//[SolutionMethod]
public BeautifulQuadruplesAnswer Straight(BeautifulQuadruplesSample sample)
{
Array.Sort(sample.arr);
Int32 a = sample.arr[0];
Int32 b = sample.arr[1];
Int32 c = sample.arr[2];
Int32 d = sample.arr[3];
Int32 res = 0;
for (Int32 ia = 1; ia <= a; ia++)
{
for (Int32 ib = ia; ib <= b; ib++)
{
for (Int32 ic = ib; ic <= c; ic++)
{
for (Int32 id = ic; id <= d; id++)
{
Int32 X = ((id ^ ic) ^ ib) ^ ia;
if (X != 0)
{
res++;
}
}
}
}
}
return(new BeautifulQuadruplesAnswer()
{
result = res
});
}
static void sampleInfo(BeautifulQuadruplesSample sample)
{
Array.Sort(sample.arr);
Int32 a = sample.arr[0];
Int32 b = sample.arr[1];
Int32 c = sample.arr[2];
Int32 d = sample.arr[3];
Int32 res = 0;
Int32 doubles = 0;
Int32 uniques = 0;
Int32 Zeroes1 = 0;
Int32 Zeroes2 = 0;
Int32 Zeroes = 0;
for (int ia = 1; ia <= a; ia++)
{
for (int ib = 1; ib <= b; ib++)
{
for (int ic = 1; ic <= c; ic++)
{
for (int id = 1; id <= d; id++)
{
if ((id < ic) || (id < ib) || (id < ia) || (ic < ib) || (ic < ia) || (ib < ia))
{
doubles++;
continue;
}
uniques++;
Int32 X = ia ^ ib;
X = X ^ ic;
X = X ^ id;
if (X == 0)
{
Zeroes++;
Zeroes1++;
if (ia != ib && ia != ic)
{
Zeroes2++;
}
Console.WriteLine($"{ia}^{ib}^{ic}^{id} == 0");
}
else
{
res++;
}
}
}
}
}
Console.WriteLine($"Total combs {a * b * c * d} Uniques {uniques} Doubles {doubles} Right answer {res } Total Zeroes {Zeroes} Zeroes2 {Zeroes2}");
}
//[SolutionMethod]
public TAnswer DP3(TSample Sample)
{
BeautifulQuadruplesSample sample = Sample as BeautifulQuadruplesSample;
Array.Sort(sample.arr);
Int32 a = sample.arr[0];
Int32 b = sample.arr[1];
Int32 c = sample.arr[2];
Int32 d = sample.arr[3];
Int32 MaxXor = (1 << (int)(Math.Log(d, 2) + 1)) - 1;
Int32[,] cnt = new Int32[MaxXor + 1, MaxXor + 1];
Int32[] tot = new Int32[MaxXor + 1];
Int32 ans = 0;
for (int i = 1; i <= a; ++i)
{
for (int j = i; j <= b; ++j)
{
++cnt[i ^ j, j];
++tot[j];
}
}
for (int i = 0; i < MaxXor; ++i)
{
for (int j = 1; j < MaxXor; ++j)
{
cnt[i, j] += cnt[i, j - 1];
}
if (i > 0)
{
tot[i] += tot[i - 1];
}
}
for (int i = 1; i <= c; ++i)
{
for (int j = i; j <= d; ++j)
{
ans += tot[i] - cnt[i ^ j, i];
}
}
return(new BeautifulQuadruplesAnswer()
{
result = ans
});
}
public TAnswer DP2(TSample Sample)
{
BeautifulQuadruplesSample sample = Sample as BeautifulQuadruplesSample;
//sampleInfo(sample);
Array.Sort(sample.arr);
Int32 a = sample.arr[0];
Int32 b = sample.arr[1];
Int32 c = sample.arr[2];
Int32 d = sample.arr[3];
Int64[] F = new Int64[d + 1];
F[0] = 0;
for (int i = 1; i <= d; i++)
{
F[i] = F[i - 1] + i;
}
Int64[,] SB = new Int64[b + 1, 2];
SB[1, 0] = d * c - F[c - 1];
SB[1, 1] = SB[1, 0];
for (int i = 2; i <= b; i++)
{
SB[i, 0] = d * c - F[c - 1] - (d * (i - 1) - F[i - 2]);
SB[i, 1] = SB[i - 1, 1] + SB[i, 0];
}
Int64[,] SA = new Int64[a + 1, 2];
SA[1, 0] = SB[b, 1];
SA[1, 1] = SB[b, 1];
for (int i = 2; i <= a; i++)
{
SA[i, 0] = SA[i - 1, 0] - SB[i - 1, 0];
SA[i, 1] = SA[i - 1, 1] + SA[i, 0];
}
Int64 Nulls = a * c - F[a - 1];
Int64 result = SA[a, 1] - Nulls;
Int32 MaxXor = (1 << (int)(Math.Log(d, 2) + 1)) - 1;
Int32[,] counts1 = new Int32[MaxXor + 1, b + 1];
for (int i = 1; i <= a; i++)
{
for (int j = i + 1; j <= b; j++)
{
counts1[i ^ j, j]++;
}
}
Int32[,] counts2 = new Int32[MaxXor + 1, c + 1];
for (int i = 1; i <= c; i++)
{
for (int j = i + 1; j <= d; j++)
{
counts2[i ^ j, i]++;
