• Title/Summary/Keyword: 사전식 순서

Search Result 3, Processing Time 0.047 seconds

Mathematical Structures of Jeong Yag-yong's Gugo Wonlyu (정약용(丁若鏞)의 산서(算書) 구고원류(勾股源流)의 수학적(數學的) 구조(構造))

  • HONG, Sung Sa;HONG, Young Hee;LEE, Seung On
    • Journal for History of Mathematics
    • /
    • v.28 no.6
    • /
    • pp.301-310
    • /
    • 2015
  • Since Jiuzhang Suanshu, the main tools in the theory of right triangles, known as Gougushu in East Asia were algebraic identities about three sides of a right triangle derived from the Pythagorean theorem. Using tianyuanshu up to siyuanshu, Song-Yuan mathematicians could skip over those identities in the theory. Chinese Mathematics in the 17-18th centuries were mainly concerned with the identities along with the western geometrical proofs. Jeong Yag-yong (1762-1836), a well known Joseon scholar and writer of the school of Silhak, noticed that those identities can be derived through algebra and then wrote Gugo Wonlyu (勾股源流) in the early 19th century. We show that Jeong reveals the algebraic structure of polynomials with the three indeterminates in the book along with their order structure. Although the title refers to right triangles, it is the first pure algebra book in Joseon mathematics, if not in East Asia.

Improvement of Practical Suffix Sorting Algorithm (실용적인 접미사 정렬 알고리즘의 개선)

  • Jeong, Tae-Young;Lee, Tae-Hyung;Park, Kun-Soo
    • Journal of KIISE:Computer Systems and Theory
    • /
    • v.36 no.2
    • /
    • pp.68-72
    • /
    • 2009
  • The suffix array is a data structure storing all suffixes of a string in lexicographical order. It is widely used in string problems instead of the suffix tree, which uses a large amount of memory space. Many researches have shown that not only the suffix array can be built in O(n), but also it can be constructed with a small time and space usage for real-world inputs. In this paper, we analyze a practical suffix sorting algorithm due to Maniscalco and Puglisi [1], and we propose an efficient algorithm which improves Maniscalco-Puglisi's running time.

Data Compression Capable of Error Control Using Block-sorting and VF Arithmetic Code (블럭정렬과 VF형 산술부호에 의한 오류제어 기능을 갖는 데이터 압축)

  • Lee, Jin-Ho;Cho, Suk-Hee;Park, Ji-Hwan;Kang, Byong-Uk
    • The Transactions of the Korea Information Processing Society
    • /
    • v.2 no.5
    • /
    • pp.677-690
    • /
    • 1995
  • In this paper, we propose the high efficiency data compression capable of error control using block-sorting, move to front(MTF) and arithmetic code with variable length in to fixed out. First, the substring with is parsed into length N is shifted one by one symbol. The cyclic shifted rows are sorted in lexicographical order. Second, the MTF technique is applied to get the reference of locality in the sorted substring. Then the preprocessed sequence is coded using VF(variable to fixed) arithmetic code which can be limited the error propagation in one codeword. The key point is how to split the fixed length codeword in proportion to symbol probabilities in VF arithmetic code. We develop the new VF arithmetic coding that split completely the codeword set for arbitrary source alphabet. In addition to, an extended representation for symbol probability is designed by using recursive Gray conversion. The performance of proposed method is compared with other well-known source coding methods with respect to entropy, compression ratio and coding times.

  • PDF