【java/算法/组合】从1，2，3，......，100这一百个数中，任取两个数，使其能被4整除的取法有几种？并用程序列举出来。
【数学解法】
100个数应该分成以下四类：
4n+1类：1，5，9，13，......，97 共25个；
4n+2类：2，4，6，10，......，98 共25个；
4n+3类：3，7，11，15，......，99 共25个；
4n+4类：4，8，12，16，......，100 共25个；
如果两个数都从4n+2类或是4n+4类中去，两数和无疑能被4整除，这两个类别的数量是2*C25_2=2*25*24/2/1=600个；
如果一个数从4n+1类取，一个数从4n+3类取，两数和也能被4整除，这个类别的数量是25*25=625种；
三类合计为1225种。
以上为数学解法，只能把种类数算出来，可以为下面的程序算法提供印证。
【程序解法】
HandredDevideFour类：
package test230425; import java.util.List; public class HandredDevideFour { public static void main(String[] args) { int[] arr=new int[100]; for(int i=1;i<=100;i++) { arr[i-1]=i; } Combination c=new Combination(arr,2); List<List<Integer>> results=c.getResults(); int idx=0; for(List<Integer> res:results) { int first=res.get(0); int second=res.get(1); int sum=first+second; if(sum%4==0) { System.out.println(String.format("%02d", ++idx) +"."+res); } } } }
Combination类：
import java.util.ArrayList; import java.util.List; import java.util.Stack; /** * 数学中排列组合中的组合器实现 * */ public class Combination { /** * 用于存放中间结果 */ private Stack<Integer> stack; /** * 用于存放结果 */ private List<List<Integer>> results; /** * 构造函数 * @param arr 进行组合的元素 * @param count 选多少个 */ public Combination(int[] arr,int count) { if(count>arr.length) { throw new ArrayIndexOutOfBoundsException(count+">"+arr.length); } stack = new Stack<>(); results=new ArrayList<>(); doSelect(arr,count,0,0); } /** * 进行选择 * @param arr 目标数组 * @param expect 期望选择数量 * @param actual 实际选择数量 * @param current 当前下标 */ private void doSelect(int[] arr, int expect, int actual, int current) { if(actual == expect) { List<Integer> list=new ArrayList<>(); for(int i:stack) { list.add(i); } results.add(list); return; } for(int i=current;i<arr.length;i++) { if(!stack.contains(arr[i])) { stack.add(arr[i]); doSelect(arr, expect, actual+1, i); stack.pop(); } } } /** * 取得组合结果 * @return */ public List<List<Integer>> getResults(){ return results; } /** * 测试 * @param args */ public static void main(String[] args) { final int[] arr= {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}; final int count=2; Combination c=new Combination(arr,count); List<List<Integer>> results=c.getResults(); int idx=0; for(List<Integer> res:results) { System.out.println(String.format("%02d", ++idx) +"."+res); } } }
【输出结果】
