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最小的空椅子數量 1

Barbara Streisand原創: 2024-10-14 16:38:31437瀏覽

The Number of the Smallest Unoccupied Chair 1

1942 年。最小的空閒椅子的數量

難度：中

主題：陣列、雜湊表、堆疊（優先權佇列）

有一個聚會，有 n 個朋友參加，編號從 0 到 n - 1。該聚會中有無限數量的椅子，編號從 0 到無限大。當朋友到達聚會時，他們會坐在人數最少的空閒椅子上。

例如，如果有朋友來時0、1、5號椅子被佔用，則他們將坐在2號椅子上。

當朋友離開聚會時，他們的椅子在他們離開的那一刻就空了。如果另一個朋友同時到達，他們可以坐在那張椅子上。

給定一個0 索引 2D 整數數組times，其中times[i] = [arrival_i, left_i]，表示到達和分別是第i^th 個朋友的離開時間，以及一個整數targetFriend。所有到達時間不同。

回傳編號為 targetFriend 的朋友將坐的椅子編號。

範例1：

輸入： 次 = [[1,4],[2,3],[4,6]], targetFriend = 1
輸出： 1
說明：
- 朋友 0 在時間 1 到達並坐在椅子 0 上。
- 朋友 1 在時間 2 到達並坐在椅子 1 上。
- 朋友 1 在時間 3 離開，椅子 1 空了。
- 朋友 0 在時間 4 離開，椅子 0 空了。
- 朋友 2 在時間 4 到達並坐在椅子 0 上。由於朋友 1 坐在椅子 1 上，所以我們回到 1。

範例2：

輸入： 次 = [[3,10],[1,5],[2,6]], targetFriend = 0
輸出： 2
說明：
- 朋友 1 在時間 1 到達並坐在椅子 0 上。
- 朋友 2 在時間 2 到達並坐在椅子 1 上。
- 朋友 0 在時間 3 到達並坐在椅子 2 上。
- 朋友 1 在時間 5 離開，椅子 0 空了。
- 朋友 2 在時間 6 離開，椅子 1 空了。
- 朋友 0 在時間 10 離開，椅子 2 空了。由於朋友 0 坐在椅子 2 上，所以我們回到 2。

範例 3：

輸入：

   times = [[33889,98676],[80071,89737],[44118,52565],[52992,84310],[78492,88209],[21695,67063],[84622,95452],[98048,98856],[98411,99433],[55333,56548],[65375,88566],[55011,62821],[48548,48656],[87396,94825],[55273,81868],[75629,91467]], 
  targetFriend = 6

