#include <bits/stdc++.h> #define mod 1000000007 using namespace std; long long dp[3000][3000]; long long sp_mod(long long a, long long b) { long long w = 1; while(b != 0) { if(b%2 == 1) { w *= a; w %= mod; } a %= mod; a *= a; a %= mod; b >>= 1; } return w; } int main() { ios_base::sync_with_stdio(0); cin.tie(0); int n, m; cin >> n >> m; for(int i = 0; i < n-1; ++i) dp[i][i+1] = m; for(int i = 2; i < n; ++i) for(int j = 0; j < n-i; ++j) { for(int k = j+1; k < i+j-1; ++k) { dp[j][j+i] += (dp[j][k] * sp_mod(m, i+j-k-1))%mod; dp[j][j+i] %= mod; } dp[j][j+i] += sp_mod(m, i) - dp[j+1][j+i-1]; dp[j][j+i] += mod; dp[j][j+i] %= mod; } cout << dp[0][n-1]; 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 | #include <bits/stdc++.h> #define mod 1000000007 using namespace std; long long dp[3000][3000]; long long sp_mod(long long a, long long b) { long long w = 1; while(b != 0) { if(b%2 == 1) { w *= a; w %= mod; } a %= mod; a *= a; a %= mod; b >>= 1; } return w; } int main() { ios_base::sync_with_stdio(0); cin.tie(0); int n, m; cin >> n >> m; for(int i = 0; i < n-1; ++i) dp[i][i+1] = m; for(int i = 2; i < n; ++i) for(int j = 0; j < n-i; ++j) { for(int k = j+1; k < i+j-1; ++k) { dp[j][j+i] += (dp[j][k] * sp_mod(m, i+j-k-1))%mod; dp[j][j+i] %= mod; } dp[j][j+i] += sp_mod(m, i) - dp[j+1][j+i-1]; dp[j][j+i] += mod; dp[j][j+i] %= mod; } cout << dp[0][n-1]; return 0; } |