最小的空椅子数量 1

1942 年。最小的空闲椅子的数量

难度：中等

主题：数组、哈希表、堆（优先级队列）

有一个聚会，有 n 个朋友参加，编号从 0 到 n - 1。该聚会中有 无限 数量的椅子，编号从 0 到无穷大。当朋友到达聚会时，他们会坐在人数最少的空闲椅子上。

• 例如，如果有朋友来时0、1、5号椅子被占用，则他们将坐在2号椅子上。

当朋友离开聚会时，他们的椅子在他们离开的那一刻就空了。如果另一个朋友同时到达，他们可以坐在那张椅子上。

给定一个 0 索引 2D 整数数组 times，其中 times[i] = [arrival_i, left_i]，表示到达和分别是第 i^th 个朋友的离开时间，以及一个整数 targetFriend。所有到达时间不同。

返回编号为 targetFriend 的朋友将坐的椅子编号。

示例1：

• 输入： 次 = [[1,4],[2,3],[4,6]], targetFriend = 1
• 输出： 1
• 说明：
  • 朋友 0 在时间 1 到达并坐在椅子 0 上。
  • 朋友 1 在时间 2 到达并坐在椅子 1 上。
  • 朋友 1 在时间 3 离开，椅子 1 空了。
  • 朋友 0 在时间 4 离开，椅子 0 空了。
  • 朋友 2 在时间 4 到达并坐在椅子 0 上。 由于朋友 1 坐在椅子 1 上，所以我们返回 1。

示例2：

• 输入： 次 = [[3,10],[1,5],[2,6]], targetFriend = 0
• 输出： 2
• 说明：
  • 朋友 1 在时间 1 到达并坐在椅子 0 上。
  • 朋友 2 在时间 2 到达并坐在椅子 1 上。
  • 朋友 0 在时间 3 到达并坐在椅子 2 上。
  • 朋友 1 在时间 5 离开，椅子 0 空了。
  • 朋友 2 在时间 6 离开，椅子 1 空了。
  • 朋友 0 在时间 10 离开，椅子 2 空了。 由于朋友 0 坐在椅子 2 上，所以我们返回 2。

示例 3：

• 输入：

   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

• 输出： 2

示例 4：

• 输入：

    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

• 输出： 0

示例 5：

• 输入：

    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

• 输出： 0

示例 6：

• 输入：

    times = 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
targetFriend = 8916

• 输出： 2235

示例7：

• 输入：

    times = 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
  targetFriend = 2145

• 输出： 9998

示例 8：

• 输入：

    times = 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
  targetFriend = 2304

• 输出： 2027

约束：

• n == times.length
• 2 4
• times[i].length == 2
• 1 5
• 0
• 每次到达_i时间都不同。

提示：

1. 按到达时间排序。
2. 对于每次到达_i，找到最小的空闲椅子并将其标记为已占用，直到离开_i。

解决方案：

我们需要模拟朋友在聚会上的到达和离开，并管理最小的可用椅子的分配。以下是分步方法：

方法：

1. 按到达时间排序：

   • 根据到达时间对时间数组进行排序。
   • 这有助于按照朋友到达的顺序处理他们。

2. 使用优先级队列（最小堆）:

   • 使用最小堆来管理未占用的椅子（availableChairs）。
   • 使用另一个最小堆来跟踪占用的椅子及其释放时间（占用的椅子）。

3. 迭代排序时间:

   • 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.

4. Track Target Friend's Chair:

   • When the targetFriend arrives, record the chair assigned to them.

5. 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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