chore: study for CuPy version of notebook solution

studies/cuda-kernels/combinations/lexicographic_formula.py

@@ -0,0 +1,32 @@
+import cupy as cp
+
+def distincts(content, counts):
+    counts_comb = counts * (counts - 1) // 2
+    offsets_comb = cp.cumsum(cp.concatenate((cp.array([0]), counts_comb)))
+    parents_comb = cp.zeros(8, dtype=int)
+    for i in range(1, len(offsets_comb)):
+        parents_comb[offsets_comb[i-1]:offsets_comb[i]] = i - 1
+
+    local_indices = cp.arange(offsets_comb[-1]) - offsets_comb[parents_comb]
+
+    n = counts[parents_comb]
+    b = 2 * n - 1
+    i = cp.floor((b - cp.sqrt(b * b - 8 * local_indices)) / 2).astype(counts_comb.dtype)
+    j = local_indices + i * (i - b + 2) // 2 + 1
+
+    starts_parents = cp.cumsum(cp.concatenate((cp.array([0]), counts)))[:-1][parents_comb]
+    i += starts_parents
+    j += starts_parents
+
+    if max(i.max(), j.max()) >= len(content):
+        raise IndexError("index exceeds the bounds of the content array.")
+
+    out_content = cp.vstack((content[i], content[j]))
+
+    return out_content
+
+content = cp.array([0, 1, 2, 3, 4, 5, 6, 7])
+counts = cp.array([2, 0, 4, 2])
+result = distincts(content, counts)
+
+print("combinations:\n", result)