01.[1, 3] 02.[1, 7] 03.[1, 11] 04.[1, 15] 05.[1, 19] 06.[1, 23] 07.[1, 27] 08.[1, 31] 09.[1, 35] 10.[1, 39] 11.[1, 43] 12.[1, 47] 13.[1, 51] 14.[1, 55] 15.[1, 59] 16.[1, 63] 17.[1, 67] 18.[1, 71] 19.[1, 75] 20.[1, 79] 21.[1, 83] 22.[1, 87] 23.[1, 91] 24.[1, 95] 25.[1, 99] 26.[2, 6] 27.[2, 10] 28.[2, 14] 29.[2, 18] 30.[2, 22] 31.[2, 26] 32.[2, 30] 33.[2, 34] 34.[2, 38] 35.[2, 42] 36.[2, 46] 37.[2, 50] 38.[2, 54] 39.[2, 58] 40.[2, 62] 41.[2, 66] 42.[2, 70] 43.[2, 74] 44.[2, 78] 45.[2, 82] 46.[2, 86] 47.[2, 90] 48.[2, 94] 49.[2, 98] 50.[3, 5] 51.[3, 9] 52.[3, 13] 53.[3, 17] 54.[3, 21] 55.[3, 25] 56.[3, 29] 57.[3, 33] 58.[3, 37] 59.[3, 41] 60.[3, 45] 61.[3, 49] 62.[3, 53] 63.[3, 57] 64.[3, 61] 65.[3, 65] 66.[3, 69] 67.[3, 73] 68.[3, 77] 69.[3, 81] 70.[3, 85] 71.[3, 89] 72.[3, 93] 73.[3, 97] 74.[4, 8] 75.[4, 12] 76.[4, 16] 77.[4, 20] 78.[4, 24] 79.[4, 28] 80.[4, 32] 81.[4, 36] 82.[4, 40] 83.[4, 44] 84.[4, 48] 85.[4, 52] 86.[4, 56] 87.[4, 60] 88.[4, 64] 89.[4, 68] 90.[4, 72] 91.[4, 76] 92.[4, 80] 93.[4, 84] 94.[4, 88] 95.[4, 92] 96.[4, 96] 97.[4, 100] 98.[5, 7] 99.[5, 11] 100.[5, 15] 101.[5, 19] 102.[5, 23] 103.[5, 27] 104.[5, 31] 105.[5, 35] 106.[5, 39] 107.[5, 43] 108.[5, 47] 109.[5, 51] 110.[5, 55] 111.[5, 59] 112.[5, 63] 113.[5, 67] 114.[5, 71] 115.[5, 75] 116.[5, 79] 117.[5, 83] 118.[5, 87] 119.[5, 91] 120.[5, 95] 121.[5, 99] 122.[6, 10] 123.[6, 14] 124.[6, 18] 125.[6, 22] 126.[6, 26] 127.[6, 30] 128.[6, 34] 129.[6, 38] 130.[6, 42] 131.[6, 46] 132.[6, 50] 133.[6, 54] 134.[6, 58] 135.[6, 62] 136.[6, 66] 137.[6, 70] 138.[6, 74] 139.[6, 78] 140.[6, 82] 141.[6, 86] 142.[6, 90] 143.[6, 94] 144.[6, 98] 145.[7, 9] 146.[7, 13] 147.[7, 17] 148.[7, 21] 149.[7, 25] 150.[7, 29] 151.[7, 33] 152.[7, 37] 153.[7, 41] 154.[7, 45] 155.[7, 49] 156.[7, 53] 157.[7, 57] 158.[7, 61] 159.[7, 65] 160.[7, 69] 161.[7, 73] 162.[7, 77] 163.[7, 81] 164.[7, 85] 165.[7, 89] 166.[7, 93] 167.[7, 97] 168.[8, 12] 169.[8, 16] 170.[8, 20] 171.[8, 24] 172.[8, 28] 173.[8, 32] 174.[8, 36] 175.[8, 40] 176.[8, 44] 177.[8, 48] 178.[8, 52] 179.[8, 56] 180.[8, 60] 181.[8, 64] 182.[8, 68] 183.[8, 72] 184.[8, 76] 185.[8, 80] 186.[8, 84] 187.[8, 88] 188.[8, 92] 189.[8, 96] 190.[8, 100] 191.[9, 11] 192.[9, 15] 193.[9, 19] 194.[9, 23] 195.[9, 27] 196.[9, 31] 197.[9, 35] 198.[9, 39] 199.[9, 43] 200.[9, 47] 201.[9, 51] 202.[9, 55] 203.[9, 59] 204.[9, 63] 205.[9, 67] 206.[9, 71] 207.[9, 75] 208.[9, 79] 209.[9, 83] 210.[9, 87] 211.[9, 91] 212.[9, 95] 213.[9, 99] 214.[10, 14] 215.[10, 18] 216.[10, 22] 217.[10, 26] 218.[10, 30] 219.[10, 34] 220.[10, 38] 221.[10, 42] 222.[10, 46] 223.[10, 50] 224.[10, 54] 225.[10, 58] 226.[10, 62] 227.[10, 66] 228.[10, 70] 229.[10, 74] 230.[10, 78] 231.[10, 82] 232.[10, 86] 233.