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籃球隊(duì)排名次
摘 要
本文以圖論的觀點(diǎn)為主旨，對球隊(duì)名次進(jìn)行排序。把參賽球隊(duì)的成績看成是隨機(jī)變量，建立隨機(jī)模型。先在確定型的情況下，把參賽球隊(duì)視為結(jié)點(diǎn)，用弧的指向表示比賽的勝負(fù)情況，通過直接或間接的方法構(gòu)造競賽圖。在理論的指導(dǎo)下，尋找有向哈密頓路徑或有向哈密頓回路，最終找出有向鏈，鏈頭表示第1名，鏈尾表示最后1名，從而可以對球隊(duì)進(jìn)行排序。再在隨機(jī)情況下，用極大似然法，結(jié)合各種參考細(xì)節(jié)，對球隊(duì)獲勝的概率進(jìn)行估計(jì)，把估計(jì)所得的概率作為確定弧的權(quán)重的參考，根據(jù)權(quán)重結(jié)合確定型情況下球隊(duì)的排序方法對隨機(jī)比賽的球隊(duì)進(jìn)行排序，從而籃球隊(duì)排序問題得到較好的解決。
關(guān)鍵詞：競賽圖；有向哈密頓路徑；哈密頓回路；極大似然估計(jì)
Abstract
This paper attempts to range the basketball teams with the theoretical basis of graph theory. The author takes the scores of the teams as random variables and establishes the random model. Under the condition of determinacy, we take the participating teams as the nodes and represent the results of the matches with arcs and directly or indirectly form the tournament graph. With the guiding of the theory, we first find out the directed Hamilton path or the Hamilton cycles and then find out the directed chains, the head of which represents the first place and the end of which the last place. Through this process we can ultimately range the team. Under the random condition, we can estimate the winning probabilities of the teams with the method of maximal plausibility combined with vary of concerned details. Then we take the estimated probabilities as the weightings of arcs. In the last place, we can range the random participating teams by taking into consideration the weightings combined with the method of ranging under the condition of determinacy. Through this way, the ranging problem of the basketball teams can be well settled.
Key words: tournament graph; directed Hamilton path; Hamilton cycles; maximal plausibility
前言
籃球運(yùn)動是以投籃為中心的對抗性運(yùn)動，籃球運(yùn)動的復(fù)雜多變以及激烈對抗等特點(diǎn)，能夠培養(yǎng)人的勇敢果斷、積極進(jìn)取的意志品質(zhì)�；@球運(yùn)動的問世，是球類游戲的高級發(fā)展，深受廣大群眾的喜愛，經(jīng)常開展此項(xiàng)運(yùn)動，對豐富業(yè)余文化生活，促進(jìn)身心健康，提高工作和學(xué)習(xí)效率都起著積極作用。目前籃球比賽采用了比較科學(xué)的評分規(guī)則，1般采用積分制，但由于籃球比賽結(jié)果有較大的隨機(jī)性且籃球比賽結(jié)果不具有傳遞性，因此研究籃球隊(duì)排名次是1個10分有意義的問題。本文結(jié)合圖論和概率論知識從另1個角度提出1種籃球隊(duì)排名次的方法。在現(xiàn)有的排名規(guī)則下對籃球隊(duì)排名進(jìn)行1些合理的細(xì)化和設(shè)想。從而實(shí)現(xiàn)籃球隊(duì)排名方式的可行性創(chuàng)新。具體做法是把球隊(duì)比賽成績看成隨機(jī)變量，建立隨機(jī)模型。從圖論的觀點(diǎn)出發(fā)，結(jié)點(diǎn)表示球隊(duì)，帶箭頭的弧表示比賽的勝負(fù)，構(gòu)造競賽圖，根據(jù)理論從競賽圖中找出有向鏈，從而得出確定型情況下球隊(duì)的排名。再采用極大似然法得出球隊(duì)隨機(jī)情況下的名次，從而為籃球隊(duì)排名次提出另1種比較科學(xué)的方法。
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