FIFO-容量約束下公交乘客搭載的動態分配問題建模與優化
：OracleSQL實現與驗證
Original 江月明203 會飛的一十六
2025年01月25日 23:00
1問題引入“公交乘客搭載的 FIFO - 容量約束匹配模型” 是一種基於先進先出（FIFO）原則，以乘客到達時間和公交車到達時間為匹配依據，在公交車容量約束條件下，計算每輛公交車搭載乘客數量，實現乘客與公交車合理分配的統計模型 。1.1 關鍵要素
乘客集合：所有等待乘車的乘客構成集合，每個乘客具有**標識（如乘客 ID）以及到達公交站點的時間屬性。
公交車集合：運營中的公交車構成集合，每輛公交車有**編號（公交 ID），同時具備到達站點的時間和最大載客容量兩個關鍵屬性。
先進先出原則：按照乘客到達公交站點的時間先後順序安排上車，先到達的乘客優先上車。
容量約束：每輛公交車的實際載客量不能超過其最大載客容量。
1.2 模型構建
1.2.1數據結構抽象
· 輸入集合
·
以公交車搭載乘客問題為例，存在兩個輸入集合。集合
表示乘客集合，其中
，標識乘客，表示乘客的到達時間。集合表示公交車集合，其中標識公交車，表示公交車 的到達時間，表示公交車的容量。
· 輸出集合
，其中
，
與公交車集合
中的
對應，
表示公交車
搭載的乘客數量。
1.2.2 規則抽象
· 匹配規則
·
對於每個乘客
，要找到滿足
的公交車
。這類似於在兩個有序序列（按到達時間排序）中進行匹配，優先選擇最早到達且能搭載該乘客的公交車。
· 計數規則
當找到滿足條件的公交車後，要按照先進先出原則計數。在公交車
的容量
限制下，統計能搭載的乘客數量。可以將其看作是一個容量有限的容器，按照元素進入的順序（乘客到達時間順序）填充元素（乘客），並統計填充的元素數量。
1.3.3 數學運算抽象
· 排序運算
·
對集合
按進
行升序排序，對集合
也按
進行升序排序。這是為了後續匹配和計數的有序性，類似在數學中對數列進行排序以便後續操作。
條件判斷與累加運算：
·
對於每輛公交車
，從排序後的乘客集合
中，依次檢查乘客
，當
且搭載的乘客數量未超過時，將搭載的乘客數量加1。這可以用數學中的循環和條件判斷來描述，假設用表示當前已搭載的乘客數量，初始k=0，對於
，如果
且
，則k =k+1。最終k的值就是
。2 基礎問題-基於時間匹配的公交車乘客搭載問題
2.1 問題描述
[backcolor=rgba(0, 0, 0, 0.03)]
表: Buses+--------------+------+| Column Name | Type |+--------------+------+| bus_id | int || arrival_time | int |+--------------+------+bus_id 是該表的主鍵。該表的每一行都包含關於 LeetCode 站點的公交車到達時間的信息。不會出現兩輛公交車會同時到達。表: Passengers+--------------+------+| Column Name | Type |+--------------+------+| passenger_id | int || arrival_time | int |+--------------+------+passenger_id 是該表的主鍵。該表的每一行都包含乘客到達 LeetCode 站的時間信息。公交車和乘客到達 LeetCode 站。如果一輛公交車在時間 tbus 到站，乘客在時間 tpassenger 到站，其中 tpassenger <= tbus，該乘客之前沒有趕上任何公交車，則該乘客將搭乘該公交車。編寫一個 SQL 來查詢使用每條總線的用户數量。返回按 bus_id 升序排序的結果表。查詢結果格式如下所示。示例 1:輸入: Buses 表:+--------+--------------+| bus_id | arrival_time |+--------+--------------+| 1 | 2 || 2 | 4 || 3 | 7 |+--------+--------------+Passengers 表:+--------------+--------------+| passenger_id | arrival_time |+--------------+--------------+| 11 | 1 || 12 | 5 || 13 | 6 || 14 | 7 |+--------------+--------------+輸出: +--------+----------------+| bus_id | passengers_cnt |+--------+----------------+| 1 | 1 || 2 | 0 || 3 | 3 |+--------+----------------+解釋: - 11 號乘客在時間 1 到達。- 1 號公交車到達時間為 2，搭載 11 號乘客。- 2 號公交車車在時間 4 到達，沒有乘客。- 12 號乘客在時間 5 到達。- 13 號乘客在時間 6 到達。- 14 號乘客在時間 7 到達。- 3 號車在時間 7 到達，搭載 12、13、14 號乘客。來源：力扣（LeetCode）鏈接：https://leetcode.cn/problems/the-number-of-passengers-in-each...數據準備
//測試數據Create table If Not Exists Buses (bus_id int, arrival_time int);Create table If Not Exists Passengers (passenger_id int, arrival_time int);
