116 lines
2.3 KiB
C++
116 lines
2.3 KiB
C++
#include <BAN/Assert.h>
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#include <BAN/Math.h>
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#include <inttypes.h>
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#include <stdio.h>
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using i8 = int8_t;
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using i16 = int16_t;
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using i32 = int32_t;
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using i64 = int64_t;
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using u8 = uint8_t;
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using u16 = uint16_t;
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using u32 = uint32_t;
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using u64 = uint64_t;
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using usize = size_t;
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struct vec_t { i64 x, y; };
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u64 fewest_tokens(vec_t a, vec_t b, vec_t p)
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{
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ASSERT(a.x * b.y != b.x * a.y);
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// n * a.x + m * b.x = p.x <==> m = (p.x - n * a.x) / b.x
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// n * a.y + m * b.y = p.y
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// n * a.y + ((p.x - n * a.x) / b.x) * b.y = p.y
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// => n * a.y + (p.x / b.x - n * a.x / b.x) * b.y = p.y
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// => n * a.y + p.x / b.x * b.y - n * a.x / b.x * b.y = p.y
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// => n * a.y - n * a.x / b.x * b.y = p.y - p.x / b.x * b.y
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// => n * a.y * b.x - n * a.x * b.y = p.y * b.x - p.x * b.y
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// => n * (a.y * b.x - a.x * b.y) = p.y * b.x - p.x * b.y
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// => n = (p.y * b.x - p.x * b.y) / (a.y * b.x - a.x * b.y)
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const i64 n_num = p.y * b.x - p.x * b.y;
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const i64 n_den = a.y * b.x - a.x * b.y;
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if (n_num % n_den)
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return 0;
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const i64 n = n_num / n_den;
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const i64 m_num = p.x - n * a.x;
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const i64 m_den = b.x;
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if (m_num % m_den)
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return 0;
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const i64 m = m_num / m_den;
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return 3 * n + m;
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}
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i64 part1(FILE* fp)
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{
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i64 result = 0;
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for (;;)
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{
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constexpr const char* format =
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"Button A: X+%" SCNd64 ", Y+%" SCNd64 "\n"
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"Button B: X+%" SCNd64 ", Y+%" SCNd64 "\n"
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"Prize: X=%" SCNd64 ", Y=%" SCNd64 "\n";
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vec_t a, b, prize;
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if (fscanf(fp, format, &a.x, &a.y, &b.x, &b.y, &prize.x, &prize.y) != 6)
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break;
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result += fewest_tokens(a, b, prize);
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}
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return result;
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}
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i64 part2(FILE* fp)
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{
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i64 result = 0;
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for (;;)
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{
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constexpr const char* format =
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"Button A: X+%" SCNu64 ", Y+%" SCNu64 "\n"
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"Button B: X+%" SCNu64 ", Y+%" SCNu64 "\n"
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"Prize: X=%" SCNu64 ", Y=%" SCNu64 "\n";
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vec_t a, b, prize;
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if (fscanf(fp, format, &a.x, &a.y, &b.x, &b.y, &prize.x, &prize.y) != 6)
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break;
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prize.x += 10000000000000;
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prize.y += 10000000000000;
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result += fewest_tokens(a, b, prize);
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}
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return result;
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}
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int main(int argc, char** argv)
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{
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const char* file_path = "/usr/share/aoc2024/day13_input.txt";
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if (argc >= 2)
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file_path = argv[1];
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FILE* fp = fopen(file_path, "r");
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if (fp == nullptr)
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{
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perror("fopen");
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return 1;
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}
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printf("part1: %" PRId64 "\n", part1(fp));
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fseek(fp, 0, SEEK_SET);
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printf("part2: %" PRId64 "\n", part2(fp));
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fclose(fp);
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}
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