2023 rcpc

2023/rcpc/d1/editorial/L. Best or Worst - juve45.cpp

@@ -0,0 +1,168 @@
+/// Ionita Alexandru
+#include <bits/stdc++.h>
+#define st first
+#define nd second
+
+using namespace std;
+
+const long long N = 500100;
+long long n, aib[N], a[N], prev, f[N];
+string s;
+
+const long long MOD = 1e9 + 7;
+
+long long powMod(long long a, long long exp) {
+	long long b = a, res = 1;
+	while(exp) {
+		if(exp % 2) res *= b;
+		b = 1LL * b * b % MOD;
+		res %= MOD;
+		exp /= 2;
+	}
+	return res;
+}
+
+long long invMod(long long x) {
+	return powMod(x, MOD - 2);
+}
+
+long long comb(long long n, long long k) {
+	if(n < k) return 0;
+	if(n == k) return 1;
+	if(k == 0) return 1;
+	return f[n] * invMod(1LL * f[k] * f[n - k] % MOD) % MOD;
+}
+
+long long lsb(long long x) {
+	return x & (-x);
+}
+
+void upd(long long pos, long long val) {
+	for(; pos < N; pos += lsb(pos)) {
+		aib[pos] += val;
+	}
+}
+
+long long que(long long pos) {
+	long long ret = 0;
+	for(; pos; pos -= lsb(pos)) {
+		ret += aib[pos];
+	}
+	return ret;
+}
+
+long long que(long long l, long long r) {
+	if(l == r && r == 0) return 0;
+	if(l == 1) return que(r);
+	return que(r) - que(l - 1);
+}
+
+
+long long compute(long long pos, long long mn, long long mx) {
+	
+	long long prev = pos;
+	long long ans = 1;
+
+	for(long long i = pos + 1; i <= n; i++) {
+		if(a[i] == 0) continue;
+		if(a[prev] > a[i]) {
+			// minim
+			long long k = mn - a[i] - 1;
+			long long lg = i - prev - 1;
+			ans = ans * comb(lg, k) % MOD;
+			mn = a[i];
+			mx += lg - k;
+			if(mx > n) return 0; // todo testcase
+			upd(a[i], -1);
+		} else {
+			long long k = a[i] - mx - 1;
+			long long lg = i - prev - 1;
+			ans = ans * comb(lg, k) % MOD;
+			mx = a[i];
+			mn -= lg - k;
+			if(mn < 1) return 0;
+			upd(a[i], -1);
+		}
+		long long banned = que(mn, mx);
+		if(banned != 1)
+			return 0;
+		prev = i;
+	}
+	return ans;
+
+}
+
+
+void solve() {
+	long long mn, mx, ans1 = 0, ans2 = 0, banned;
+
+	cin >> n;
+
+	f[0] = 1; 
+	for(long long i = 1; i <= n + 1; i++) 
+		if(que(i, i) == 1)
+			upd(i, -1);
+
+	for(long long i = 1; i <= n; i++) {
+		f[i] = f[i - 1] * i % MOD;
+		cin >> a[i];
+		if(a[i])
+			upd(a[i], 1);
+	}
+
+	long long prev = 0;
+
+	n++;
+	a[n] = n;
+	f[n] = f[n - 1] * n % MOD;
+	upd(a[n], 1);
+
+	for(long long i = 1; i <= n; i++) {
+		if(a[i]) {
+
+			mn = a[i];
+			mx = a[i] + i - 1;
+			if(mx <= n) {
+				banned = que(mn, mx);
+				if(banned == 1) {
+					ans1 = powMod(2, max(i - 2, 0LL));
+					ans1 = ans1 * compute(i, mn, mx) % MOD;
+				}
+			}
+
+			if(i == 1) break;
+
+			// memset(aib, 0, sizeof aib);
+
+			for(long long j = 1; j <= n; j++)
+				if(a[j] && que(a[j], a[j]) == 0)
+					upd(a[j], 1);
+			
+			mx = a[i];
+			mn = a[i] - i + 1;
+			if(mn > 0) {
+				banned = que(mn, mx);
+				if(banned == 1) {
+					ans2 = powMod(2, max(i - 2, 0LL));
+					ans2 = ans2 * compute(i, mn, mx) % MOD;
+				}
+			}
+			break;
+		}
+	}
+	cout << (ans1 + ans2) % MOD << '\n';
+}
+
+
+int main() {
+	int t;
+	ios_base::sync_with_stdio(false);
+
+	cin >> t;
+
+	for(int i = 1; i <= t; i++) {
+		solve();
+	}
+
+
+}