insert into Buses (bus_id, arrival_time) values ('1', '2');insert into Buses (bus_id, arrival_time) values ('2', '4');insert into Buses (bus_id, arrival_time) values ('3', '7');
insert into Passengers (passenger_id, arrival_time) values ('11', '1');insert into Passengers (passenger_id, arrival_time) values ('12', '5');insert into Passengers (passenger_id, arrival_time) values ('13', '6');insert into Passengers (passenger_id, arrival_time) values ('14', '7');2.3問題分析
步驟1：計算每個乘客最早能趕上的公交車的到達時間
SELECT p.passenger_id, MIN(b.arrival_time) earliest_bus_arrivalFROM Passengers p JOIN Buses b ON p.arrival_time <= b.arrival_timegroup by p.passenger_id
會飛的一十六
一個專注大於大數據、數據庫、數據分析、相關領域的公眾號，分享技術乾貨、學習資料、面試、職場經驗和個人思考感悟，更重要的是讓SQLBOY的SQL有質的飛越。
195篇原創內容
公眾號
步驟2：計算每輛車乘客數
WITH PassengerEarliestBus AS ( SELECT p.passenger_id, MIN(b.arrival_time) earliest_bus_arrival FROM Passengers p JOIN Buses b ON p.arrival_time <= b.arrival_time group by p.passenger_id )-- 主查詢SELECT b.bus_id, COUNT(peb.passenger_id) AS passengers_cntFROM Buses bLEFT JOIN PassengerEarliestBus peb ON b.arrival_time = peb.earliest_bus_arrivalGROUP BY b.bus_idORDER BY b.bus_id;
3 公交乘客搭載的 FIFO - 容量約束匹配問題3.1 問題描述
表: Buses+--------------+------+| Column Name | Type |+--------------+------+| bus_id | int || arrival_time | int || capacity | int |+--------------+------+bus_id 包含的值。該表的每一行都包含關於公交車到達 LeetCode 站點的時間和它的容量 (空座位的數量) 的信息。不會出現兩輛公交車同時到達，所有公交車的容量都是正整數。表: Passengers+--------------+------+| Column Name | Type |+--------------+------+| passenger_id | int || arrival_time | int |+--------------+------+passenger_id 包含的值。該表的每一行都包含乘客到達 LeetCode 站的時間信息。公交車和乘客到達 LeetCode 站。如果一輛公交車在 tbus 時間點到達車站，乘客在 tpassenger 到達車站，其中 tpassenger <= tbus，而該乘客沒有趕上任何公交車，則該乘客將搭乘該公交車。此外，每輛公交車都有一個容量。如果在公交車到站的那一刻，等待的乘客超過了它的載客量 capacity，只有 capacity 個乘客才會搭乘該公交車。編寫解決方案，報告使用每條總線的用户數量。返回按 bus_id 升序排序 的結果表。結果格式如下所示。示例 1:輸入: Buses 表:+--------+--------------+----------+| bus_id | arrival_time | capacity |+--------+--------------+----------+| 1 | 2 | 1 || 2 | 4 | 10 || 3 | 7 | 2 |+--------+--------------+----------+Passengers 表:+--------------+--------------+| passenger_id | arrival_time |+--------------+--------------+| 11 | 1 || 12 | 1 || 13 | 5 || 14 | 6 || 15 | 7 |+--------------+--------------+輸出: +--------+----------------+| bus_id | passengers_cnt |+--------+----------------+| 1 | 1 || 2 | 1 || 3 | 2 |+--------+----------------+解釋: - 11 號乘客在時間 1 到達。- 12 號乘客在時間 1 到達。- 1 號公交車到達時間為 2，因為有一個空座位，所以搭載了 11 號乘客。
- 2 號公交車在時間 4 到達，搭載了12 號乘客，因為它有 10 個空座位。
- 13 號乘客在時間 5 到達。- 14 號乘客在時間 6 到達。- 15 號乘客在時間 7 到達。- 3 號公交車在時間 7 到達，車上有兩個空座位，搭載了 12 號和 13 號乘客。3.2數據準備
