java判断一个整数是不是完全平方数

今天被问了这个问题，做了一些思考，下面对这些思路进行整理，我一共整理出4种实现方法。

1 遍历平方法

这种方法的思路是把比给出的目标数num小的整数都做一次平方运算，如果num等于某一个平方就返回true。这里做了一些优化，及不需要把小于num的数全部计算一次，只需要计算小于等于n的就可以。

public static boolean lowIsSquare(int num) {if (num < 0)return false;for (int i = 0; i <= num / 2; i++) {if (i * i == num)return true;}return false;
}

2 开方判断法

这种方法的思路是把给出的num做开方运算判断，开方后的数字是不是整数。这里使用了try包裹住开方运算，是为了防止负数，也可以先加一步if判断实现相同的效果。

public static boolean isSquare(int num) {double a = 0;try {a = Math.sqrt(num); } catch (Exception e) {return false;}int b = (int) a;return a - b == 0;
}

3 公式法

高中时候学习过等差数列，n^2=1+3+5+……+2n-1。利用这个思路可以得到下面的方法，循环地减1、3、5……如果在某一个时刻值等于0，说明它是一个平方数。如果变成了负数，说明它不是平方数。

public static boolean advancedIsSquare(int num) {if (num < 0)return false;for (int i = 1; num > 0; i += 2)num -= i;return 0 == num;
}