輸出： 2

範例 4：

輸入：

    times = [[4435,4436],[2958,2959],[743,744],[3439,3440],[5872,5873],[2507,2508],[3809,3810],[5084,5085],[6509,6510],[7740,7741],[1189,1190],[1277,1278],[7655,7656],[3229,3230],[4527,4528],[2242,2243],[1933,1934],[3348,3349],[6063,6064],[5344,5345],[5708,5709],[4439,4440],[4596,4597],[7572,7573],[330,331],[5153,5154],[2777,2778],[2127,2128],[7024,7025],[6983,6984],[2313,2314],[5961,5962],[7141,7142],[6150,6151],[1011,1012],[2146,2147],[1367,1368],[6741,6742],[64,65],[841,842],[6973,6974],[5002,5003],[2029,2030],[6131,6132],[947,948],[81,82],[2331,2332],[3740,3741],[1486,1487],[6176,6177],[3000,3001],[2805,2806],[6278,6279],[5273,5274],[660,661],[4833,4834],[8293,8294],[7490,7491],[2628,2629],[4032,4033],[5403,5404],[8062,8063],[5043,5044],[6038,6039],[3977,3978],[7045,7046],[1161,1162],[63,64],[2013,2014],[2400,2401],[5947,5948],[4563,4564],[6593,6594],[114,115],[2566,2567],[5297,5298],[8069,8070],[1675,1676],[1746,1747],[7713,7714],[4814,4815],[7651,7652],[6304,6305],[5638,5639],[5881,5882],[1761,1762],[3250,3251],[4391,4392],[1800,1801],[1136,1137],[6489,6490],[556,557],[3729,3730],[7901,7902],[7866,7867],[8312,8313],[1785,1786],[6200,6201],[4469,4470],[5619,5620],[4732,4733],[8039,8040],[4670,4671],[4558,4559],[8076,8077],[3743,3744],[4839,4840],[418,419],[3764,3765],[1118,1119],[3442,3443],[4605,4606],[6806,6807],[179,180],[7753,7754],[1321,1322],[6133,6134],[2456,2457],[6385,6386],[1584,1585],[6111,6112],[5156,5157],[2930,2931],[927,928],[710,711],[501,502],[2308,2309],[1971,1972],[5560,5561],[6216,6217],[5779,5780],[7486,7487],[5750,5751],[6462,6463],[2796,2797],[1543,1544],[6411,6412],[831,832],[5540,5541],[5981,5982],[3925,3926],[199,200],[8332,8333],[7338,7339],[5528,5529],[4962,4963],[3102,3103],[2063,2064],[255,256],[4317,4318],[2207,2208],[1996,1997],[1409,1410],[5095,5096],[7212,7213],[674,675],[2321,2322],[2571,2572],[4678,4679],[5542,5543],[6126,6127],[5270,5271],[6373,6374],[5856,5857],[353,354],[4295,4296],[8216,8217],[6102,6103],[7374,7375],[1578,1579],[3779,3780],[1015,1016],[5278,5279],[2320,2321],[6854,6855],[1722,1723],[1706,1707],[6310,6311],[3080,3081],[3520,3521],[6321,6322],[4505,4506],[4145,4146],[3026,3027],[5105,5106],[3284,3285],[1817,1818],[4374,4375],[4891,4892],[1640,1641],[5057,5058],[1152,1153],[7393,7394],[745,746],[8204,8205],[8321,8322],[7775,7776],[5796,5797],[2626,2627],[3991,3992],[3565,3566],[3671,3672],[6487,6488],[1592,1593],[1144,1145],[5966,5967],[1443,1444],[8224,8225],[1803,1804],[2046,2047],[3586,3587],[1162,1163],[3201,3202],[3783,3784],[6890,6891],[1695,1696],[155,156],[7390,7391],[8173,8174],[5515,5516],[3704,3705],[5422,5423],[4458,4459],[6899,6900],[2169,2170],[1555,1556],[1370,1371],[6224,6225],[7695,7696],[2369,2370],[1560,1561],[1445,1446],[2987,2988],[8114,8115],[673,674],[111,112],[5395,5396],[7122,7123],[1178,1179],[6485,6486],[5101,5102],[62,63],[1345,1346],[3386,3387],[2851,2852],[4294,4295],[5702,5703],[256,257],[7196,7197],[2587,2588],[4850,4851],[2293,2294],[7654,7655],[3251,3252],[5506,5507],[3583,3584],[7467,7468],[6560,6561],[6747,6748],[1240,1241],[7933,7934],[3237,3238],[7539,7540],[4903,4904],[409,410],[2261,2262],[6335,6336],[5310,5311],[2938,2939],[2565,2566],[7909,7910],[3418,3419],[278,279],[3253,3254],[6954,6955],[1582,1583],[898,899],[7749,7750],[4865,4866],[2713,2714],[3320,3321],[1737,1738],[4504,4505],[5339,5340],[2002,2003],[7453,7454],[8145,8146],[2200,2201],[3889,3890],[4155,4156],[513,514],[2335,2336],[874,875],[3055,3056],[7335,7336],[790,791],[7653,7654],[4806,4807],[2526,2527],[5168,5169],[1190,1191],[870,871],[2082,2083],[2756,2757],[4408,4409],[6135,6136],[5137,5138],[7000,7001],[1513,1514],[5991,5992],[291,292],[8218,8219],[8297,8298],[3582,3583],[3578,3579],[4497,4498],[731,732],[6307,6308],[3272,3273],[8197,8198],[77,78],[3389,3390],[2586,2587],[8155,8156],[8067,8068],[3658,3659],[1885,1886],[3631,3632],[1449,1450],[5850,5851],[306,307],[4711,4712],[3195,3196],[6623,6624],[6154,6155],[497,498],[3717,3718],[918,919],[3493,3494],[4436,4437],[2114,2115],[5575,5576],[6764,6765],[5600,5601],[1710,1711