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# Instructions | ||
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Make a chain of dominoes. | ||
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Compute a way to order a given set of domino stones so that they form a correct domino chain. | ||
In the chain, the dots on one half of a stone must match the dots on the neighboring half of an adjacent stone. | ||
Additionally, the dots on the halves of the stones without neighbors (the first and last stone) must match each other. | ||
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For example given the stones `[2|1]`, `[2|3]` and `[1|3]` you should compute something | ||
like `[1|2] [2|3] [3|1]` or `[3|2] [2|1] [1|3]` or `[1|3] [3|2] [2|1]` etc, where the first and last numbers are the same. | ||
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For stones `[1|2]`, `[4|1]` and `[2|3]` the resulting chain is not valid: `[4|1] [1|2] [2|3]`'s first and last numbers are not the same. | ||
4 != 3 | ||
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Some test cases may use duplicate stones in a chain solution, assume that multiple Domino sets are being used. |
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# Introduction | ||
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In Toyland, the trains are always busy delivering treasures across the city, from shiny marbles to rare building blocks. | ||
The tracks they run on are made of colorful domino-shaped pieces, each marked with two numbers. | ||
For the trains to move, the dominoes must form a perfect chain where the numbers match. | ||
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Today, an urgent delivery of rare toys is on hold. | ||
You've been handed a set of track pieces to inspect. | ||
If they can form a continuous chain, the train will be on its way, bringing smiles across Toyland. | ||
If not, the set will be discarded, and another will be tried. | ||
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The toys are counting on you to solve this puzzle. | ||
Will the dominoes connect the tracks and send the train rolling, or will the set be left behind? |
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{ | ||
"authors": [ | ||
"keiravillekode" | ||
], | ||
"files": { | ||
"solution": [ | ||
"dominoes.s" | ||
], | ||
"test": [ | ||
"dominoes_test.c" | ||
], | ||
"example": [ | ||
".meta/example.s" | ||
] | ||
}, | ||
"blurb": "Make a chain of dominoes." | ||
} |
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.text | ||
.globl can_chain | ||
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/* int root(int number, void*, uint8_t *table); */ | ||
root: | ||
mov w9, w0 | ||
ldrb w0, [x2, x0] | ||
cmp w0, w9 | ||
bne root | ||
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ret | ||
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/* void merge(size_t domino_count, const domino_t *dominoes, uint8_t *table); */ | ||
merge: | ||
mov x14, lr /* preserve return address */ | ||
lsl w10, w0, #2 /* number of bytes occupied by dominoes array */ | ||
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.merge_loop: | ||
sub w10, w10, #2 | ||
ldrh w0, [x1, x10] /* number on domino half */ | ||
bl root | ||
mov w11, w0 | ||
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sub w10, w10, #2 | ||
ldrh w0, [x1, x10] /* number on domino half */ | ||
bl root | ||
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strb w0, [x2, x11] /* link domino halves in table */ | ||
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cbnz w10, .merge_loop | ||
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ret x14 | ||
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/* extern int can_chain(size_t domino_count, const domino_t *dominoes); */ | ||
can_chain: | ||
stp xzr, xzr, [sp, #-16]! | ||
mov x15, lr /* preserve return address */ | ||
cmp w0, wzr | ||
beq .accept | ||
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mov x2, sp | ||
lsl w9, w0, #2 /* number of bytes occupied by dominoes array */ | ||
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.count_numbers: | ||
sub w9, w9, #2 | ||
ldrh w10, [x1, x9] /* number on domino half */ | ||
ldrb w11, [x2, x10] | ||
add w11, w11, #1 /* increment tally */ | ||
strb w11, [x2, x10] | ||
cbnz w9, .count_numbers | ||
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mov w9, #16 | ||
mov w14, #255 | ||
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.parity: | ||
sub w9, w9, #1 | ||
ldrb w10, [sp, x9] | ||
tst w10, #1 /* check if number appears an odd number of times */ | ||
bne .reject | ||
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tst w10, w10 | ||
csel w11, w14, w9, eq | ||
strb w11, [sp, x9] /* populate disjoint set (union find) array */ | ||
