Create 1842_x7536110.cpp

QUSTOJ/1842_x7536110.cpp

@@ -0,0 +1,126 @@
+#include <cstdio>
+#include <cstring>
+#include <algorithm>
+#include <iostream>
+#include <cmath>
+#include <map>
+#include <vector>
+#include <stack>
+using namespace std;
+#define mod 1004535809LL
+#define G 3LL
+#define maxn 455555
+ 
+long long x1[maxn], x2[maxn];
+long long qpow (long long a, long long b) {
+    long long ret=1;
+    while (b) {
+        if (b&1) ret = (ret*a)%mod;
+        a = (a*a)%mod;
+        b >>= 1;
+    }
+    return ret;
+}
+ 
+void change (long long *y, int len) {
+    int i, j, k;
+    for(i = 1, j = len / 2; i < len - 1; i++) {
+        if (i < j) swap(y[i], y[j]);
+        k = len / 2;
+        while (j >= k) {
+            j -= k;
+            k /= 2;
+        }
+        if (j < k) j += k;
+    }
+}
+ 
+void ntt (long long *y, int len, int on) {
+    change (y, len);
+    int id = 0;
+    for(int h = 2; h <= len; h <<= 1) {
+        id++;
+        long long wn = qpow (G, (mod - 1) / (1<<id));
+        for(int j = 0; j < len; j += h) {
+            long long w = 1;
+            for(int k = j; k < j + h / 2; k++) {
+                long long u = y[k] % mod;
+                long long t = w * (y[k + h / 2] % mod) % mod;
+                y[k] = (u + t) % mod;
+                y[k + h / 2] = ((u - t) % mod + mod) % mod;
+                w = w * wn % mod;
+            }
+        }
+    }
+    if (on == -1) {
+        for (int i = 1; i < len / 2; i++)
+            swap (y[i], y[len - i]);
+        long long inv = qpow(len, mod - 2);
+        for(int i = 0; i < len; i++)
+            y[i] = y[i] % mod * inv % mod;
+    }
+}
+ 
+long long n, m;
+long long f[maxn], g[maxn], h[maxn];
+//n个点的有环图 n个点的图 n个点的树
+long long fac[maxn], rev[maxn];
+ 
+void solve (int l, int r) { //cout << l << " " << r << endl;
+    if (l == r) {
+        f[l] += h[l];
+        f[l] %= mod;
+        return;
+    }
+    int mid = (l+r) >> 1;
+    solve (l, mid);
+    int len = 1;
+    while (len <= r-l+1) {len <<= 1;}
+    for (int i = 0; i < len; i++) {
+        x1[i] = x2[i] = 0;
+    }
+    for (int i = l; i <= mid; i++) {
+        x1[i-l] = f[i]*rev[i]%mod;
+    }
+    for (int i = 1; i <= r-l; i++) {
+        x2[i-1] = h[i]*rev[i-1]%mod;
+    }
+    ntt (x1, len, 1), ntt (x2, len, 1);
+    for (int i = 0; i < len; i++) x1[i] = x1[i] * x2[i] % mod;
+    ntt (x1, len, -1);
+    for (int i = mid+1; i <= r; i++) {
+        f[i] += x1[i-l-1]*fac[i-1] %mod;
+        f[i] %= mod;
+    }
+    //cout << l << " " << r << endl;
+    //for (int i = 1; i <= 4; i++) cout << f[i] << " "; cout << endl;
+    solve (mid+1, r);
+}
+ 
+int main () {
+   // freopen ("in", "r", stdin);
+  //  freopen ("out", "w", stdout);
+  //  //int t1 = clock ();
+    g[1] = h[1] = 1;
+    for (int i = 2; i <= 200000; i++) {
+        h[i] = qpow (i, i-2);
+        g[i] = qpow (2, 1LL*i*(i-1)/2);
+    }
+    fac[0] = 1;
+    for (int i = 1; i <= 200000; i++) fac[i] = fac[i-1] * i % mod;
+    rev[200000] = qpow (fac[200000], mod - 2);
+    for (int i = 200000-1; i >= 0; i--) rev[i] = rev[i+1] * (i+1) % mod;
+    int t;
+    scanf ("%d", &t);
+    while (t--) {
+        scanf ("%lld", &n);
+        memset (f, 0, sizeof f);
+        solve (1, n);
+        long long ans = g[n]-f[n];
+        (ans %= mod) += mod; ans %= mod;
+        printf ("%lld\n", ans);
+    }
+    //int t2 = clock ();
+    //cout << t2-t1 << endl;
+    return 0;
+}