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Solution.cs
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117 lines (108 loc) · 2.91 KB
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public class Solution
{
int mod = (int)1e9 + 7;
public int MagicalSum(int m, int k, int[] nums)
{
int n = nums.Length;
long[] fac = new long[m + 1];
fac[0] = 1;
for (int i = 1; i <= m; i++)
{
fac[i] = fac[i - 1] * i % mod;
}
long[] ifac = new long[m + 1];
ifac[0] = 1;
ifac[1] = 1;
for (int i = 2; i <= m; i++)
{
ifac[i] = FastPow(i, mod - 2, mod);
}
for (int i = 2; i <= m; i++)
{
ifac[i] = ifac[i - 1] * ifac[i] % mod;
}
long[][] numsPower = new long[n][];
for (int i = 0; i < n; i++)
{
numsPower[i] = new long[m + 1];
numsPower[i][0] = 1;
for (int j = 1; j <= m; j++)
{
numsPower[i][j] = numsPower[i][j - 1] * nums[i] % mod;
}
}
long[][][][] f = new long[n][][][];
for (int i = 0; i < n; i++)
{
f[i] = new long[m + 1][][];
for (int j = 0; j <= m; j++)
{
f[i][j] = new long[m * 2 + 1][];
for (int p = 0; p <= m * 2; p++)
{
f[i][j][p] = new long[k + 1];
}
}
}
for (int j = 0; j <= m; j++)
{
f[0][j][j][0] = numsPower[0][j] * ifac[j] % mod;
}
for (int i = 0; i + 1 < n; i++)
{
for (int j = 0; j <= m; j++)
{
for (int p = 0; p <= m * 2; p++)
{
for (int q = 0; q <= k; q++)
{
int q2 = (p % 2) + q;
if (q2 > k) break;
for (int r = 0; r + j <= m; r++)
{
int p2 = p / 2 + r;
f[i + 1][j + r][p2][q2] += f[i][j][p][q] * numsPower[i + 1][r] % mod * ifac[r] % mod;
f[i + 1][j + r][p2][q2] %= mod;
}
}
}
}
}
long res = 0;
for (int p = 0; p <= 2 * m; p++)
{
for (int q = 0; q <= k; q++)
{
if (BitCount(p) + q == k)
{
res = (res + f[n - 1][m][p][q] * fac[m] % mod) % mod;
}
}
}
return (int)res;
}
int BitCount(int n)
{
int count = 0;
while (n > 0)
{
if ((n & 1) != 0) count++;
n >>= 1;
}
return count;
}
long FastPow(long x, long y, long mod)
{
long res = 1, cur = x % mod;
while (y > 0)
{
if ((y & 1) == 1)
{
res = res * cur % mod;
}
y >>= 1;
cur = cur * cur % mod;
}
return res;
}
}