#946. 连通性（floyd）

https://sjzezoj.com/submission/69673

S2OJ/946/946.cpp

@@ -0,0 +1,230 @@
+#include <iostream>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 105;
+const int mod = 1e9 + 7;
+
+// clang-format off
+int f[N][N]{
+#ifdef ONLINE_JUDGE
+{1},
+{1, 1},
+{2, 2, 2},
+{8, 7, 6, 5},
+{64, 51, 38, 25, 15},
+{1024, 814, 584, 356, 155, 52},
+{32768, 27562, 20950, 13674, 6794, 1731, 203},
+{2097152, 1881132, 1559050, 1143026, 688940, 285399, 42597, 877},
+{268435456, 252352192, 225134416, 183912440, 130448704, 73134373, 25675622, 2389418, 4140},
+{719476260, 437453186, 285852834, 198930901, 417447372, 493700668, 936095345, 770727467, 287447420, 21147},
+{371842544, 598590656, 444061297, 956708189, 127125386, 834823998, 128227000, 223478915, 929725695, 302765502, 115975},
+{766762396, 413139421, 351102112, 112130130, 188617941, 339825372, 543187105, 114675694, 623357729, 261270827, 104995134, 678570},
+{329376018, 705367106, 201640714, 352379330, 550132198, 846985547, 818860561, 624544091, 494980544, 959053918, 443889176, 751093169, 4213597},
+{124160285, 828328425, 906083967, 147213859, 527558165, 193958029, 794519533, 742501375, 789123747, 444469745, 993581787, 979243161, 593627163, 27644437},
+{121047601, 912065930, 1351624, 402906644, 713933492, 50841084, 863660427, 577705270, 887029586, 145474376, 588251882, 706568129, 777275244, 642664828, 190899322},
+{243880903, 599607852, 442677191, 436289683, 281113930, 146582434, 584824855, 564630340, 394164220, 378918082, 150572902, 532909740, 763622255, 37460367, 184612284, 382958538},
+{489373567, 413411086, 951426968, 887302037, 155903135, 283219023, 620782126, 905791112, 644465700, 989656495, 523232248, 664652865, 948982217, 20783496, 743914774, 684000569, 480142077},
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+{157921350, 585213032, 124127002, 444551557, 903311742, 164413448, 386967031, 407995046, 262661729, 344515452, 135908010, 878209413, 368549114, 629205902, 255793356, 578014821, 143082468, 257436696, 76801385},
+{134084614, 402761743, 842286714, 498687688, 314252511, 433353429, 874023832, 163451857, 900776051, 750447840, 374976568, 374596374, 409363634, 1428564, 912190395, 954400021, 334527550, 458752164, 941524580, 742164233},
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+{686331837, 758771584, 485081276, 510183332, 730280308, 184674456, 873283293, 908734440, 930495524, 921797799, 212061161, 804809207, 51215048, 121939666, 630812700, 361452271, 26060826, 260673621, 368617358, 224024063, 925630581, 990272358, 706900318},
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+{742004924, 254372018, 291387829, 267349513, 54024762, 671245107, 613585423, 508809588, 231811039, 104767602, 167910887, 114090978, 909920550, 592620873, 356390422, 542638360, 87578277, 455438768, 894088070, 835976016, 969566965, 323042316, 212287755, 517833930, 442679595, 261582652, 823187406, 532793112, 159122123},