[10, 90] 234.[10, 94] 235.[10, 98] 236.[11, 13] 237.[11, 17] 238.[11, 21] 239.[11, 25] 240.[11, 29] 241.[11, 33] 242.[11, 37] 243.[11, 41] 244.[11, 45] 245.[11, 49] 246.[11, 53] 247.[11, 57] 248.[11, 61] 249.[11, 65] 250.[11, 69] 251.[11, 73] 252.[11, 77] 253.[11, 81] 254.[11, 85] 255.[11, 89] 256.[11, 93] 257.[11, 97] 258.[12, 16] 259.[12, 20] 260.[12, 24] 261.[12, 28] 262.[12, 32] 263.[12, 36] 264.[12, 40] 265.[12, 44] 266.[12, 48] 267.[12, 52] 268.[12, 56] 269.[12, 60] 270.[12, 64] 271.[12, 68] 272.[12, 72] 273.[12, 76] 274.[12, 80] 275.[12, 84] 276.[12, 88] 277.[12, 92] 278.[12, 96] 279.[12, 100] 280.[13, 15] 281.[13, 19] 282.[13, 23] 283.[13, 27] 284.[13, 31] 285.[13, 35] 286.[13, 39] 287.[13, 43] 288.[13, 47] 289.[13, 51] 290.[13, 55] 291.[13, 59] 292.[13, 63] 293.[13, 67] 294.[13, 71] 295.[13, 75] 296.[13, 79] 297.[13, 83] 298.[13, 87] 299.[13, 91] 300.[13, 95] 301.[13, 99] 302.[14, 18] 303.[14, 22] 304.[14, 26] 305.[14, 30] 306.[14, 34] 307.[14, 38] 308.[14, 42] 309.[14, 46] 310.[14, 50] 311.[14, 54] 312.[14, 58] 313.[14, 62] 314.[14, 66] 315.[14, 70] 316.[14, 74] 317.[14, 78] 318.[14, 82] 319.[14, 86] 320.[14, 90] 321.[14, 94] 322.[14, 98] 323.[15, 17] 324.[15, 21] 325.[15, 25] 326.[15, 29] 327.[15, 33] 328.[15, 37] 329.[15, 41] 330.[15, 45] 331.[15, 49] 332.[15, 53] 333.[15, 57] 334.[15, 61] 335.[15, 65] 336.[15, 69] 337.[15, 73] 338.[15, 77] 339.[15, 81] 340.[15, 85] 341.[15, 89] 342.[15, 93] 343.[15, 97] 344.[16, 20] 345.[16, 24] 346.[16, 28] 347.[16, 32] 348.[16, 36] 349.[16, 40] 350.[16, 44] 351.[16, 48] 352.[16, 52] 353.[16, 56] 354.[16, 60] 355.[16, 64] 356.[16, 68] 357.[16, 72] 358.[16, 76] 359.[16, 80] 360.[16, 84] 361.[16, 88] 362.[16, 92] 363.[16, 96] 364.[16, 100] 365.[17, 19] 366.[17, 23] 367.[17, 27] 368.[17, 31] 369.[17, 35] 370.[17, 39] 371.[17, 43] 372.[17, 47] 373.[17, 51] 374.[17, 55] 375.[17, 59] 376.[17, 63] 377.[17, 67] 378.[17, 71] 379.[17, 75] 380.[17, 79] 381.[17, 83] 382.[17, 87] 383.[17, 91] 384.[17, 95] 385.[17, 99] 386.[18, 22] 387.[18, 26] 388.[18, 30] 389.[18, 34] 390.[18, 38] 391.[18, 42] 392.[18, 46] 393.[18, 50] 394.[18, 54] 395.[18, 58] 396.[18, 62] 397.[18, 66] 398.[18, 70] 399.[18, 74] 400.[18, 78] 401.[18, 82] 402.[18, 86] 403.[18, 90] 404.[18, 94] 405.[18, 98] 406.[19, 21] 407.[19, 25] 408.[19, 29] 409.[19, 33] 410.[19, 37] 411.[19, 41] 412.[19, 45] 413.[19, 49] 414.[19, 53] 415.[19, 57] 416.[19, 61] 417.[19, 65] 418.[19, 69] 419.[19, 73] 420.[19, 77] 421.[19, 81] 422.[19, 85] 423.[19, 89] 424.