],[432,433],[143,144],[7482,7483],[1622,1623],[627,628],[7316,7317],[5421,5422],[6229,6230],[2136,2137],[7038,7039],[2306,2307],[3379,3380],[6253,6254],[2989,2990],[689,690],[6189,6190],[3533,3534],[476,477],[4241,4242],[5534,5535],[6768,6769],[3661,3662],[7,8],[785,786],[5756,5757],[7310,7311],[1472,1473],[7442,7443],[2715,2716],[20,21],[123,124],[1446,1447],[818,819],[6563,6564],[4941,4942],[1320,1321],[506,507],[346,347],[2011,2012],[2366,2367],[3241,3242],[104,105],[5454,5455],[130,131],[1601,1602],[1275,1276],[5520,5521],[4323,4324],[6612,6613],[3265,3266],[5312,5313],[4680,4681],[8286,8287],[1906,1907],[6341,6342],[2020,2021],[6916,6917],[3673,3674],[5025,5026],[6756,6757],[4320,4321],[7215,7216],[4047,4048],[580,581],[7121,7122],[6690,6691],[3183,3184],[863,864],[2411,2412],[7776,7777],[4429,4430],[5510,5511],[7689,7690],[3984,3985],[4425,4426],[8162,8163],[4682,4683],[4006,4007],[6069,6070],[3275,3276],[4106,4107],[5818,5819],[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13],[6050,6051],[293,294],[5119,5120],[207,208],[3759,3760],[6246,6247],[2596,2597],[3649,3650],[1527,1528],[92,93],[1606,1607],[4090,4091],[313,314],[3341,3342],[3259,3260],[2203,2204],[7954,7955],[7509,7510],[2342,2343],[6212,6213],[3760,3761],[6876,6877],[5602,5603],[2139,2140],[5982,5983],[1833,1834],[4417,4418],[4084,4085],[3036,3037],[6107,6108],[1387,1388],[6280,6281],[7052,7053],[6881,6882],[1331,1332],[8165,8166],[6528,6529],[5387,5388],[5364,5365],[3630,3631],[7129,7130],[1575,1576],[7894,7895],[7726,7727],[7814,7815],[3311,3312],[6059,6060],[7428,7429],[762,763],[2561,2562],[3922,3923],[5204,5205],[635,636],[6969,6970],[2865,2866],[8096,8097],[8324,8325],[2017,2018],[7367,7368],[5975,5976],[4275,4276],[8134,8135],[2086,2087],[8264,8265],[2117,2118],[5693,5694],[4924,4925],[4936,4937],[3416,3417],[3664,3665],[2692,2693],[7815,7816],[2606,2607],[2833,2834],[6330,6331],[6645,6646],[8176,8177],[1198,1199],[479,480],[7239,7240],[415,416],[3100,3101],[3867,3868],[2151,2152],[8125,8126],[5472,5473],[3144,3145],[5271,5272],[4759,4760],[6891,6892],[4996,4997],[4975,4976],[405,406],[1459,1460],[3838,3839],[1465,1466],[4568,4569],[3345,3346],[6753,6754],[6633,6634],[8019,8020],[7593,7594],[6179,6180],[6827,6828],[3942,3943],[4751,4752],[7892,7893],[2906,2907],[5110,5111],[5636,5637],[5777,5778],[1487,1488],[4813,4814],[5995,5996],[1018,1019],[1004,1005],[440,441],[6670,6671],[5244,5245],[3186,3187],[980,981],[5000,5001],[4410,4411],[5690,5691],[3314,3315],[3654,3655],[3602,3603],[7470,7471],[1927,1928],[3113,3114],[3194,3195],[7871,7872],[1705,1706],[1210,1211],[1404,1405],[6851,6852],[2687,2688],[2738,2739],[7256,7257],[56,57],[7524,7525],[4109,4110],[6159,6160],[6177,6178],[3196,3197],[8290,8291],[2534,2535],[7952,7953],[2162,2163],[6058,6059],[1488,1489],[5696,5697],[4405,4406],[5100,5101],[326,327],[5062,5063],[7882,7883],[2665,2666],[3974,3975],[7799,7800],[2420,2421],[7295,7296],[1406,1407],[3040,3041],[5768,5769],[6606,6607],[2554,2555],[3893,3894],[4824,4825],[5132,5133],[2724,2725],[101,102],[7878,7879],[4225,4226],[10,11],[1583,1584],[3169,3170],[7907,7908],[849,850],[1621,1622],[5965,5966],[6262,6263],[1353,1354],[916,917],[7877,7878],[1652,1653],[7924,7925],[4018,4019],[6804,6805],[3910,3911],[2505,2506],[3864,3865],[4847,4848],[5822,5823],[4604,4605],[3408,3409],[4154,4155],[3492,3493],[7382,7383],[2501,2502],[1694,1695],[612,613],[6568,6569],[5532,5533],[7178,7179],[1605,1606],[1909,1910],[6976,6977],[5815,5816],[8043,8044],[4948,4949],[5189,5190],[2389,2390],[1867,1868],[1492,1493],[3456,3457],[4137,4138],[3512,3513],[1249,1250],[7783,7784],[840,841],[7457,7458],[5635,5636],[6598,6599],[8267,8268],[6265,6266],[8050,8051],[3261,3262],[909,910],[796,797],[1067,1068],[2829,2830],[4271,4272],[1183,1184],[4749,4750],[1777,1778],[3660,3661],[6228,6229],[1373,1374],[7464,7465],[3544,3545],[2891,2892],[6119,6120],[5612,5613],[3313,3314],[5895,5896],[7968,7969],[324,325],[6924,6925],[2699,2700],[2847,2848],[6636,6637],[6283,6284],[8029,8030],[5492,5493],[7735,7736],[8306,8307],[4268,4269]], 
  targetFriend = 4519

