912. Sort an Array
Medium
Given an array of integers nums
, sort the array in ascending order and return it.
You must solve the problem without using any built-in functions in O(nlog(n))
time complexity and with the smallest space complexity possible.
Example 1:
- Input: nums = [5,2,3,1]
- Output: [1,2,3,5]
- Explanation: After sorting the array, the positions of some numbers are not changed (for example, 2 and 3), while the positions of other numbers are changed (for example, 1 and 5).
Example 2:
- Input: nums = [5,1,1,2,0,0]
- Output: [0,0,1,1,2,5]
- Explanation: Note that the values of nums are not necessairly unique.
Example 3:
- Input: nums = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1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,49352,49353,49354,49355,49356,49357,49358,49359,49360,49361,49362,49363,49364,49365,49366,49367,49368,49369,49370,49371,49372,49373,49374,49375,49376,49377,49378,49379,49380,49381,49382,49383,49384,49385,49386,49387,49388,49389,49390,49391,49392,49393,49394,49395,49396,49397,49398,49399,49400,49401,49402,49403,49404,49405,49406,49407,49408,49409,49410,49411,49412,49413,49414,49415,49416,49417,49418,49419,49420,49421,49422,49423,49424,49425,49426,49427,49428,49429,49430,49431,49432,49433,49434,49435,49436,49437,49438,49439,49440,49441,49442,49443,49444,49445,49446,49447,49448,49449,49450,49451,49452,49453,49454,49455,49456,49457,49458,49459,49460,49461,49462,49463,49464,49465,49466,49467,49468,49469,49470,49471,49472,49473,49474,49475,49476,49477,49478,49479,49480,49481,49482,49483,49484,49485,49486,49487,49488,49489,49490,49491,49492,49493,49494,49495,49496,49497,49498,49499,49500,49501,49502,49503,49504,49505,49506,49507,49508,49509,49510,49511,49512,49513,49514,49515,49516,49517,49518,49519,49520,49521,49522,49523,49524,49525,49526,49527,49528,49529,49530,49531,49532,49533,49534,49535,49536,49537,49538,49539,49540,49541,49542,49543,49544,49545,49546,49547,49548,49549,49550,49551,49552,49553,49554,49555,49556,49557,49558,49559,49560,49561,49562,49563,49564,49565,49566,49567,49568,49569,49570,49571,49572,49573,49574,49575,49576,49577,49578,49579,49580,49581,49582,49583,49584,49585,49586,49587,49588,49589,49590,49591,49592,49593,49594,49595,49596,49597,49598,49599,49600,49601,49602,49603,49604,49605,49606,49607,49608,49609,49610,49611,49612,49613,49614,49615,49616,49617,49618,49619,49620,49621,49622,49623,49624,49625,49626,49627,49628,49629,49630,49631,49632,49633,49634,49635,49636,49637,49638,49639,49640,49641,49642,49643,49644,49645,49646,49647,49648,49649,49650,49651,49652,49653,49654,49655,49656,49657,49658,49659,49660,49661,49662,49663,49664,49665,49666,49667,49668,49669,49670,49671,49672,49673,49674,49675,49676,49677,49678,49679,49680,49681,49682,49683,49684,49685,49686,49687,49688,49689,49690,49691,49692,49693,49694,49695,49696,49697,49698,49699,49700,49701,49702,49703,49704,49705,49706,49707,49708,49709,49710,49711,49712,49713,49714,49715,49716,49717,49718,49719,49720,49721,49722,49723,49724,49725,49726,49727,49728,49729,49730,49731,49732,49733,49734,49735,49736,49737,49738,49739,49740,49741,49742,49743,49744,49745,49746,49747,49748,49749,49750,49751,49752,49753,49754,49755,49756,49757,49758,49759,49760,49761,49762,49763,49764,49765,49766,49767,49768,49769,49770,49771,49772,49773,49774,49775,49776,49777,49778,49779,49780,49781,49782,49783,49784,49785,49786,49787,49788,49789,49790,49791,49792,49793,49794,49795,49796,49797,49798,49799,49800,49801,49802,49803,49804,49805,49806,49807,49808,49809,49810,49811,49812,49813,49814,49815,49816,49817,49818,49819,49820,49821,49822,49823,49824,49825,49826,49827,49828,49829,49830,49831,49832,49833,49834,49835,49836,49837,49838,49839,49840,49841,49842,49843,49844,49845,49846,49847,49848,49849,49850,49851,49852,49853,49854,49855,49856,49857,49858,49859,49860,49861,49862,49863,49864,49865,49866,49867,49868,49869,49870,49871,49872,49873,49874,49875,49876,49877,49878,49879,49880,49881,49882,49883,49884,49885,49886,49887,49888,49889,49890,49891,49892,49893,49894,49895,49896,49897,49898,49899,49900,49901,49902,49903,49904,49905,49906,49907,49908,49909,49910,49911,49912,49913,49914,49915,49916,49917,49918,49919,49920,49921,49922,49923,49924,49925,49926,49927,49928,49929,49930,49931,49932,49933,49934,49935,49936,49937,49938,49939,49940,49941,49942,49943,49944,49945,49946,49947,49948,49949,49950,49951,49952,49953,49954,49955,49956,49957,49958,49959,49960,49961,49962,49963,49964,49965,49966,49967,49968,49969,49970,49971,49972,49973,49974,49975,49976,49977,49978,49979,49980,49981,49982,49983,49984,49985,49986,49987,49988,49989,49990,49991,49992,49993,49994,49995,49996,49997,49998,49999,50000]
- Output: [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277...]
- Explanation: Note that the values of nums are not necessairly unique.
Constraints:
1 <= nums.length <= 5 * 104
-5 * 104 <= nums[i] <= 5 * 104
Solution:
To solve this problem, we can follow these steps:
- Divide: Recursively divide the array into two halves until each subarray contains a single element.
- Conquer: Merge the sorted halves to produce sorted subarrays.
- Combine: Continue merging the subarrays until we get the final sorted array.
Let's implement this solution in PHP: 912. Sort an Array
<?php
// Example usage:
$nums1 = [5, 2, 3, 1];
$result1 = sortArray($nums1);
echo implode(", ", $result1); // Output: 1, 2, 3, 5
// Example usage:
$nums2 = [5,1,1,2,0,0]
$result2 = sortArray($nums2);
echo implode(", ", $result2); // Output: 0,0,1,1,2,5
// Example usage:
$nums3 = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277...];
$result3 = sortArray($nums3);
echo implode(", ", $result3); // Output: 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277...
?>
Explanation:
-
mergeSort Function:
- The
mergeSort
function checks if the array has one or no elements (base case). If true, it returns because the array is already sorted. - It then splits the array into two halves (
left
andright
). - It recursively calls
mergeSort
on each half. - Finally, it merges the sorted halves using the
merge
function.
- The
-
merge Function:
- The
merge
function takes three parameters: the original array, and the two halves (left
andright
). - It initializes three pointers (
i
,j
, andk
) for traversing theleft
,right
, and original arrays, respectively. - It compares the elements from
left
andright
, and places the smaller element into the original array. - It handles any remaining elements in the
left
orright
arrays after the main loop.
- The
-
sortArray Function:
- The
sortArray
function is a wrapper that calls themergeSort
function and returns the sorted array.
- The
This implementation ensures the array is sorted in (O(n \log n)) time complexity and uses (O(n)) space complexity. This is efficient and meets the problem constraints.
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