[19, 93] 425.[19, 97] 426.[20, 24] 427.[20, 28] 428.[20, 32] 429.[20, 36] 430.[20, 40] 431.[20, 44] 432.[20, 48] 433.[20, 52] 434.[20, 56] 435.[20, 60] 436.[20, 64] 437.[20, 68] 438.[20, 72] 439.[20, 76] 440.[20, 80] 441.[20, 84] 442.[20, 88] 443.[20, 92] 444.[20, 96] 445.[20, 100] 446.[21, 23] 447.[21, 27] 448.[21, 31] 449.[21, 35] 450.[21, 39] 451.[21, 43] 452.[21, 47] 453.[21, 51] 454.[21, 55] 455.[21, 59] 456.[21, 63] 457.[21, 67] 458.[21, 71] 459.[21, 75] 460.[21, 79] 461.[21, 83] 462.[21, 87] 463.[21, 91] 464.[21, 95] 465.[21, 99] 466.[22, 26] 467.[22, 30] 468.[22, 34] 469.[22, 38] 470.[22, 42] 471.[22, 46] 472.[22, 50] 473.[22, 54] 474.[22, 58] 475.[22, 62] 476.[22, 66] 477.[22, 70] 478.[22, 74] 479.[22, 78] 480.[22, 82] 481.[22, 86] 482.[22, 90] 483.[22, 94] 484.[22, 98] 485.[23, 25] 486.[23, 29] 487.[23, 33] 488.[23, 37] 489.[23, 41] 490.[23, 45] 491.[23, 49] 492.[23, 53] 493.[23, 57] 494.[23, 61] 495.[23, 65] 496.[23, 69] 497.[23, 73] 498.[23, 77] 499.[23, 81] 500.[23, 85] 501.[23, 89] 502.[23, 93] 503.[23, 97] 504.[24, 28] 505.[24, 32] 506.[24, 36] 507.[24, 40] 508.[24, 44] 509.[24, 48] 510.[24, 52] 511.[24, 56] 512.[24, 60] 513.[24, 64] 514.[24, 68] 515.[24, 72] 516.[24, 76] 517.[24, 80] 518.[24, 84] 519.[24, 88] 520.[24, 92] 521.[24, 96] 522.[24, 100] 523.[25, 27] 524.[25, 31] 525.[25, 35] 526.[25, 39] 527.[25, 43] 528.[25, 47] 529.[25, 51] 530.[25, 55] 531.[25, 59] 532.[25, 63] 533.[25, 67] 534.[25, 71] 535.[25, 75] 536.[25, 79] 537.[25, 83] 538.[25, 87] 539.[25, 91] 540.[25, 95] 541.[25, 99] 542.[26, 30] 543.[26, 34] 544.[26, 38] 545.[26, 42] 546.[26, 46] 547.[26, 50] 548.[26, 54] 549.[26, 58] 550.[26, 62] 551.[26, 66] 552.[26, 70] 553.[26, 74] 554.[26, 78] 555.[26, 82] 556.[26, 86] 557.[26, 90] 558.[26, 94] 559.[26, 98] 560.[27, 29] 561.[27, 33] 562.[27, 37] 563.[27, 41] 564.[27, 45] 565.[27, 49] 566.[27, 53] 567.[27, 57] 568.[27, 61] 569.[27, 65] 570.[27, 69] 571.[27, 73] 572.[27, 77] 573.[27, 81] 574.[27, 85] 575.[27, 89] 576.[27, 93] 577.[27, 97] 578.[28, 32] 579.[28, 36] 580.[28, 40] 581.[28, 44] 582.[28, 48] 583.[28, 52] 584.[28, 56] 585.[28, 60] 586.[28, 64] 587.[28, 68] 588.[28, 72] 589.[28, 76] 590.[28, 80] 591.[28, 84] 592.[28, 88] 593.[28, 92] 594.[28, 96] 595.[28, 100] 596.[29, 31] 597.[29, 35] 598.[29, 39] 599.[29, 43] 600.[29, 47] 601.[29, 51] 602.[29, 55] 603.[29, 59] 604.[29, 63] 605.[29, 67] 606.[29, 71] 607.[29, 75] 608.[29, 79] 609.[29, 83] 610.[29, 87] 611.[29, 91] 612.[29, 95] 613.[29, 99] 614.[30, 34] 615.