一道演算法題(回溯+剪枝)
假設集合A有n個子集,每個子集有m個元素,元素都為正負數。找出任意相加為0的元素,將他們消掉,要求每次消掉的都是最大正數,且儘可能多的負元素。
分析
窮舉行不通,因為窮舉的時間複雜度將達到,不可能跑完。而貪心演算法可以簡化問題,但不具備完整的說服力,不過可借鑑它的思想。所以,最終可選擇回溯並結合剪枝,這樣平均時間複雜度下降很多,但實際計算與真實資料有很大關係。
此外,為進一步解決計算量問題,且防止陷入無窮執行,引入三個閾值因子,可根據實際資料和業務情況調節。
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threshold,組合數量閾值。
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calculation_threshold,單個元素計算量閾值。
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total_calculation_threshold,總計算量閾值。
分散式
任務中沒有相互依賴性,天然支援分散式,只需要在取數那裡分別取數即可。
效果說明
對資料進行升序排序,每輪進行一億次(可配置)搜尋後,很大很大概率已經能準確找到最想要的答案,時間也能很好控制。
start time : 1544195518997 [0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 19, 19, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20, 21, 21, 22, 22, 22, 22, 23, 23, 24, 24, 25, 25, 25, 25, 25, 25, 26, 26, 26, 26, 26, 26, 27, 27, 27, 27, 27, 27, 27, 27, 27, 28, 28, 38] [28, 28, 28, 28, 28, 28, 29, 29, 29, 30, 30, 31, 31, 31, 31, 32, 32, 32, 32, 33, 33, 33, 33, 33, 34, 34, 34, 34, 34, 35, 35, 35, 35, 35, 35, 35, 35, 35, 36, 36, 37, 37, 37, 37, 37, 37, 38, 38, 38, 38, 38, 38, 61] [39, 39, 39, 40, 40, 40, 40, 40, 40, 40, 41, 41, 41, 41, 41, 41, 42, 42, 42, 42, 42, 42, 42, 42, 42, 43, 43, 44, 44, 44, 44, 44, 46, 46, 46, 46, 46, 47, 47, 49] [47, 47, 47, 47, 48, 48, 48, 48, 48, 48, 48, 48, 50, 50, 50, 50, 50, 51, 51, 52, 52, 52, 52, 52, 53, 53, 53, 53, 53, 53, 98] [53, 53, 53, 54, 54, 54, 54, 55, 55, 55, 55, 56, 56, 56, 56, 56, 56, 57, 57, 57, 57, 57, 58, 58, 69, 99] [58, 59, 59, 59, 59, 59, 59, 60, 60, 60, 61, 61, 61, 61, 62, 62, 62, 62, 62, 62, 63, 63, 66] [63, 63, 63, 63, 63, 64, 64, 64, 64, 64, 64, 64, 64, 65, 65, 65, 66, 66, 66, 80] [66, 66, 66, 66, 67, 67, 67, 68, 68, 68, 68, 69, 69, 69, 70, 87, 99] [71, 71, 71, 71, 71, 71, 71, 71, 72, 72, 72, 73, 73, 73, 97] end time : 1544195524950 counter :900000009 elapsed time : 5953ms 複製程式碼