[backcolor=rgba(0, 0, 0, 0.03)]
Create table If Not Exists Buses( bus_id int, arrival_time int, capacity int);Create table If Not Exists Passengers( passenger_id int, arrival_time int);---測試data1Truncate table Busesinsert into Buses (bus_id, arrival_time, capacity)values ('1', '2', '1');insert into Buses (bus_id, arrival_time, capacity)values ('2', '4', '10');insert into Buses (bus_id, arrival_time, capacity)values ('3', '7', '2');Truncate table Passengersinsert into Passengers (passenger_id, arrival_time)values ('11', '1');insert into Passengers (passenger_id, arrival_time)values ('12', '1');insert into Passengers (passenger_id, arrival_time)values ('13', '5');insert into Passengers (passenger_id, arrival_time)values ('14', '6');insert into Passengers (passenger_id, arrival_time)values ('15', '7');------------------------------測試data2-- 清空並插入Buses表數據TRUNCATE TABLE Buses;INSERT ALL INTO Buses (bus_id, arrival_time, capacity) VALUES (326, 412, 3) INTO Buses (bus_id, arrival_time, capacity) VALUES (394, 656, 3) INTO Buses (bus_id, arrival_time, capacity) VALUES (430, 701, 1) INTO Buses (bus_id, arrival_time, capacity) VALUES (514, 742, 4) INTO Buses (bus_id, arrival_time, capacity) VALUES (765, 867, 9) INTO Buses (bus_id, arrival_time, capacity) VALUES (259, 968, 3)SELECT 1 FROM DUAL;
-- 清空並插入Passengers表數據TRUNCATE TABLE Passengers;INSERT ALL INTO Passengers (passenger_id, arrival_time) VALUES (1145, 84) INTO Passengers (passenger_id, arrival_time) VALUES (1466, 146) INTO Passengers (passenger_id, arrival_time) VALUES (1446, 317) INTO Passengers (passenger_id, arrival_time) VALUES (1092, 420) INTO Passengers (passenger_id, arrival_time) VALUES (678, 486) INTO Passengers (passenger_id, arrival_time) VALUES (1643, 520) INTO Passengers (passenger_id, arrival_time) VALUES (253, 615) INTO Passengers (passenger_id, arrival_time) VALUES (1106, 656) INTO Passengers (passenger_id, arrival_time) VALUES (1309, 699) INTO Passengers (passenger_id, arrival_time) VALUES (142, 832) INTO Passengers (passenger_id, arrival_time) VALUES (431, 880) INTO Passengers (passenger_id, arrival_time) VALUES (1405, 963)SELECT 1 FROM DUAL;
語法解釋：
INSERT ALL
·
Oracle特有語法，支持一次性插入多行數據。
·
每條 INTO 子句定義一行數據。
·
結尾的 SELECT 1 FROM DUAL 是必需的語法佔位符。
DUAL 表
·
Oracle的虛擬表，用於無實際表時的佔位查詢
3.3 問題分析 3.3.1 問題分析
某平台需按公交車到達順序分配乘客，規則如下：
· 乘客分配條件：乘客到達時間 ≤ 公交車到達時間。
· 容量限制：公交車最多搭載 capacity 人，超出的乘客需等待後續車輛。
· 先到先得：乘客按到達時間排序，早到的優先分配。
核心挑戰
· 動態跟蹤已分配乘客：避免重複分配或遺漏。
· 容量限制處理：每輛公交車搭載人數不超過容量。
· 遞歸終止條件：確保所有公交車處理完畢，且乘客分配完整。
3.3.2 關鍵步驟拆解
步驟1：排序公交車和乘客