[30, 38] 616.[30, 42] 617.[30, 46] 618.[30, 50] 619.[30, 54] 620.[30, 58] 621.[30, 62] 622.[30, 66] 623.[30, 70] 624.[30, 74] 625.[30, 78] 626.[30, 82] 627.[30, 86] 628.[30, 90] 629.[30, 94] 630.[30, 98] 631.[31, 33] 632.[31, 37] 633.[31, 41] 634.[31, 45] 635.[31, 49] 636.[31, 53] 637.[31, 57] 638.[31, 61] 639.[31, 65] 640.[31, 69] 641.[31, 73] 642.[31, 77] 643.[31, 81] 644.[31, 85] 645.[31, 89] 646.[31, 93] 647.[31, 97] 648.[32, 36] 649.[32, 40] 650.[32, 44] 651.[32, 48] 652.[32, 52] 653.[32, 56] 654.[32, 60] 655.[32, 64] 656.[32, 68] 657.[32, 72] 658.[32, 76] 659.[32, 80] 660.[32, 84] 661.[32, 88] 662.[32, 92] 663.[32, 96] 664.[32, 100] 665.[33, 35] 666.[33, 39] 667.[33, 43] 668.[33, 47] 669.[33, 51] 670.[33, 55] 671.[33, 59] 672.[33, 63] 673.[33, 67] 674.[33, 71] 675.[33, 75] 676.[33, 79] 677.[33, 83] 678.[33, 87] 679.[33, 91] 680.[33, 95] 681.[33, 99] 682.[34, 38] 683.[34, 42] 684.[34, 46] 685.[34, 50] 686.[34, 54] 687.[34, 58] 688.[34, 62] 689.[34, 66] 690.[34, 70] 691.[34, 74] 692.[34, 78] 693.[34, 82] 694.[34, 86] 695.[34, 90] 696.[34, 94] 697.[34, 98] 698.[35, 37] 699.[35, 41] 700.[35, 45] 701.[35, 49] 702.[35, 53] 703.[35, 57] 704.[35, 61] 705.[35, 65] 706.[35, 69] 707.[35, 73] 708.[35, 77] 709.[35, 81] 710.[35, 85] 711.[35, 89] 712.[35, 93] 713.[35, 97] 714.[36, 40] 715.[36, 44] 716.[36, 48] 717.[36, 52] 718.[36, 56] 719.[36, 60] 720.[36, 64] 721.[36, 68] 722.[36, 72] 723.[36, 76] 724.[36, 80] 725.[36, 84] 726.[36, 88] 727.[36, 92] 728.[36, 96] 729.[36, 100] 730.[37, 39] 731.[37, 43] 732.[37, 47] 733.[37, 51] 734.[37, 55] 735.[37, 59] 736.[37, 63] 737.[37, 67] 738.[37, 71] 739.[37, 75] 740.[37, 79] 741.[37, 83] 742.[37, 87] 743.[37, 91] 744.[37, 95] 745.[37, 99] 746.[38, 42] 747.[38, 46] 748.[38, 50] 749.[38, 54] 750.[38, 58] 751.[38, 62] 752.[38, 66] 753.[38, 70] 754.[38, 74] 755.[38, 78] 756.[38, 82] 757.[38, 86] 758.[38, 90] 759.[38, 94] 760.[38, 98] 761.[39, 41] 762.[39, 45] 763.[39, 49] 764.[39, 53] 765.[39, 57] 766.[39, 61] 767.[39, 65] 768.[39, 69] 769.[39, 73] 770.[39, 77] 771.[39, 81] 772.[39, 85] 773.[39, 89] 774.[39, 93] 775.[39, 97] 776.[40, 44] 777.[40, 48] 778.[40, 52] 779.[40, 56] 780.[40, 60] 781.[40, 64] 782.[40, 68] 783.[40, 72] 784.[40, 76] 785.[40, 80] 786.[40, 84] 787.[40, 88] 788.[40, 92] 789.[40, 96] 790.[40, 100] 791.[41, 43] 792.[41, 47] 793.[41, 51] 794.[41, 55] 795.[41, 59] 796.[41, 63] 797.[41, 67] 798.[41, 71] 799.[41, 75] 800.[41, 79] 801.[41, 83] 802.[41, 87] 803.[41, 91] 804.[41, 95] 805.[41, 99] 806.