Recursive Quicksort: Why this partition is wrong? - c++

Question

I'm coding a recursive 3-way partitioning in C++, but I don't see what's wrong here. (It is 97% of the time correct, sometimes incorrect. That's making me hard to debug.)
Expected invariant: After the partitioning, A[p, ..., p + less1 + less2 - 1] is less than pivot, A[p + less1 + less2, ..., p + less1 + less2 + same1 + same2 - 1] is the same with pivot, the rest is bigger than pivot.
Wrong result: "The middle" part (the part with values the same with pivot) doesn't locate correctly.
Reproducable test case:
A = {0, 1, 4, 7, 6, 9, 3, 10, 11, 12, 2, 8, 5}
p = 0, r = 12, pivot = 11
Expected output of less : 11
Current output : 10
Code:
template <typename T>
void PPartition(std::vector<T>& A, size_t p, size_t r, const T& pivot, std::size_t& less, std::size_t& same) {
if (p == r) {
less = A[p] < pivot;
same = A[p] == pivot;
return;
}
std::size_t m = (p + r) / 2;
std::size_t less1 = 0, less2 = 0, same1 = 0, same2 = 0;
PPartition(A, p, m, pivot, less1, same1);
PPartition(A, m + 1, r, pivot, less2, same2);
if (less2 > m - p + 1 - less1) {
// sends "less" part of the right to the left
for (std::size_t k = 0; k < m - p + 1 - less1; k++) {
std::swap(A[p + less1 + k], A[m + less2 - k]);
}
// maintains "equal" part
for (std::size_t k = 0; k < same1 + same2; k++) {
std::swap(A[p + less1 + less2 + k], A[m + less2 + same2 - k]);
}
} else {
// sends "less" part of the right to the left
for (std::size_t k = 0; k < less2; k++) {
std::swap(A[p + less1 + k], A[m + less2 - k]);
}
// maintains "equal" part
for (std::size_t k = 0; k < same1 + same2; k++) {
std::swap(A[p + less1 + less2 + k], A[m + less2 + same2 - k]);
}
}
less = less1 + less2;
same = same1 + same2;
}

Answer 1

Self-answer:
If less2 == 0, then We shouldn't swap "middle" partition of the left part with the right part.
template <typename T>
void PPartition(std::vector<T>& A, size_t p, size_t r, const T& pivot, std::size_t& less, std::size_t& same) {
if (p == r) {
less = A[p] < pivot;
same = A[p] == pivot;
return;
}
std::size_t m = (p + r) / 2;
std::size_t less1 = 0, less2 = 0, same1 = 0, same2 = 0;
PPartition(A, p, m, pivot, less1, same1);
PPartition(A, m + 1, r, pivot, less2, same2);
if (less2 > m - p + 1 - less1) {
for (std::size_t k = 0; k < m - p + 1 - less1; k++) {
std::swap(A[p + less1 + k], A[m + less2 - k]);
}
for (std::size_t k = 0; k < same1 + same2 && p + less1 + k < m + same2 - k; k++) {
std::swap(A[p + less1 + less2 + k], A[m + less2 + same2 - k]);
}
} else {
for (std::size_t k = 0; k < less2; k++) {
std::swap(A[p + less1 + k], A[m + less2 - k]);
}
if (less2 > 0) {
for (std::size_t k = 0; k < same1 + same2; k++) {
std::swap(A[p + less1 + less2 + k], A[m + less2 + same2 - k]);
}
} else {
for (std::size_t k = 0; k < same2; k++) {
std::swap(A[p + less1 + same1 + k], A[m + same2 - k]);
}
}
}
less = less1 + less2;
same = same1 + same2;
}