initialize_crs_adjacency Subroutine

    subroutine initialize_crs_adjacency(self, elements)
        class(type_crs_adjacency_element), intent(inout) :: self
        type(holder_elements), intent(in) :: elements(:)

        integer(int32) :: num_elements
        integer(int32) :: i, j
        integer(int32) :: pair_count, capacity
        integer(int32), allocatable :: coo_row(:), coo_col(:), temp_row(:), temp_col(:)

        num_elements = size(elements)
        self%num_row = num_elements
        if (num_elements <= 1) return

        ! --- Step 1 & 2: 隣接ペアを全探索で探し、一時的なCOO形式で格納 ---
        pair_count = 0
        capacity = num_elements * 5
        call allocate_array(coo_row, length=capacity)
        call allocate_array(coo_col, length=capacity)

        do i = 1, num_elements
            do j = i + 1, num_elements
                if (are_elements_adjacent(elements(i)%e, elements(j)%e)) then
                    if ((pair_count + 2) > capacity) then
                        capacity = capacity * 2
                        call allocate_array(temp_row, length=capacity)
                        call allocate_array(temp_col, length=capacity)
                        temp_row(1:pair_count) = coo_row(1:pair_count)
                        temp_col(1:pair_count) = coo_col(1:pair_count)

                        call deallocate_array(coo_row)
                        call deallocate_array(coo_col)

                        call move_alloc(temp_row, coo_row)
                        call move_alloc(temp_col, coo_col)
                    end if

                    pair_count = pair_count + 1
                    coo_row(pair_count) = i
                    coo_col(pair_count) = j

                    pair_count = pair_count + 1
                    coo_row(pair_count) = j
                    coo_col(pair_count) = i
                end if
            end do
        end do

        self%nnz = pair_count

        ! --- Step 3: COO形式からCRS形式へ変換 ---
        call allocate_array(self%ptr, length=self%num_row + 1_int32)
        call allocate_array(self%ind, length=self%nnz)
        self%ptr = 0

        ! Pass 1: 各行の非ゼロ要素数(次数)をカウント
        do i = 1, self%nnz
            self%ptr(coo_row(i) + 1) = self%ptr(coo_row(i) + 1) + 1
        end do

        ! Pass 2: 累積和を計算して、ptr配列を完成させる
        self%ptr(1) = 1
        do i = 2, self%num_row + 1
            self%ptr(i) = self%ptr(i) + self%ptr(i - 1)
        end do

        ! Pass 3: ind配列を構築する
        call allocate_array(temp_row, length=self%num_row)
        temp_row(:) = self%ptr(1:self%num_row)

        do i = 1, self%nnz
            j = temp_row(coo_row(i))
            self%ind(j) = coo_col(i)
            temp_row(coo_row(i)) = j + 1
        end do

        call deallocate_array(temp_row)

        call deallocate_array(coo_row)
        call deallocate_array(coo_col)

    end subroutine initialize_crs_adjacency