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+{281603733, 138407398, 86019269, 423308164, 628795846, 196796182, 753173513, 211764797, 295659241, 103252080, 288984637, 771817728, 16686897, 911761734, 806397108, 707831875, 367736611, 552407519, 611427745, 718194558, 336182887, 810354363, 887085822, 909120864, 176944207, 791461859, 781904784, 510230751, 5315151, 713990472, 643061399, 514126877, 586617380, 141247706, 717662001, 515959429, 921071412, 887143166, 111509430, 677896109, 927611633, 470842496, 323293107, 483632474, 358769673, 592995655, 738389897, 604489119, 683802635, 357484946, 492249407, 408062292, 680778048, 518340476, 587555941, 439454013, 349031703, 958250869, 501459390, 781878478, 357327972, 241401516, 821549611, 688310064, 604285228, 247863808, 577392423, 986288040, 510121040, 810270456, 705782997, 135408659, 222045211, 109164359, 546498796, 735527859, 499665364, 920156496, 454090236, 45419401, 872538891, 937602773, 873764254, 498024959, 825571197, 183796880, 486598130, 830745106, 971488731, 968532926, 653339758, 85583050, 60685446, 991118276, 960698403, 525607421, 217367693, 585600641, 639945593, 481066808, 193120002},
+#endif
+};
+// clang-format on
+
+constexpr int binpow(int a, int b, int mod = ::mod) {
+    int res = 1;
+    a %= mod;
+
+    while (b) {
+        if (b & 1) res = static_cast<long long>(res) * a % mod;
+        a = static_cast<long long>(a) * a % mod;
+        b >>= 1;
+    }
+
+    return res;
+}
+
+namespace gen {
+    const int n = 100;
+
+    int c[N][N];
+    int g[N], h[N][N];
+
+    void main() {
+        // === Init ===
+
+        for (int i = 0; i <= n; i++) {
+            c[i][0] = 1;
+
+            for (int j = 1; j <= i; j++) {
+                c[i][j] = (static_cast<long long>(c[i - 1][j]) + c[i - 1][j - 1]) % mod;
+            }
+        }
+
+        // === calc g[] ===
+
+        g[0] = 1;
+
+        for (int i = 1; i <= n; i++) {
+            g[i] = binpow(2, c[i][2]);
+
+            for (int j = 1; j < i; j++) {
+                g[i] = ((static_cast<long long>(g[i]) - static_cast<long long>(g[j]) * binpow(2, c[i - j][2]) % mod * c[i - 1][j - 1] % mod) % mod + mod) % mod;
+            }
+        }
+
+        // === calc h[][] ===
+
+        for (int i = 1; i <= n; i++) {
+            for (int j = 1; j <= n; j++) {
+                h[i][j] = static_cast<long long>(g[j]) * binpow(binpow(2, j) - 1, i) % mod * binpow(2, c[i][2]) % mod;
+            }
+        }
+
+        // === calc f[][] ===
+
+        f[0][0] = 1;
+
+        for (int i = 1; i <= n; i++) {
+            f[i][0] = binpow(2, c[i][2]);
+
+            for (int j = 1; j <= i; j++) {
+                for (int k = 1; k <= j; k++) {
+                    f[i][j] = (static_cast<long long>(f[i][j]) + static_cast<long long>(f[i - k][j - k]) * c[j - 1][k - 1] % mod) % mod;
+                }
+
+                for (int k = 1; k <= j; k++) {
+                    for (int l = 1; l <= i - j; l++) {
+                        f[i][j] = (static_cast<long long>(f[i][j]) + static_cast<long long>(f[i - k - l][j - k]) * c[j - 1][k - 1] % mod * c[i - j][l] % mod * h[k][l] % mod) % mod;
+                    }
+                }
+            }
+        }
+    }
+
+    __attribute__((noreturn)) void print() {
+        for (int i = 0; i <= n; i++) {
+            cout << "{";
+
+            for (int j = 0; j < i; j++) {
+                cout << f[i][j] << ", ";
+            }
+
+            cout << f[i][i] << "}," << endl;
+        }
+
+        exit(EXIT_SUCCESS);
+    }
+}  // namespace gen
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    // === Generator ===
+
+#ifndef ONLINE_JUDGE
+    gen::main();
+    gen::print();
+#endif
+
+    // === Answer ===
+
+    int t;
+
+    cin >> t;
+
+    while (t--) {
+        int n, m;
+
+        cin >> n >> m;
+
+        cout << f[n][m] << endl;
+    }
+
+    return 0;
+}