cbnz w9, .parity | ||
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bl merge | ||
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mov w9, #16 | ||
mov w11, wzr | ||
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.count_roots: | ||
sub w9, w9, #1 | ||
ldrb w10, [x2, x9] | ||
cmp w10, w9 | ||
cinc w11, w11, eq | ||
cbnz w9, .count_roots | ||
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cmp w11, #1 | ||
bne .reject | ||
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.accept: | ||
mov w0, #1 | ||
add sp, sp, #16 /* restore stack pointer */ | ||
ret x15 | ||
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.reject: | ||
mov w0, wzr | ||
add sp, sp, #16 /* restore stack pointer */ | ||
ret x15 |
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# This is an auto-generated file. | ||
# | ||
# Regenerating this file via `configlet sync` will: | ||
# - Recreate every `description` key/value pair | ||
# - Recreate every `reimplements` key/value pair, where they exist in problem-specifications | ||
# - Remove any `include = true` key/value pair (an omitted `include` key implies inclusion) | ||
# - Preserve any other key/value pair | ||
# | ||
# As user-added comments (using the # character) will be removed when this file | ||
# is regenerated, comments can be added via a `comment` key. | ||
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[31a673f2-5e54-49fe-bd79-1c1dae476c9c] | ||
description = "empty input = empty output" | ||
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[4f99b933-367b-404b-8c6d-36d5923ee476] | ||
description = "singleton input = singleton output" | ||
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[91122d10-5ec7-47cb-b759-033756375869] | ||
description = "singleton that can't be chained" | ||
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[be8bc26b-fd3d-440b-8e9f-d698a0623be3] | ||
description = "three elements" | ||
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[99e615c6-c059-401c-9e87-ad7af11fea5c] | ||
description = "can reverse dominoes" | ||
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[51f0c291-5d43-40c5-b316-0429069528c9] | ||
description = "can't be chained" | ||
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[9a75e078-a025-4c23-8c3a-238553657f39] | ||
description = "disconnected - simple" | ||
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[0da0c7fe-d492-445d-b9ef-1f111f07a301] | ||
description = "disconnected - double loop" | ||
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[b6087ff0-f555-4ea0-a71c-f9d707c5994a] | ||
description = "disconnected - single isolated" | ||
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[2174fbdc-8b48-4bac-9914-8090d06ef978] | ||
description = "need backtrack" | ||
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[167bb480-dfd1-4318-a20d-4f90adb4a09f] | ||
description = "separate loops" | ||
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[cd061538-6046-45a7-ace9-6708fe8f6504] | ||
description = "nine elements" | ||
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[44704c7c-3adb-4d98-bd30-f45527cf8b49] | ||
description = "separate three-domino loops" |
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AS = aarch64-linux-gnu-as | ||
CC = aarch64-linux-gnu-gcc | ||
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CFLAGS = -g -Wall -Wextra -pedantic -Werror | ||
LDFLAGS = | ||
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ALL_LDFLAGS = -pie -Wl,--fatal-warnings | ||
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ALL_CFLAGS = -std=c99 -fPIE $(CFLAGS) | ||
ALL_LDFLAGS += $(LDFLAGS) | ||
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C_OBJS = $(patsubst %.c,%.o,$(wildcard *.c)) | ||
AS_OBJS = $(patsubst %.s,%.o,$(wildcard *.s)) | ||
ALL_OBJS = $(filter-out example.o,$(C_OBJS) $(AS_OBJS) vendor/unity.o) | ||
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CC_CMD = $(CC) $(ALL_CFLAGS) -c -o $@ $< | ||
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all: tests | ||
qemu-aarch64 -L /usr/aarch64-linux-gnu ./$< | ||
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tests: $(ALL_OBJS) | ||
@$(CC) $(ALL_CFLAGS) $(ALL_LDFLAGS) -o $@ $(ALL_OBJS) | ||
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%.o: %.s | ||
@$(AS) -o $@ $< | ||
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%.o: %.c | ||
@$(CC_CMD) | ||
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vendor/unity.o: vendor/unity.c vendor/unity.h vendor/unity_internals.h | ||
@$(CC_CMD) | ||
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clean: | ||
@rm -f *.o vendor/*.o tests | ||
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.PHONY: all clean |
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.text | ||
.globl can_chain | ||
