#include <cstdio> #include <cstdint> #include <vector> #include <algorithm> const int P = 1000000007; using namespace std; inline int mul(int x, int y) { return (int)(((int64_t)x * (int64_t)y) % P); } vector<vector<int> > pascal; inline int pas(int n, int k) { if ((n < 0) || (k < 0) || (k > n)) { return 0; } return pascal[n][k]; } void init_pascal(int n) { pascal.resize(n + 8); pascal[0].push_back(1); int i, j; for (i = 1; i <= n + 4; ++i) { pascal[i].reserve(i + 2); for (j = 0; j <= i; ++j) { pascal[i].push_back(((j > 0 ? pascal[i - 1][j - 1] : 0) + (j < i ? pascal[i - 1][j] : 0)) % P); } } } int pow2(int x) { if (x == 0) { return 1; } int64_t half = (int64_t)pow2(x / 2); if (x % 2) { return (int)((2 * half * half) % P); } else { return (int)((half * half) % P); } } vector<vector<int> > fun; int f(int T, int B, int N) { if ((T < 0) || (B + N < 0)) { return 0; } return fun[T][B + N]; } void init_f(int a, int d, int N, int max_y, int max_x) { int i, sum, x, y, x2, nudge; fun.resize(N + 8); for(i = 0; i <= N + 4; ++i) { fun[i].resize(2 * N + 8); } for(y = 0; y <= max_y; ++y) { for(x = 0; x <= max_x; ++x) { x2 = x - N; nudge = 0; if (y % 2 == (x2 + 1000000) % 2) { nudge = mul(pas(a, (x2 + y) / 2), pas(d, (y - x2) / 2)); } fun[y][x] = (((f(y, x2 - 1, N) + f(y - 1, x2, N)) % P + P - f(y - 1, x2 - 1, N)) % P + nudge) % P; } } } typedef pair<int, vector<bool> > ball_t; int main () { int N, i, dim, j, l, m, T, B; char ch; bool second, third; scanf("%d", &N); init_pascal(N); vector<ball_t> balls(3); for (i = 0; i < 3; ++i) { scanf("%d ", &dim); if (dim >= N) { printf("%d\n", pow2(N)); return 0; } balls[i].first = N - dim - 1; for (j = 0; j < N; ++j) { scanf("%c", &ch); balls[i].second.push_back(ch == '1'); } } sort(balls.begin(), balls.end()); for (i = 0; i < N; ++i) { if (balls[0].second[i]) { balls[0].second[i] = false; balls[1].second[i] = !balls[1].second[i]; balls[2].second[i] = !balls[2].second[i]; } } int a = 0, b = 0, c = 0, d = 0; for (i = 0; i < N; ++i) { second = balls[1].second[i]; third = balls[2].second[i]; if (second && third) { ++d; } else if (second && !third) { ++c; } else if (!second && third) { ++b; } else { ++a; } } int x = balls[0].first, y = balls[1].first, z = balls[2].first; int max_x = 0, max_y = 0; for (l = 0; l <= b; ++l) { for (m = 0; m <= min(c, x - l); ++m) { max_y = max(max_y, x - l - m); max_x = max(max_x, min(y - l - c - d + m, z - b - m - d + l)); } } init_f(a, d, N, max_y, N + max_x); int sum = 0; for (l = 0; l <= b; ++l) { for (m = 0; m <= min(c, x - l); ++m) { T = x - l - m; B = min(y - l - c - d + m, z - b - m - d + l); sum = (sum + mul(mul(pas(b, l), pas(c, m)), f(T, B, N))) % P; } } printf("%d\n", (pow2(N) - sum + P) % P); return 0; }
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 | #include <cstdio> #include <cstdint> #include <vector> #include <algorithm> const int P = 1000000007; using namespace std; inline int mul(int x, int y) { return (int)(((int64_t)x * (int64_t)y) % P); } vector<vector<int> > pascal; inline int pas(int n, int k) { if ((n < 0) || (k < 0) || (k > n)) { return 0; } return pascal[n][k]; } void init_pascal(int n) { pascal.resize(n + 8); pascal[0].push_back(1); int i, j; for (i = 1; i <= n + 4; ++i) { pascal[i].reserve(i + 2); for (j = 0; j <= i; ++j) { pascal[i].push_back(((j > 0 ? pascal[i - 1][j - 1] : 0) + (j < i ? pascal[i - 1][j] : 0)) % P); } } } int pow2(int x) { if (x == 0) { return 1; } int64_t half = (int64_t)pow2(x / 2); if (x % 2) { return (int)((2 * half * half) % P); } else { return (int)((half * half) % P); } } vector<vector<int> > fun; int f(int T, int B, int N) { if ((T < 0) || (B + N < 0)) { return 0; } return fun[T][B + N]; } void init_f(int a, int d, int N, int max_y, int max_x) { int i, sum, x, y, x2, nudge; fun.resize(N + 8); for(i = 0; i <= N + 4; ++i) { fun[i].resize(2 * N + 8); } for(y = 0; y <= max_y; ++y) { for(x = 0; x <= max_x; ++x) { x2 = x - N; nudge = 0; if (y % 2 == (x2 + 1000000) % 2) { nudge = mul(pas(a, (x2 + y) / 2), pas(d, (y - x2) / 2)); } fun[y][x] = (((f(y, x2 - 1, N) + f(y - 1, x2, N)) % P + P - f(y - 1, x2 - 1, N)) % P + nudge) % P; } } } typedef pair<int, vector<bool> > ball_t; int main () { int N, i, dim, j, l, m, T, B; char ch; bool second, third; scanf("%d", &N); init_pascal(N); vector<ball_t> balls(3); for (i = 0; i < 3; ++i) { scanf("%d ", &dim); if (dim >= N) { printf("%d\n", pow2(N)); return 0; } balls[i].first = N - dim - 1; for (j = 0; j < N; ++j) { scanf("%c", &ch); balls[i].second.push_back(ch == '1'); } } sort(balls.begin(), balls.end()); for (i = 0; i < N; ++i) { if (balls[0].second[i]) { balls[0].second[i] = false; balls[1].second[i] = !balls[1].second[i]; balls[2].second[i] = !balls[2].second[i]; } } int a = 0, b = 0, c = 0, d = 0; for (i = 0; i < N; ++i) { second = balls[1].second[i]; third = balls[2].second[i]; if (second && third) { ++d; } else if (second && !third) { ++c; } else if (!second && third) { ++b; } else { ++a; } } int x = balls[0].first, y = balls[1].first, z = balls[2].first; int max_x = 0, max_y = 0; for (l = 0; l <= b; ++l) { for (m = 0; m <= min(c, x - l); ++m) { max_y = max(max_y, x - l - m); max_x = max(max_x, min(y - l - c - d + m, z - b - m - d + l)); } } init_f(a, d, N, max_y, N + max_x); int sum = 0; for (l = 0; l <= b; ++l) { for (m = 0; m <= min(c, x - l); ++m) { T = x - l - m; B = min(y - l - c - d + m, z - b - m - d + l); sum = (sum + mul(mul(pas(b, l), pas(c, m)), f(T, B, N))) % P; } } printf("%d\n", (pow2(N) - sum + P) % P); return 0; } |