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91 lines
2.9 KiB
C++
91 lines
2.9 KiB
C++
// Optimized ISBN-10 counter.
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//
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// Three improvements over the original:
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//
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// 1. NO HEAP ALLOCATION — original calls intToVector() on every iteration,
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// which does a heap alloc+free (std::vector) for each of 10^10 numbers.
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// Here we use only stack variables.
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//
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// 2. ALGORITHMIC REDUCTION — ISBN-10 validity condition:
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// 10*d0 + 9*d1 + ... + 2*d8 + 1*d9 ≡ 0 (mod 11)
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// Given any 9-digit prefix d0..d8 we can solve for d9 directly:
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// d9 = (11 - S mod 11) mod 11 where S = sum of weighted prefix
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// The number is valid iff 0 ≤ d9 ≤ 9 (i.e. d9 ≠ 10).
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// → Only 10^9 outer iterations instead of 10^10.
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//
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// 3. INCREMENTAL WEIGHTED SUM — instead of multiplying each digit by its
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// weight inside the innermost loop, partial sums are maintained
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// incrementally as digits change, so the innermost body is almost free.
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// The compiler can also vectorise the innermost digit loop.
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//
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// Compile: g++ -O2 -fopenmp bench_optimized.cpp -o bench_opt
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// (OpenMP is optional; remove -fopenmp if not available – it just runs
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// the outer loop on a single thread.)
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#include <chrono>
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#include <iostream>
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#ifdef _OPENMP
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#include <omp.h>
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#endif
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int main() {
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auto start = std::chrono::high_resolution_clock::now();
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long long count = 0;
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// Nested loops over the 9 prefix digits.
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// s_k = partial weighted sum up through digit k.
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// weight for digit at position i (0-based, MSB first) = 10 - i
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// so outer digit d0 has weight 10, d1 has weight 9, ..., d8 has
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// weight 2.
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#ifdef _OPENMP
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#pragma omp parallel for reduction(+ : count) schedule(static)
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#endif
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for (int d0 = 0; d0 <= 9; d0++) {
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int s0 = 10 * d0;
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for (int d1 = 0; d1 <= 9; d1++) {
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int s1 = s0 + 9 * d1;
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for (int d2 = 0; d2 <= 9; d2++) {
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int s2 = s1 + 8 * d2;
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for (int d3 = 0; d3 <= 9; d3++) {
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int s3 = s2 + 7 * d3;
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for (int d4 = 0; d4 <= 9; d4++) {
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int s4 = s3 + 6 * d4;
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for (int d5 = 0; d5 <= 9; d5++) {
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int s5 = s4 + 5 * d5;
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for (int d6 = 0; d6 <= 9; d6++) {
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int s6 = s5 + 4 * d6;
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for (int d7 = 0; d7 <= 9; d7++) {
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int s7 = s6 + 3 * d7;
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// Innermost: vary d8, weight 2.
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for (int d8 = 0; d8 <= 9; d8++) {
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int s = s7 + 2 * d8;
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// Required check digit (weight 1):
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int d9 = (11 - s % 11) % 11;
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if (d9 <= 9)
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++count;
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}
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}
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}
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}
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}
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}
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}
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}
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}
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auto end = std::chrono::high_resolution_clock::now();
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double elapsed = std::chrono::duration<double>(end - start).count();
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std::cout << "Valid ISBNs: " << count << "\n";
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std::cout << "Time: " << elapsed << " s\n";
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#ifdef _OPENMP
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std::cout << "Threads: " << omp_get_max_threads() << "\n";
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#endif
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return 0;
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}
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