对于一个串S，当它同时满足如下条件时，它就是一个01偏串：1、只由0和1两种符组成；2、在S的每一个前缀中，0的个数不超过1的个数；3、S中0的个数和1的个数相等。现在给定01偏串S，请计算一下S在所有长度为n的01偏串中作为子串出现的次数的总和。由于结果比较大，结果对1e9+7取余后输出。样例解释：在第二个样例中，长度为4的偏串共两个1010，1100。10在1010中出现了两次，在1100中出现了1次。所以答案是3。
#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; #define pau system("pause") #define ll long long #define pii pair #define pb push_back #define mp make_pair #define clr(a, x) memset(a, x, sizeof(a)) const double pi = acos(-1.0); const int INF = 0x3f3f3f3f; const int MOD = 1e9 + 7; const double EPS = 1e-9; int t, n, l; char s[100015]; int res[1015] = { 1, 641102369, 578095319, 5832229, 259081142, 974067448, 316220877, 690120224, 251368199, 980250487, 682498929, 134623568, 95936601, 933097914, 167332441, 598816162, 336060741, 248744620, 626497524, 288843364, 491101308, 245341950, 565768255, 246899319, 968999, 586350670, 638587686, 881746146, 19426633, 850500036, 76479948, 268124147, 842267748, 886294336, 485348706, 463847391, 544075857, 898187927, 798967520, 82926604, 723816384, 156530778, 721996174, 299085602, 323604647, 172827403, 398699886, 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965785236, 992656683, 916291845, 881482632, 899946391, 321900901, 512634493, 303338827, 121000338, 967284733, 492741665, 152233223, 165393390, 680128316, 917041303, 532702135, 741626808, 496442755, 536841269, 131384366, 377329025, 301196854, 859917803, 676511002, 373451745, 847645126, 823495900, 576368335, 73146164, 954958912, 847549272, 241289571, 646654592, 216046746, 205951465, 3258987, 780882948, 822439091, 598245292, 869544707, 698611116 }; ll mpow(ll x, int y) { if (!y) return 1; ll res = mpow(x, y >> 1); if (y & 1) return res * res % MOD * x % MOD; else return res * res % MOD; } ll get_val(int x) { int y = x / 1000000; ll result = res[y]; for (int i = y * 1000000 + 1; i <= x; ++i) { result = result * i % MOD; } return result; } int main() { scanf("%d", &t); while (t--) { scanf("%d%s", &n, s + 1); l = strlen(s + 1); if (l > n || n & 1) { puts("0"); continue; } else { int h = n - l >> 1; if ((h << 1 | 1) >= MOD) { puts("0"); continue; } else { ll x = get_val(h << 1 | 1); ll y = get_val(h + 1); ll z = get_val(h); ll answer = x * mpow(y, MOD - 2) % MOD * mpow(z, MOD - 2) % MOD; printf("%I64d\n", answer); } } } return 0; }
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