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can_chain: | ||
ret |
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#include "vendor/unity.h" | ||
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#include <stddef.h> | ||
#include <stdint.h> | ||
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#define ARRAY_SIZE(x) (sizeof(x) / sizeof((x)[0])) | ||
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typedef struct { | ||
uint16_t first; | ||
uint16_t second; | ||
} domino_t; | ||
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extern int can_chain(size_t domino_count, const domino_t *dominoes); | ||
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void setUp(void) { | ||
} | ||
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void tearDown(void) { | ||
} | ||
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void test_empty_input__empty_output(void) { | ||
TEST_ASSERT_TRUE(can_chain(0, NULL)); | ||
} | ||
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void test_singleton_input__singleton_output(void) { | ||
TEST_IGNORE(); | ||
const domino_t dominoes[] = {{1, 1}}; | ||
TEST_ASSERT_TRUE(can_chain(ARRAY_SIZE(dominoes), dominoes)); | ||
} | ||
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void test_singleton_that_cant_be_chained(void) { | ||
TEST_IGNORE(); | ||
const domino_t dominoes[] = {{1, 2}}; | ||
TEST_ASSERT_FALSE(can_chain(ARRAY_SIZE(dominoes), dominoes)); | ||
} | ||
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void test_three_elements(void) { | ||
TEST_IGNORE(); | ||
const domino_t dominoes[] = {{1, 2}, {3, 1}, {2, 3}}; | ||
TEST_ASSERT_TRUE(can_chain(ARRAY_SIZE(dominoes), dominoes)); | ||
} | ||
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void test_can_reverse_dominoes(void) { | ||
TEST_IGNORE(); | ||
const domino_t dominoes[] = {{1, 2}, {1, 3}, {2, 3}}; | ||
TEST_ASSERT_TRUE(can_chain(ARRAY_SIZE(dominoes), dominoes)); | ||
} | ||
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void test_cant_be_chained(void) { | ||
TEST_IGNORE(); | ||
const domino_t dominoes[] = {{1, 2}, {4, 1}, {2, 3}}; | ||
TEST_ASSERT_FALSE(can_chain(ARRAY_SIZE(dominoes), dominoes)); | ||
} | ||
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void test_disconnected__simple(void) { | ||
TEST_IGNORE(); | ||
const domino_t dominoes[] = {{1, 1}, {2, 2}}; | ||
TEST_ASSERT_FALSE(can_chain(ARRAY_SIZE(dominoes), dominoes)); | ||
} | ||
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void test_disconnected__double_loop(void) { | ||
TEST_IGNORE(); | ||
const domino_t dominoes[] = {{1, 2}, {2, 1}, {3, 4}, {4, 3}}; | ||
TEST_ASSERT_FALSE(can_chain(ARRAY_SIZE(dominoes), dominoes)); | ||
} | ||
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void test_disconnected__single_isolated(void) { | ||
TEST_IGNORE(); | ||
const domino_t dominoes[] = {{1, 2}, {2, 3}, {3, 1}, {4, 4}}; | ||
TEST_ASSERT_FALSE(can_chain(ARRAY_SIZE(dominoes), dominoes)); | ||
} | ||
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void test_need_backtrack(void) { | ||
TEST_IGNORE(); | ||
const domino_t dominoes[] = {{1, 2}, {2, 3}, {3, 1}, {2, 4}, {2, 4}}; | ||
TEST_ASSERT_TRUE(can_chain(ARRAY_SIZE(dominoes), dominoes)); | ||
} | ||
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void test_separate_loops(void) { | ||
TEST_IGNORE(); | ||
const domino_t dominoes[] = {{1, 2}, {2, 3}, {3, 1}, {1, 1}, {2, 2}, {3, 3}}; | ||
TEST_ASSERT_TRUE(can_chain(ARRAY_SIZE(dominoes), dominoes)); | ||
} | ||
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void test_nine_elements(void) { | ||
TEST_IGNORE(); | ||
const domino_t dominoes[] = {{1, 2}, {5, 3}, {3, 1}, {1, 2}, {2, 4}, {1, 6}, {2, 3}, {3, 4}, {5, 6}}; | ||
TEST_ASSERT_TRUE(can_chain(ARRAY_SIZE(dominoes), dominoes)); | ||
} | ||
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void test_separate_threedomino_loops(void) { | ||
TEST_IGNORE(); | ||
const domino_t dominoes[] = {{1, 2}, {2, 3}, {3, 1}, {4, 5}, {5, 6}, {6, 4}}; | ||
TEST_ASSERT_FALSE(can_chain(ARRAY_SIZE(dominoes), dominoes)); | ||
} | ||
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int main(void) { | ||
UNITY_BEGIN(); | ||
RUN_TEST(test_empty_input__empty_output); | ||
RUN_TEST(test_singleton_input__singleton_output); | ||
RUN_TEST(test_singleton_that_cant_be_chained); | ||
RUN_TEST(test_three_elements); | ||
RUN_TEST(test_can_reverse_dominoes); | ||
RUN_TEST(test_cant_be_chained); | ||
RUN_TEST(test_disconnected__simple); | ||
RUN_TEST(test_disconnected__double_loop); | ||
RUN_TEST(test_disconnected__single_isolated); | ||
RUN_TEST(test_need_backtrack); | ||
RUN_TEST(test_separate_loops); | ||
RUN_TEST(test_nine_elements); | ||
RUN_TEST(test_separate_threedomino_loops); | ||
return UNITY_END(); | ||
} |
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