}
}
for (int i = 1; i <= MaxXor; i++)
{
for (int j = c; j >= 1; j--)
{
counts2[i, j - 1] += counts2[i, j];
}
}
for (int i = 1; i <= MaxXor; i++)
{
for (int j = 1; j <= b; j++)
{
result -= counts2[i, j] * counts1[i, j];
}
}
return(new BeautifulQuadruplesAnswer()
{
result = result
});
}
//[SolutionMethod]
public BeautifulQuadruplesAnswer DP(BeautifulQuadruplesSample sample)
{
Array.Sort(sample.arr);
Int32 a = sample.arr[0];
Int32 b = sample.arr[1];
Int32 c = sample.arr[2];
Int32 d = sample.arr[3];
Int32[] RP = new Int32[d + 1];
RP[0] = 0;
RP[1] = 0;
RP[2] = 1;
for (int i = 3; i < d + 1; i++)
{
RP[i] = RP[i - 1] + i - 1;
}
/*
* Int32 MaxXor = (1 << (int)(Math.Log(d, 2) + 1)) - 1;
*
* Int32[,] dp = new Int32[4, MaxXor];
*
*
* Int32 NP = a * c + a * b;
* Int32 TotalCombinations = a * b * c * d;
* //Int32 doubles = a * ((b - a) * (d - c));
* Int32 doubles = 0;
* for (int ia = 1; ia <= a; ia++)
* {
* for (int ib = ia; ib <= b; ib++)
* {
* for (int ic = ib; ic <= c; ic++)
* {
* for (int id = ic; id <= d; id++)
* {
* doubles++;
* }
* }
* }
* }
*/
//Int32[] ar = Enumerable.Range(1, a).Concat(Enumerable.Range(1, b)).Concat(Enumerable.Range(1, c)).Concat(Enumerable.Range(1, d)).ToArray();
Int32[] ar = Enumerable.Range(1, d).ToArray();
Int32 MaxXor = (1 << (int)(Math.Log(d, 2) + 1)) - 1;
Int32[] counts = new Int32[d + 1];
foreach (var val in ar)
{
counts[val]++;
}
ar = ar.Distinct().ToArray();
Int32 n = ar.Length;
Int64[,] dp = new Int64[n + 1, MaxXor + 1];
dp[0, 0] = 1;
for (Int32 i = 1; i <= n; i++)
{
for (int j = 0; j <= MaxXor; j++)
{
dp[i, j] =
(((dp[i - 1, j] * (1 + counts[ar[i - 1]] / 2)))
+
((dp[i - 1, j ^ ar[i - 1]] * ((counts[ar[i - 1]] + 1) / 2))))
;
}
}
Int32 res = 0;
Int32 doubles = 0;
for (int ia = 1; ia <= a; ia++)
{
for (int ib = 1; ib <= b; ib++)
{
for (int ic = 1; ic <= c; ic++)
{
for (int id = 1; id <= d; id++)
{
if ((id < ic) || (id < ib) || (id < ia) || (ic < ib) || (ic < ia) || (ib < ia))
{
doubles++;
continue;
}
Int32 X = ia ^ ib;
X = X ^ ic;
X = X ^ id;
if (X == 0)
{
Console.WriteLine($"{ia}^{ib}^{ic}^{id} == 0");
}
else
{
res++;
}
}
}
}
}
Int32 bBccBd = 0;
for (int x = 1; x <= b - 2; x++)
{
for (int z = 3; z <= b; z++)
{
for (int y = x + 1; y < z; y++)
{
Console.WriteLine($"{z} {y} {x}");
bBccBd++;
}
}
}
Int32 uniques = 0;
Int32 uniques1 = 0;
for (int ia = 1; ia <= a; ia++)
{
for (int ib = ia; ib <= b; ib++)
{
for (int ic = ib; ic <= c; ic++)
{
uniques1 += d - ic + 1;
}
}
}
Int32[] FB = new Int32[d + 1];
Int32[] FBFB = new Int32[d + 1];
FB[0] = 0;
FBFB[0] = 0;
for (int i = 1; i <= d; i++)
{
FB[i] = FB[i - 1] + i;
FBFB[i] = FBFB[i - 1] + FB[i];
}
Int32[] sc = new Int32[c + 1];
sc[0] = 0;
for (int ic = 1; ic <= c; ic++)
{
sc[ic] = ic * d - FB[ic] + ic;
}
Int32[] sb = new Int32[b + 1];
sb[0] = sc[c];
for (int ib = 1; ib <= b; ib++)
{
sb[ib] = sb[ib - 1] - ib + sc[b] + 1;
}
for (int ia = 1; ia <= a; ia++)
{
for (int ib = ia; ib <= b; ib++)
{
uniques += 123;
}
}
Int32[,] fbdp = new Int32[d + 1, d + 1];
for (int i = 0; i <= d; i++)
{
for (int j = i; j <= d; j++)
{
fbdp[i, j] = FB[j] - FB[i];
}
}
Console.WriteLine($"{uniques} {uniques1}");
Int32 NP = a * c + a * b;
res = uniques1 - NP;
//Console.WriteLine(bBccBd);
//doubles = RP[a] * 3 + RP[b] * 2 + RP[c];
//res = TotalCombinations - doubles - NP;
return(new BeautifulQuadruplesAnswer()
{
result = res
});
}