[42, 46] 807.[42, 50] 808.[42, 54] 809.[42, 58] 810.[42, 62] 811.[42, 66] 812.[42, 70] 813.[42, 74] 814.[42, 78] 815.[42, 82] 816.[42, 86] 817.[42, 90] 818.[42, 94] 819.[42, 98] 820.[43, 45] 821.[43, 49] 822.[43, 53] 823.[43, 57] 824.[43, 61] 825.[43, 65] 826.[43, 69] 827.[43, 73] 828.[43, 77] 829.[43, 81] 830.[43, 85] 831.[43, 89] 832.[43, 93] 833.[43, 97] 834.[44, 48] 835.[44, 52] 836.[44, 56] 837.[44, 60] 838.[44, 64] 839.[44, 68] 840.[44, 72] 841.[44, 76] 842.[44, 80] 843.[44, 84] 844.[44, 88] 845.[44, 92] 846.[44, 96] 847.[44, 100] 848.[45, 47] 849.[45, 51] 850.[45, 55] 851.[45, 59] 852.[45, 63] 853.[45, 67] 854.[45, 71] 855.[45, 75] 856.[45, 79] 857.[45, 83] 858.[45, 87] 859.[45, 91] 860.[45, 95] 861.[45, 99] 862.[46, 50] 863.[46, 54] 864.[46, 58] 865.[46, 62] 866.[46, 66] 867.[46, 70] 868.[46, 74] 869.[46, 78] 870.[46, 82] 871.[46, 86] 872.[46, 90] 873.[46, 94] 874.[46, 98] 875.[47, 49] 876.[47, 53] 877.[47, 57] 878.[47, 61] 879.[47, 65] 880.[47, 69] 881.[47, 73] 882.[47, 77] 883.[47, 81] 884.[47, 85] 885.[47, 89] 886.[47, 93] 887.[47, 97] 888.[48, 52] 889.[48, 56] 890.[48, 60] 891.[48, 64] 892.[48, 68] 893.[48, 72] 894.[48, 76] 895.[48, 80] 896.[48, 84] 897.[48, 88] 898.[48, 92] 899.[48, 96] 900.[48, 100] 901.[49, 51] 902.[49, 55] 903.[49, 59] 904.[49, 63] 905.[49, 67] 906.[49, 71] 907.[49, 75] 908.[49, 79] 909.[49, 83] 910.[49, 87] 911.[49, 91] 912.[49, 95] 913.[49, 99] 914.[50, 54] 915.[50, 58] 916.[50, 62] 917.[50, 66] 918.[50, 70] 919.[50, 74] 920.[50, 78] 921.[50, 82] 922.[50, 86] 923.[50, 90] 924.[50, 94] 925.[50, 98] 926.[51, 53] 927.[51, 57] 928.[51, 61] 929.[51, 65] 930.[51, 69] 931.[51, 73] 932.[51, 77] 933.[51, 81] 934.[51, 85] 935.[51, 89] 936.[51, 93] 937.[51, 97] 938.[52, 56] 939.[52, 60] 940.[52, 64] 941.[52, 68] 942.[52, 72] 943.[52, 76] 944.[52, 80] 945.[52, 84] 946.[52, 88] 947.[52, 92] 948.[52, 96] 949.[52, 100] 950.[53, 55] 951.[53, 59] 952.[53, 63] 953.[53, 67] 954.[53, 71] 955.[53, 75] 956.[53, 79] 957.[53, 83] 958.[53, 87] 959.[53, 91] 960.[53, 95] 961.[53, 99] 962.[54, 58] 963.[54, 62] 964.[54, 66] 965.[54, 70] 966.[54, 74] 967.[54, 78] 968.[54, 82] 969.[54, 86] 970.[54, 90] 971.[54, 94] 972.[54, 98] 973.[55, 57] 974.[55, 61] 975.[55, 65] 976.[55, 69] 977.[55, 73] 978.[55, 77] 979.[55, 81] 980.[55, 85] 981.[55, 89] 982.[55, 93] 983.[55, 97] 984.[56, 60] 985.[56, 64] 986.[56, 68] 987.[56, 72] 988.[56, 76] 989.[56, 80] 990.[56, 84] 991.[56, 88] 992.[56, 92] 993.[56, 96] 994.[56, 100] 995.[57, 59] 996.