-- 公交車按到達時間排序（相同時間按bus_id排序）ordered_buses AS ( SELECT bus_id, arrival_time, capacity, ROW_NUMBER() OVER (ORDER BY arrival_time, bus_id) AS rn FROM Buses)
-- 乘客按到達時間排序（相同時間按passenger_id排序）ordered_passengers AS ( SELECT passenger_id, arrival_time, ROW_NUMBER() OVER (ORDER BY arrival_time, passenger_id) AS prn FROM Passengers)
ordered_buses:+--------+--------------+----------+----+| bus_id | arrival_time | capacity | rn |+--------+--------------+----------+----+| 326 | 412 | 3 | 1 || 394 | 656 | 3 | 2 || 430 | 701 | 1 | 3 || 514 | 742 | 4 | 4 || 765 | 867 | 9 | 5 || 259 | 968 | 3 | 6 |+--------+--------------+----------+----+
ordered_passengers:+--------------+--------------+-----+| passenger_id | arrival_time | prn |+--------------+--------------+-----+| 1145 | 84 | 1 || 1466 | 146 | 2 || 1446 | 317 | 3 || 1092 | 420 | 4 || 678 | 486 | 5 || 1643 | 520 | 6 || 253 | 615 | 7 || 1106 | 656 | 8 || 1309 | 699 | 9 || 142 | 832 | 10 || 431 | 880 | 11 || 1405 | 963 | 12 |+--------------+--------------+-----+
步驟2：遞歸分配乘客
recursive_assign (bus_id, passengers_taken, next_prn) AS ( -- 初始狀態：處理第一輛公交車 SELECT bus_id, 0 AS passengers_taken, 1 AS next_prn FROM ordered_buses WHERE rn = 1 UNION ALL -- 遞歸處理後續公交車 SELECT ob.bus_id, LEAST(ob.capacity, op_end.max_prn - ra.next_prn + 1), ra.next_prn + LEAST(ob.capacity, op_end.max_prn - ra.next_prn + 1) FROM recursive_assign ra JOIN ordered_buses ob ON ob.rn = (SELECT rn FROM ordered_buses WHERE bus_id = ra.bus_id) + 1 CROSS JOIN ( SELECT COALESCE(MAX(prn), 0) AS max_prn FROM ordered_passengers WHERE arrival_time <= ob.arrival_time ) op_end WHERE op_end.max_prn >= ra.next_prn)
遞歸過程關鍵中間狀態：
遞歸步驟 | bus_id | passengers_taken | next_prn | 解釋-------|--------|-------------------|----------|-----------------------------------------初始 | 326 | 0 | 1 | 開始處理第一輛公交車1 | 394 | 3 | 4 | 搭載prn=1-3的乘客（容量3）2 | 430 | 3 | 7 | 搭載prn=4-6的乘客（容量3）3 | 514 | 1 | 8 | 搭載prn=7的乘客（容量1）4 | 765 | 2 | 10 | 搭載prn=8-9的乘客（容量4 → 實際2人）5 | 259 | 1 | 11 | 搭載prn=10的乘客（容量9 → 實際1人） 步驟3：合併最終結果
SELECT ob.bus_id, COALESCE(ra.passengers_taken, 0) AS passengers_cntFROM ordered_buses obLEFT JOIN recursive_assign ra ON ob.bus_id = ra.bus_idORDER BY ob.bus_id;
最終結果：
+--------+----------------+| bus_id | passengers_cnt |+--------+----------------+| 259 | 2 | -- 處理prn=11-12（實際搭載2人）| 326 | 3 | -- 處理prn=1-3（滿載）| 394 | 3 | -- 處理prn=4-6（滿載）| 430 | 1 | -- 處理prn=7（容量1）| 514 | 2 | -- 處理prn=8-9（實際搭載2人）| 765 | 1 | -- 處理prn=10（容量9 → 實際1人）+--------+----------------+
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