4 查找法

事先把可能的平方数计算出来，存在数组中，然后使用二分查找去搜索。

public static boolean serachIsSquare(int num) {/** 获取平方数列表* int a = 0;* for (int i = 0; i < 1000; i++) {    //46340* a = i * i;* System.out.print(a + ",");* }* */int[] arr = { 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441,484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1600,1681, 1764, 1849, 1936, 2025, 2116, 2209, 2304, 2401, 2500, 2601, 2704, 2809, 2916, 3025, 3136, 3249,3364, 3481, 3600, 3721, 3844, 3969, 4096, 4225, 4356, 4489, 4624, 4761, 4900, 5041, 5184, 5329, 5476,5625, 5776, 5929, 6084, 6241, 6400, 6561, 6724, 6889, 7056, 7225, 7396, 7569, 7744, 7921, 8100, 8281,8464, 8649, 8836, 9025, 9216, 9409, 9604, 9801, 10000, 10201, 10404, 10609, 10816, 11025, 11236, 11449,11664, 11881, 12100, 12321, 12544, 12769, 12996, 13225, 13456, 13689, 13924, 14161, 14400, 14641, 14884,15129, 15376, 15625, 15876, 16129, 16384, 16641, 16900, 17161, 17424, 17689, 17956, 18225, 18496, 18769,19044, 19321, 19600, 19881, 20164, 20449, 20736, 21025, 21316, 21609, 21904, 22201, 22500, 22801, 23104,23409, 23716, 24025, 24336, 24649, 24964, 25281, 25600, 25921, 26244, 26569, 26896, 27225, 27556, 27889,28224, 28561, 28900, 29241, 29584, 29929, 30276, 30625, 30976, 31329, 31684, 32041, 32400, 32761, 33124,33489, 33856, 34225, 34596, 34969, 35344, 35721, 36100, 36481, 36864, 37249, 37636, 38025, 38416, 38809,39204, 39601, 40000, 40401, 40804, 41209, 41616, 42025, 42436, 42849, 43264, 43681, 44100, 44521, 44944,45369, 45796, 46225, 46656, 47089, 47524, 47961, 48400, 48841, 49284, 49729, 50176, 50625, 51076, 51529,51984, 52441, 52900, 53361, 53824, 54289, 54756, 55225, 55696, 56169, 56644, 57121, 57600, 58081, 58564,59049, 59536, 60025, 60516, 61009, 61504, 62001, 62500, 63001, 63504, 64009, 64516, 65025, 65536, 66049,66564, 67081, 67600, 68121, 68644, 69169, 69696, 70225, 70756, 71289, 71824, 72361, 72900, 73441, 73984,74529, 75076, 75625, 76176, 76729, 77284, 77841, 78400, 78961, 79524, 80089, 80656, 81225, 81796, 82369,82944, 83521, 84100, 84681, 85264, 85849, 86436, 87025, 87616, 88209, 88804, 89401, 90000, 90601, 91204,91809, 92416, 93025, 93636, 94249, 94864, 95481, 96100, 96721, 97344, 97969, 98596, 99225, 99856,100489, 101124, 101761, 102400, 103041, 103684, 104329, 104976, 105625, 106276, 106929, 107584, 108241,108900, 109561, 110224, 110889, 111556, 112225, 112896, 113569, 114244, 114921, 115600, 116281, 116964,117649, 118336, 119025, 119716, 120409, 121104, 121801, 122500, 123201, 123904, 124609, 125316, 126025,126736, 127449, 128164, 128881, 129600, 130321, 131044, 131769, 132496, 133225, 133956, 134689, 135424,136161, 136900, 137641, 138384, 139129, 139876, 140625, 141376, 142129, 142884, 143641, 144400, 145161,145924, 146689, 147456, 148225, 148996, 149769, 150544, 151321, 152100, 152881, 153664, 154449, 155236,156025, 156816, 157609, 158404, 159201, 160000, 160801, 161604, 162409, 163216, 164025, 164836, 165649,166464, 167281, 168100, 168921, 169744, 170569, 171396, 172225, 173056, 173889, 174724, 175561, 176400,177241, 178084, 178929, 179776, 180625, 181476, 182329, 183184, 184041, 184900, 185761, 186624, 187489,188356, 189225, 190096, 190969, 191844, 192721, 193600, 194481, 195364, 196249, 197136, 198025, 198916,199809, 200704, 201601, 202500, 203401, 204304, 205209, 206116, 207025, 207936, 208849, 209764, 210681,211600, 212521, 213444, 214369, 215296, 216225, 217156, 218089, 219024, 219961, 220900, 221841, 222784,223729, 224676, 225625, 226576, 227529, 228484, 229441, 230400, 231361, 232324, 233289, 234256, 235225,236196, 237169, 238144, 239121, 240100, 241081, 242064, 243049, 244036, 245025, 246016, 247009, 248004,249001, 250000, 251001, 252004, 253009, 254016, 255025, 256036, 257049, 258064, 259081, 260100, 261121,262144, 263169, 264196, 265225, 266256, 267289, 268324, 269361, 270400, 271441, 272484, 273529, 274576,275625, 276676, 277729, 278784, 279841, 280900, 281961, 283024, 284089, 285156, 286225, 287296, 288369,289444, 290521, 291600, 292681, 293764, 294849, 295936, 297025, 298116, 299209, 