#include <bits/stdc++.h>
using namespace std;
const int N = 1005;
int n, k, M;
int fact[N], factInv[N];
int dp[N][N][2], pref[N][N][2];
int pascal[N][N];
void add(int &w, int u) {
w += u;
if (w >= M) w -= M;
if (w < 0) w += M;
}
int mul(int w, int u) {
return (long long)w * u % M;
}
int newton(int n, int k) {
if (k < 0 || k > n) return 0;
return pascal[n][k];
}
int main() {
scanf("%d %d %d", &n, &k, &M);
k = min(k, 11);
for (int i = 0; i <= n; i++) {
pascal[i][i] = pascal[i][0] = 1;
}
for (int i = 1; i <= n; i++) {
for (int j = 1; j <= n; j++) {
pascal[i][j] = pascal[i - 1][j - 1] + pascal[i - 1][j];
if (pascal[i][j] >= M) {
pascal[i][j] -= M;
}
}
}
dp[0][0][0] = pref[0][0][0] = 1;
dp[0][1][1] = pref[0][1][1] = 1;
for (int i = 1; i <= k; i++) {
pref[0][i][0] += pref[0][i - 1][0];
pref[0][i][1] += pref[0][i - 1][1];
}
for (int i = 1; i <= n; i++) {
for (int j = 1; j <= k; j++) {
for (int ile = 0; ile < i; ile++) {
// For 0
int goodCombinations = 0;
add(goodCombinations, mul(dp[ile][j][1], pref[i - ile - 1][j][0]));
add(goodCombinations, mul(pref[ile][j][1], dp[i - ile - 1][j][0]));
add(goodCombinations, -mul(dp[ile][j][1], dp[i - ile - 1][j][0]));
add(dp[i][j][0], mul(newton(i - 1, ile), goodCombinations));
// For 1
goodCombinations = 0;
add(goodCombinations, mul(dp[ile][j][1], pref[i - ile - 1][j - 1][1]));
add(goodCombinations, mul(pref[ile][j - 1][1], dp[i - ile - 1][j][1]));
add(goodCombinations, mul(dp[ile][j - 1][1], dp[i - ile - 1][j - 1][1]));
add(dp[i][j][1], mul(newton(i - 1, ile), goodCombinations));
}
pref[i][j][0] = pref[i][j - 1][0] + dp[i][j][0];
if (pref[i][j][0] >= M) pref[i][j][0] -= M;
pref[i][j][1] = pref[i][j - 1][1] + dp[i][j][1];
if (pref[i][j][1] >= M) {
pref[i][j][1] -= M;
}
}
}
int ans = 0;
for (int i = 0; i < n; i++) {
int goodCombinations = 0;
add(goodCombinations, mul(dp[i][k][0], pref[n - 1 - i][k][0]));
add(goodCombinations, mul(pref[i][k][0], dp[n - 1 - i][k][0]));
add(goodCombinations, -mul(dp[i][k][0], dp[n - 1 - i][k][0]));
add(ans, mul(newton(n - 1, i), goodCombinations));
}
printf("%d\n", ans);
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 | #include <bits/stdc++.h> using namespace std; const int N = 1005; int n, k, M; int fact[N], factInv[N]; int dp[N][N][2], pref[N][N][2]; int pascal[N][N]; void add(int &w, int u) { w += u; if (w >= M) w -= M; if (w < 0) w += M; } int mul(int w, int u) { return (long long)w * u % M; } int newton(int n, int k) { if (k < 0 || k > n) return 0; return pascal[n][k]; } int main() { scanf("%d %d %d", &n, &k, &M); k = min(k, 11); for (int i = 0; i <= n; i++) { pascal[i][i] = pascal[i][0] = 1; } for (int i = 1; i <= n; i++) { for (int j = 1; j <= n; j++) { pascal[i][j] = pascal[i - 1][j - 1] + pascal[i - 1][j]; if (pascal[i][j] >= M) { pascal[i][j] -= M; } } } dp[0][0][0] = pref[0][0][0] = 1; dp[0][1][1] = pref[0][1][1] = 1; for (int i = 1; i <= k; i++) { pref[0][i][0] += pref[0][i - 1][0]; pref[0][i][1] += pref[0][i - 1][1]; } for (int i = 1; i <= n; i++) { for (int j = 1; j <= k; j++) { for (int ile = 0; ile < i; ile++) { // For 0 int goodCombinations = 0; add(goodCombinations, mul(dp[ile][j][1], pref[i - ile - 1][j][0])); add(goodCombinations, mul(pref[ile][j][1], dp[i - ile - 1][j][0])); add(goodCombinations, -mul(dp[ile][j][1], dp[i - ile - 1][j][0])); add(dp[i][j][0], mul(newton(i - 1, ile), goodCombinations)); // For 1 goodCombinations = 0; add(goodCombinations, mul(dp[ile][j][1], pref[i - ile - 1][j - 1][1])); add(goodCombinations, mul(pref[ile][j - 1][1], dp[i - ile - 1][j][1])); add(goodCombinations, mul(dp[ile][j - 1][1], dp[i - ile - 1][j - 1][1])); add(dp[i][j][1], mul(newton(i - 1, ile), goodCombinations)); } pref[i][j][0] = pref[i][j - 1][0] + dp[i][j][0]; if (pref[i][j][0] >= M) pref[i][j][0] -= M; pref[i][j][1] = pref[i][j - 1][1] + dp[i][j][1]; if (pref[i][j][1] >= M) { pref[i][j][1] -= M; } } } int ans = 0; for (int i = 0; i < n; i++) { int goodCombinations = 0; add(goodCombinations, mul(dp[i][k][0], pref[n - 1 - i][k][0])); add(goodCombinations, mul(pref[i][k][0], dp[n - 1 - i][k][0])); add(goodCombinations, -mul(dp[i][k][0], dp[n - 1 - i][k][0])); add(ans, mul(newton(n - 1, i), goodCombinations)); } printf("%d\n", ans); return 0; } |
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