輸出： 0

範例 5：

輸入：

    times = [[4,5],[12,13],[5,6],[1,2],[8,9],[9,10],[6,7],[3,4],[7,8],[13,14],[15,16],[14,15],[10,11],[11,12],[2,3],[16,17]], 
  targetFriend = 15

輸出： 0

範例 6：

輸入：

    times = 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
targetFriend = 8916

輸出： 2235

範例7：

輸入：

    times = 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
  targetFriend = 2145

輸出： 9998

範例 8：

輸入：

    times = 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86,55036],[53984,80137],[53844,72029],[33738,73258],[80111,82629],[65507,67509],[52494,92626],[18332,82791],[67015,99477],[86680,91871],[21368,41390],[32123,42273],[58643,79347],[87701,96330],[26985,86069],[49328,65131],[31341,55675],[81660,83840],[28679,32325],[62646,71476],[57622,65773],[27028,30375],[9056,48649],[77773,80473],[272,34726],[75285,96308],[9017,61836],[87434,97212],[89037,93199],[16034,64371],[57108,85908],[45755,60381],[32035,61080],[51690,85926],[29145,30888],[44648,96814],[53160,77292],[87022,97089],[73592,74991],[30938,39313],[49489,97856],[69620,91040],[1011,18077],[84392,85070],[87272,94231],[16335,93002],[49364,60041],[28710,56180],[59052,83621],[27686,79269],[74416,90928],[87357,92766],[80774,87802],[14076,90746],[94339,99332],[75763,86596],[63383,93769],[59895,73139],[83540,88443],[96623,99150],[69150,78386],[61429,67945],[13919,14015],[39728,64230],[76180,81498],[91780,99729],[86548,96274],[63234,67411],[84270,96047],[40285,66600],[13748,24491],[4312,62378],[38226,58094],[42589,84335],[32568,37037],[4737,68165],[81276,90528],[11229,88057],[28774,78938],[92910,97647],[43287,46058],[39620,46487],[77929,94902],[36157,44786],[68495,93186],[27447,46666],[44783,56524],[39702,93491],[7791,32096],[86498,97564],[94954,95205],[80138,83000],[24697,96806],[96591,99575],[24198,75648],[29049,96667],[73627,76349],[35714,68834],[45866,71800],[20923,62307],[47528,81140],[50537,91615],[32054,61642],[79662,95219],[50106,84006],[94468,95076],[53176,93717],[13375,66767],[32381,87250],[26756,96235],[69469,74822],[34224,49015],[85980,97996],[35221,68853],[55624,86046],[15042,16664],[94595,96418],[43974,92547],[85189,91509],[96348,99366],[22357,78119],[59320,66960],[86399,92181],[20131,60347],[40743,62120],[36257,76302],[99944,99945],[89604,90347],[48381,75857],[31929,37570],[47785,96032],[42848,66985],[51979,89937],[93165,95468],[72549,75195],[10705,34954],[62236,85752],[12842,24323],[60274,71433],[60790,81470],[74453,97975],[85539,99189],[55379,87354],[72712,99647],[67369,97492],[10359,25025],[34167,64858],[97297,97695],[39325,80268],[24046,89216],[70660,89661],[10346,65711],[97703,98757],[72019,81633],[67881,85499],[38989,45535],[30462,51983],[93420,99013],[81852,89801],[23592,84614],[25322,50101],[71411,96166],[80823,93814],[52807,85935],[49200,71161],[89104,91384],[93268,96483],[99864,99874],[5544,83853],[30805,61641],[10341,61439],[46482,74062],[76637,97125],[10024,12036],[30514,83647],[68939,94235],[48084,89459],[16998,82805],[90274,98154],[533,43354],[27316,61628],[65682,69511],[13705,52980],[37807,80290],[2169,36901],[36046,84215],[23199,69856],[22639,63704],[60598,80014],[57538,81494],[48430,55677],[85105,93377],[15868,88183],[15006,42307],[50325,99723],[67893,69296],[64088,64973],[22791,94011],[47247,59178],[77072,87094],[85238,95248],[19315,39650],[55335,87588],[92684,93604],[27018,62313],[61370,93303],[83505,94290],[9855,66263],[28804,56949],[34360,85936],[57324,99024],[73707,98170],[85546,89725],[49480,83039],[5331,49757],[17281,62338],[85043,88187],[49658,67659],[71593,89875],[78597,83263],[67735,73518],[28502,44035],[91999,93977],[74107,92145],[42234,68754],[34683,42127],[83903,97296],[20905,70688],[85520,92607],[74663,93556],[11751,61642],[57528,73186],[19444,28262],[13297,87392],[70579,92875],[37935,44350],[13758,89781],[51884,84491],[96215,99733],[229,2029],[85371,96934],[11118,80772],[94288,98680],[1191,10224],[26534,55573],[69549,95592],[54766,62266],[33669,34271],[88876,88928],[18933,66247],[763,21777],[99921,99968],[56767,79229],[80269,98879],[17193,47571],[65085,91969],[10164,80635],[54031,74963],[59540,95484],[3048,26407],[77022,98224],[48022,72115],[67393,70805],[92986,94959],[72203,80462],[86317,87659],[70582,72108],[1918,63103],[73575,82849],[56530,87778],[64256,77416],[1711,55738],[90032,92781],[21243,49960],[68833,92535],[74307,87866],[83064,95162],[28616,56840]], 
  targetFriend = 2304

