5.23d

Source/FWT FMT/LuoguP5387.cpp

@@ -0,0 +1,76 @@
+#include <cstdio>
+typedef long long Int64;
+#define asInt64 static_cast<Int64>
+const int mod = 998244353, size = 1 << 20;
+const Int64 inv2 = (mod + 1) / 2;
+Int64 powm(Int64 a, Int64 k) {
+    Int64 res = 1;
+    while (k) {
+        if (k & 1)
+            res = res * a % mod;
+        k >>= 1, a = a * a % mod;
+    }
+    return res;
+}
+int add(int a, int b) {
+    a += b;
+    return a < mod ? a : a - mod;
+}
+int sub(int a, int b) {
+    a -= b;
+    return a >= 0 ? a : a + mod;
+}
+void FWT(int n, int *A) {
+    for (int i = 2; i <= n; i <<= 1) {
+        int m = i >> 1;
+        for (int j = 0; j < n; j += i)
+            for (int k = 0; k < m; ++k) {
+                int &x = A[j + k], &y = A[j + m + k], t = y;
+                y = sub(x, t);
+                x = add(x, t);
+            }
+    }
+}
+void IFWT(int n, int *A) {
+    for (int i = 2; i <= n; i <<= 1) {
+        int m = i >> 1;
+        for (int j = 0; j < n; j += i)
+            for (int k = 0; k < m; ++k) {
+                int &x = A[j + k], &y = A[j + m + k], t = y;
+                y = sub(x, t) * inv2 % mod;
+                x = add(x, t) * inv2 % mod;
+            }
+    }
+}
+int A[size], B[size];
+int sg(int x) {
+    return x - (1 << (31 - __builtin_clz(x)));
+}
+int main() {
+    Int64 k;
+    int m;
+    scanf("%lld%d", &k, &m);
+    int sum = powm(m, k);
+    for (int i = 1; i <= m; ++i) {
+        int val = sg(i);
+        ++A[val];
+    }
+    int p = 1 << (31 - __builtin_clz(m));
+    FWT(p, A);
+    B[0] = 1;
+    FWT(p, B);
+    while (k) {
+        if (k & 1) {
+            for (int i = 0; i < p; ++i)
+                B[i] = asInt64(B[i]) * A[i] % mod;
+        }
+        k >>= 1;
+        if (k) {
+            for (int i = 0; i < p; ++i)
+                A[i] = asInt64(A[i]) * A[i] % mod;
+        }
+    }
+    IFWT(p, B);
+    printf("%d\n", sub(sum, B[0]));
+    return 0;
+}

Source/FWT FMT/LuoguP5387TestA.cpp

@@ -0,0 +1,25 @@
+#include <cstdio>
+int sg[2005];
+void calcSG(int x) {
+    bool use[2005] = {};
+    for (int y = 1; y < x; ++y)
+        if ((x ^ y) < x && (x ^ y) >= 1)
+            use[sg[x ^ y]] = true;
+    for (int z = 0;; ++z)
+        if (!use[z]) {
+            sg[x] = z;
+            return;
+        }
+}
+int sgo1(int x) {
+    return x - (1 << (31 - __builtin_clz(x)));
+}
+int main() {
+    for (int i = 1; i <= 2000; ++i) {
+        calcSG(i);
+        printf("%d %d %d\n", i, sg[i], sgo1(i));
+        if (sg[i] != sgo1(i))
+            throw;
+    }
+    return 0;
+}

Source/FWT FMT/LuoguP5387TestB.cpp

@@ -0,0 +1,19 @@
+#include <cstdio>
+int sg(int x) {
+    return x - (1 << (31 - __builtin_clz(x)));
+}
+int cnt = 0;
+void DFS(int v, int m, int xorv) {
+    if (v) {
+        for (int i = 1; i <= m; ++i)
+            DFS(v - 1, m, xorv ^ sg(i));
+    } else
+        cnt += (xorv != 0);
+}
+int main() {
+    int v, m;
+    scanf("%d%d", &v, &m);
+    DFS(v, m, 0);
+    printf("%d\n", cnt);
+    return 0;
+}