tail, tail);
}
// there should be only two reasons why we're stopped:
// - because we hit the limits of the list
// - because we found someone who beat us.
if (index < headtails[tail])
{
printf(" " "hit someone with a better tail" "\n");
printf(" " "prevtail = %i (0b%08b)" "\n", prevtail, prevtail);
if (prevtail == -1)
{
// if we got beat imeedately, connect to them.
assert(headtails[tail] == tail);
assert(in[tail]);
next[index] = tail;
printf(" " "next[%i] = %i" "\n", index, next[index]);
}
else
{
// we must be coming out of the top half
// and if we lost, then we know there must be elements in the
// second half that should come after us.
// and that we should connect to their head.
// so we should point to the bottom half's "head"
// and we also know that the bottom half's haed comes right before
// our previous's tail.
int bottomhalfhead = headtails[prevtail + 1];
printf(" " "bottomhalfhead = %i" "\n", bottomhalfhead);
assert(bottomhalfhead != -1);
next[index] = bottomhalfhead;
printf(" " "next[%i] = %i" "\n", index, next[index]);
}
}
else
{
printf(" " "hit the lower limit of the list" "\n");
next[index] = -1;
printf(" " "next[%i] = %i" "\n", index, next[index]);
}
in[index] = true;
}
int main()
{
puts("hello, world!");
init();
print();
insert(42); print();
/* insert(200); print();*/
/* insert(128); print();*/
insert(224); print();
/* insert(1); print();*/
/* */
/* insert(255); print();*/
insert(96); print();
insert(97); print();
insert(98); print();
insert(99); print();
return 0;
}