第二个版本，使用GMP进行无损精度计算，不过这个版本就很慢了

ReciprocalSearch2.cpp

@@ -0,0 +1,139 @@
+#include <stdio.h>
+#include <chrono>
+
+#pragma warning(disable:4146)
+#include <gmpxx.h>
+
+#define min(a,b) (((a)<(b))?(a):(b))
+
+inline bool check(int i1, int i2, int i3, int i4, int i5, int i6, int i7, int i8, int i9, int i10) {
+    int a[10];
+
+    a[0] = i1;
+    a[1] = i2;
+    a[2] = i3;
+    a[3] = i4;
+    a[4] = i5;
+    a[5] = i6;
+    a[6] = i7;
+    a[7] = i8;
+    a[8] = i9;
+    a[9] = i10;
+
+    for (int k = 8; k >= 0; --k)
+    {
+        if (i10 <= a[k])
+            return false;
+    }
+
+    mpz_class s1 = 1;
+    for (int k = 0; k < 10; ++k) {
+        s1 *= a[k];
+    }
+
+    mpz_class s2 = 0;
+    for (int k = 0; k < 10; ++k) {
+        s2 += s1 / a[k];
+    }
+
+    return s1 == s2;
+}
+
+inline int ceil(const mpq_class& m) {
+    const mpz_class num = m.get_num();
+    const mpz_class den = m.get_den();
+    const mpz_class quotient = num / den;
+    if (quotient >= 100)
+        return 100;
+
+    int r = quotient.get_si();
+    if ((num % den) != 0)
+        ++r;
+
+    return r;
+}
+
+int main() {
+    const auto start = std::chrono::steady_clock::now();
+
+    int total = 0;
+
+    mpq_class ii[101];
+
+    for (int i = 1; i <= 100; i++) {
+        mpz_class num(1);
+        mpz_class den(i);
+        ii[i] = mpq_class(num, den);
+    }
+
+    for (int i1 = 2; i1 <= 10; i1++) {
+        const auto m1 = 1 - ii[i1];
+
+        const int u2 = min(92, ceil(9 / m1));
+        for (int i2 = i1 + 1; i2 <= u2; i2++) {
+            const auto m2 = m1 - ii[i2];
+
+            const int u3 = min(93, ceil(8 / m2));
+            for (int i3 = i2 + 1; i3 <= u3; i3++) {
+                const auto m3 = m2 - ii[i3];
+                if (m3 <= 0) continue;
+
+                const int u4 = min(94, ceil(7 / m3));
+                for (int i4 = i3 + 1; i4 <= u4; i4++) {
+                    const auto m4 = m3 - ii[i4];
+                    if (m4 <= 0) continue;
+
+                    const int u5 = min(95, ceil(6 / m4));
+                    for (int i5 = i4 + 1; i5 <= u5; i5++) {
+                        const auto m5 = m4 - ii[i5];
+                        if (m5 <= 0) continue;
+
+                        const int u6 = min(96, ceil(5 / m5));
+                        for (int i6 = i5 + 1; i6 < u6; i6++) {
+                            const auto m6 = m5 - ii[i6];
+                            if (m6 <= 0) continue;
+
+                            const int u7 = min(97, ceil(4 / m6));
+                            for (int i7 = i6 + 1; i7 <= u7; i7++) {
+                                const auto m7 = m6 - ii[i7];
+                                if (m7 <= 0) continue;
+
+                                const int u8 = min(98, ceil(3 / m7));
+                                for (int i8 = i7 + 1; i8 <= u8; i8++) {
+                                    const auto m8 = m7 - ii[i8];
+                                    if (m8 <= 0) continue;
+
+                                    const int u9 = min(99, ceil(2 / m8));
+                                    for (int i9 = i8 + 1; i9 <= u9; i9++) {
+                                        const auto m9 = m8 - ii[i9];
+                                        if (m9 <= 0) continue;
+
+                                        const mpq_class last = 1 / m9;
+
+                                        const mpz_class num = last.get_num();
+                                        const mpz_class den = last.get_den();
+                                        if ((num % den) != 0) continue;
+
+                                        const mpz_class quotinent = num / den;
+                                        if (quotinent > 100) continue;
+
+                                        int i10 = quotinent.get_si();
+                                        if (i10 <= i9) continue;
+
+                                        if (check(i1, i2, i3, i4, i5, i6, i7, i8, i9, i10)) {
+                                            ++total;
+                                            printf("%5d: %d %d %d %d %d %d %d %d %d %d\n", total, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10);
+                                        }
+                                    }
+                                }
+                            }
+                        }
+                    }
+                }
+            }
+        }
+    }
+
+    const auto end = std::chrono::steady_clock::now();
+    printf("%.3f seconds\n", std::chrono::duration_cast<std::chrono::milliseconds>(end - start).count() / 1000.0);
+}