300304, 301401, 302500,303601, 304704, 305809, 306916, 308025, 309136, 310249, 311364, 312481, 313600, 314721, 315844, 316969,318096, 319225, 320356, 321489, 322624, 323761, 324900, 326041, 327184, 328329, 329476, 330625, 331776,332929, 334084, 335241, 336400, 337561, 338724, 339889, 341056, 342225, 343396, 344569, 345744, 346921,348100, 349281, 350464, 351649, 352836, 354025, 355216, 356409, 357604, 358801, 360000, 361201, 362404,363609, 364816, 366025, 367236, 368449, 369664, 370881, 372100, 373321, 374544, 375769, 376996, 378225,379456, 380689, 381924, 383161, 384400, 385641, 386884, 388129, 389376, 390625, 391876, 393129, 394384,395641, 396900, 398161, 399424, 400689, 401956, 403225, 404496, 405769, 407044, 408321, 409600, 410881,412164, 413449, 414736, 416025, 417316, 418609, 419904, 421201, 422500, 423801, 425104, 426409, 427716,429025, 430336, 431649, 432964, 434281, 435600, 436921, 438244, 439569, 440896, 442225, 443556, 444889,446224, 447561, 448900, 450241, 451584, 452929, 454276, 455625, 456976, 458329, 459684, 461041, 462400,463761, 465124, 466489, 467856, 469225, 470596, 471969, 473344, 474721, 476100, 477481, 478864, 480249,481636, 483025, 484416, 485809, 487204, 488601, 490000, 491401, 492804, 494209, 495616, 497025, 498436,499849, 501264, 502681, 504100, 505521, 506944, 508369, 509796, 511225, 512656, 514089, 515524, 516961,518400, 519841, 521284, 522729, 524176, 525625, 527076, 528529, 529984, 531441, 532900, 534361, 535824,537289, 538756, 540225, 541696, 543169, 544644, 546121, 547600, 549081, 550564, 552049, 553536, 555025,556516, 558009, 559504, 561001, 562500, 564001, 565504, 567009, 568516, 570025, 571536, 573049, 574564,576081, 577600, 579121, 580644, 582169, 583696, 585225, 586756, 588289, 589824, 591361, 592900, 594441,595984, 597529, 599076, 600625, 602176, 603729, 605284, 606841, 608400, 609961, 611524, 613089, 614656,616225, 617796, 619369, 620944, 622521, 624100, 625681, 627264, 628849, 630436, 632025, 633616, 635209,636804, 638401, 640000, 641601, 643204, 644809, 646416, 648025, 649636, 651249, 652864, 654481, 656100,657721, 659344, 660969, 662596, 664225, 665856, 667489, 669124, 670761, 672400, 674041, 675684, 677329,678976, 680625, 682276, 683929, 685584, 687241, 688900, 690561, 692224, 693889, 695556, 697225, 698896,700569, 702244, 703921, 705600, 707281, 708964, 710649, 712336, 714025, 715716, 717409, 719104, 720801,722500, 724201, 725904, 727609, 729316, 731025, 732736, 734449, 736164, 737881, 739600, 741321, 743044,744769, 746496, 748225, 749956, 751689, 753424, 755161, 756900, 758641, 760384, 762129, 763876, 765625,767376, 769129, 770884, 772641, 774400, 776161, 777924, 779689, 781456, 783225, 784996, 786769, 788544,790321, 792100, 793881, 795664, 797449, 799236, 801025, 802816, 804609, 806404, 808201, 810000, 811801,813604, 815409, 817216, 819025, 820836, 822649, 824464, 826281, 828100, 829921, 831744, 833569, 835396,837225, 839056, 840889, 842724, 844561, 846400, 848241, 850084, 851929, 853776, 855625, 857476, 859329,861184, 863041, 864900, 866761, 868624, 870489, 872356, 874225, 876096, 877969, 879844, 881721, 883600,885481, 887364, 889249, 891136, 893025, 894916, 896809, 898704, 900601, 902500, 904401, 906304, 908209,910116, 912025, 913936, 915849, 917764, 919681, 921600, 923521, 925444, 927369, 929296, 931225, 933156,935089, 937024, 938961, 940900, 942841, 944784, 946729, 948676, 950625, 952576, 954529, 956484, 958441,960400, 962361, 964324, 966289, 968256, 970225, 972196, 974169, 976144, 978121, 980100, 982081, 984064,986049, 988036, 990025, 992016, 994009, 996004, 998001 };if (commonBinarySearch(arr, num) == -1)return false;elsereturn true;}
private static int commonBinarySearch(int[] arr, int key) {int lo = 0;int mid = 0;int hi = arr.length - 1;if (key < arr[lo] || key > arr[hi] || lo > hi) {return -1;}while (lo <= hi) {mid = lo + (hi - lo) / 2;if (arr[mid] > key) {hi = mid - 1;} else if (arr[mid] < key) {lo = mid + 1;} else {return mid;}}return -1;
}

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