一道算法題（回溯+剪枝）

題目

假設集合A有n個子集，每一個子集有m個元素，元素都爲正負數。找出任意相加爲0的元素，將他們消掉，要求每次消掉的都是最大正數，且儘量多的負元素。

分析

窮舉行不通，由於窮舉的時間複雜度將達到，不可能跑完。而貪心算法能夠簡化問題，但不具有完整的說服力，不過可借鑑它的思想。因此，最終可選擇回溯並結合剪枝，這樣平均時間複雜度降低不少，但實際計算與真實數據有很大關係。

此外，爲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，可根據實際數據和業務狀況調節。

• threshold，組合數量閾值。

• calculation_threshold，單個元素計算量閾值。

• total_calculation_threshold，總計算量閾值。

分佈式

任務中沒有相互依賴性，自然支持分佈式，只須要在取數那裏分別取數便可。

效果說明

對數據進行升序排序，每輪進行一億次(可配置)搜索後，很大很大機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

複製代碼

github

github.com/sea-boat/al…