MD ARIFUL HAQUE

Posted on Oct 11

1942. The Number of the Smallest Unoccupied Chair

#php #leetcode #algorithms #programming

Difficulty: Medium

Topics: Array, Hash Table, Heap (Priority Queue)

There is a party where n friends numbered from 0 to n - 1 are attending. There is an infinite number of chairs in this party that are numbered from 0 to infinity. When a friend arrives at the party, they sit on the unoccupied chair with the smallest number.

For example, if chairs 0, 1, and 5 are occupied when a friend comes, they will sit on chair number 2.

When a friend leaves the party, their chair becomes unoccupied at the moment they leave. If another friend arrives at that same moment, they can sit in that chair.

You are given a 0-indexed 2D integer array times where times[i] = [arrival_i, leaving_i], indicating the arrival and leaving times of the i^th friend respectively, and an integer targetFriend. All arrival times are distinct.

Return the chair number that the friend numbered targetFriend will sit on.

Example 1:

Input: times = [[1,4],[2,3],[4,6]], targetFriend = 1
Output: 1
Explanation:
- Friend 0 arrives at time 1 and sits on chair 0.
- Friend 1 arrives at time 2 and sits on chair 1.
- Friend 1 leaves at time 3 and chair 1 becomes empty.
- Friend 0 leaves at time 4 and chair 0 becomes empty.
- Friend 2 arrives at time 4 and sits on chair 0.\ Since friend 1 sat on chair 1, we return 1.

Example 2:

Input: times = [[3,10],[1,5],[2,6]], targetFriend = 0
Output: 2
Explanation:
- Friend 1 arrives at time 1 and sits on chair 0.
- Friend 2 arrives at time 2 and sits on chair 1.
- Friend 0 arrives at time 3 and sits on chair 2.
- Friend 1 leaves at time 5 and chair 0 becomes empty.
- Friend 2 leaves at time 6 and chair 1 becomes empty.
- Friend 0 leaves at time 10 and chair 2 becomes empty. Since friend 0 sat on chair 2, we return 2.

Example 3:

Input:

   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

Output: 2

Example 4:

Input:

    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

Output: 0

Example 5:

Input:

    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

Output: 0

Example 6:

Input:

    times = 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6,43445],[96390,98128],[79130,84102],[67953,79317],[3304,94712],[6100,81072],[60090,68651],[95592,98653],[91910,96484],[17483,27396],[68045,94109],[51713,55497],[66883,85207],[71812,90747],[55547,86170],[94084,98047],[78765,89656],[1851,85789],[89524,94770],[28382,39087],[94900,99751],[72288,97845],[41646,68287],[46607,99138],[40334,59877],[1933,33339],[53649,68575],[12717,55003],[11477,33554],[34959,99309],[78701,91719],[40710,87832],[58558,82954],[90330,97319],[82640,99908],[58282,62089],[27491,29638],[94358,96424],[93454,93509],[67979,92098],[65776,94287],[66977,79832],[43331,79353],[82368,93325],[77173,88510],[94389,95430],[52505,64972],[20478,90383],[10687,60099],[35150,75388],[29919,37196],[75941,85297],[9095,73943],[9777,53774],[63704,89242],[51630,90367],[23926,30973],[56330,85114],[74828,91169],[66985,93360],[70343,80843]], 
targetFriend = 8916

Output: 2235

Example 7:

Input:

    times = 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
  targetFriend = 2145

Output: 9998

Example 8:

Input:

    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

Output: 2027

Constraints:

n == times.length
2 <= n <= 10⁴
times[i].length == 2
1 <= arrivali < leavingi <= 10⁵
0 <= targetFriend <= n - 1
Each arrival_i time is distinct.

Hint:

Sort times by arrival time.
for each arrival_i find the smallest unoccupied chair and mark it as occupied until leaving_i.

Solution:

We need to simulate the arrival and departure of friends at a party and manage the assignment of the smallest available chairs. Here's the step-by-step approach:

Approach:

Sort by Arrival Times:
- Sort the times array based on the arrival time.
- This helps process friends in the order of their arrivals.
Use Priority Queues (Min-Heaps):
- Use a min-heap to manage unoccupied chairs (availableChairs).
- Use another min-heap to track the occupied chairs along with their release times (occupiedChairs).
Iterate Through Sorted Times:
- 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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1942. The Number of the Smallest Unoccupied Chair

Approach:

Explanation:

Complexity:

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