輸出： 2027

約束：

n == times.length
2 4
times[i].length == 2
1 5
0
每次到達_i時間都不同。

提示：

依到達時間排序。
對於每次到達_i，找到最小的空閒椅子並將其標記為已佔用，直到離開_i。

解：

我們需要模擬朋友在派對上的到達和離開，並管理最小的可用椅子的分配。以下是逐步方法：

方法：

依到達時間排序：
- 根據到達時間對時間數組進行排序。
- 這有助於按照朋友到達的順序處理他們。
使用優先權佇列（最小堆）:
- 使用最小堆來管理未佔用的椅子（availableChairs）。
- 使用另一個最小堆來追蹤佔用的椅子及其釋放時間（佔用的椅子）。
迭代排序時間:
- For each friend's arrival:
  - Free up chairs of friends who have already left by comparing the current time to the friends' departure times. Move those chairs back to availableChairs.
  - Assign the smallest available chair (from availableChairs) to the arriving friend. If no chairs are free, assign the next smallest unused chair.
  - Push this chair and the friend's leaving time into occupiedChairs.
Track Target Friend's Chair:
- When the targetFriend arrives, record the chair assigned to them.
Edge Cases:
- Consider cases where multiple friends arrive at the same time.
- Ensure that the smallest chair is always assigned.

Let's implement this solution in PHP: 1942. The Number of the Smallest Unoccupied Chair

<?php
/**
 * @param Integer[][] $times
 * @param Integer $targetFriend
 * @return Integer
 */
function smallestChair($times, $targetFriend) {
    ...
    ...
    ...
    /**
     * go to ./solution.php
     */
}

// Example usage:
$cost1 = [[15, 96], [36, 2]];
$cost2 = [[1, 3, 5], [4, 1, 1], [1, 5, 3]];
$cost3 = [[2, 5, 1], [3, 4, 7], [8, 1, 2], [6, 2, 4], [3, 8, 8]];

// Example usage:
$times1 = [[1, 4], [2, 3], [4, 6]];
$targetFriend1 = 1;
echo smallestChair($times1, $targetFriend1);  // Output: 1

$times2 = [[3, 10], [1, 5], [2, 6]];
$targetFriend2 = 0;
echo smallestChair($times2, $targetFriend2);  // Output: 2
?>

Explanation:

Sorting ensures friends are processed in order of their arrival times.
Using a min-heap for available chairs allows us to always assign the smallest unoccupied chair.
Occupied chairs heap helps track when friends leave, making their chairs available again.
When the targetFriend arrives, we directly return the chair assigned to them.

Complexity:

Time Complexity: O(n log n), primarily due to sorting the times array and managing the heaps.
Space Complexity: O(n), for storing chairs in the heaps.

This solution efficiently handles the assignment of chairs, ensuring that each friend gets the smallest available chair, and accurately tracks when chairs become available again.

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