[57, 63] 997.[57, 67] 998.[57, 71] 999.[57, 75] 1000.[57, 79] 1001.[57, 83] 1002.[57, 87] 1003.[57, 91] 1004.[57, 95] 1005.[57, 99] 1006.[58, 62] 1007.[58, 66] 1008.[58, 70] 1009.[58, 74] 1010.[58, 78] 1011.[58, 82] 1012.[58, 86] 1013.[58, 90] 1014.[58, 94] 1015.[58, 98] 1016.[59, 61] 1017.[59, 65] 1018.[59, 69] 1019.[59, 73] 1020.[59, 77] 1021.[59, 81] 1022.[59, 85] 1023.[59, 89] 1024.[59, 93] 1025.[59, 97] 1026.[60, 64] 1027.[60, 68] 1028.[60, 72] 1029.[60, 76] 1030.[60, 80] 1031.[60, 84] 1032.[60, 88] 1033.[60, 92] 1034.[60, 96] 1035.[60, 100] 1036.[61, 63] 1037.[61, 67] 1038.[61, 71] 1039.[61, 75] 1040.[61, 79] 1041.[61, 83] 1042.[61, 87] 1043.[61, 91] 1044.[61, 95] 1045.[61, 99] 1046.[62, 66] 1047.[62, 70] 1048.[62, 74] 1049.[62, 78] 1050.[62, 82] 1051.[62, 86] 1052.[62, 90] 1053.[62, 94] 1054.[62, 98] 1055.[63, 65] 1056.[63, 69] 1057.[63, 73] 1058.[63, 77] 1059.[63, 81] 1060.[63, 85] 1061.[63, 89] 1062.[63, 93] 1063.[63, 97] 1064.[64, 68] 1065.[64, 72] 1066.[64, 76] 1067.[64, 80] 1068.[64, 84] 1069.[64, 88] 1070.[64, 92] 1071.[64, 96] 1072.[64, 100] 1073.[65, 67] 1074.[65, 71] 1075.[65, 75] 1076.[65, 79] 1077.[65, 83] 1078.[65, 87] 1079.[65, 91] 1080.[65, 95] 1081.[65, 99] 1082.[66, 70] 1083.[66, 74] 1084.[66, 78] 1085.[66, 82] 1086.[66, 86] 1087.[66, 90] 1088.[66, 94] 1089.[66, 98] 1090.[67, 69] 1091.[67, 73] 1092.[67, 77] 1093.[67, 81] 1094.[67, 85] 1095.[67, 89] 1096.[67, 93] 1097.[67, 97] 1098.[68, 72] 1099.[68, 76] 1100.[68, 80] 1101.[68, 84] 1102.[68, 88] 1103.[68, 92] 1104.[68, 96] 1105.[68, 100] 1106.[69, 71] 1107.[69, 75] 1108.[69, 79] 1109.[69, 83] 1110.[69, 87] 1111.[69, 91] 1112.[69, 95] 1113.[69, 99] 1114.[70, 74] 1115.[70, 78] 1116.[70, 82] 1117.[70, 86] 1118.[70, 90] 1119.[70, 94] 1120.[70, 98] 1121.[71, 73] 1122.[71, 77] 1123.[71, 81] 1124.[71, 85] 1125.[71, 89] 1126.[71, 93] 1127.[71, 97] 1128.[72, 76] 1129.[72, 80] 1130.[72, 84] 1131.[72, 88] 1132.[72, 92] 1133.[72, 96] 1134.[72, 100] 1135.[73, 75] 1136.[73, 79] 1137.[73, 83] 1138.[73, 87] 1139.[73, 91] 1140.[73, 95] 1141.[73, 99] 1142.[74, 78] 1143.[74, 82] 1144.[74, 86] 1145.[74, 90] 1146.[74, 94] 1147.[74, 98] 1148.[75, 77] 1149.[75, 81] 1150.[75, 85] 1151.[75, 89] 1152.[75, 93] 1153.[75, 97] 1154.[76, 80] 1155.[76, 84] 1156.[76, 88] 1157.[76, 92] 1158.[76, 96] 1159.[76, 100] 1160.[77, 79] 1161.[77, 83] 1162.[77, 87] 1163.[77, 91] 1164.[77, 95] 1165.[77, 99] 1166.[78, 82] 1167.[78, 86] 1168.[78, 90] 1169.[78, 94] 1170.[78, 98] 1171.[79, 81] 1172.[79, 85] 1173.[79, 89] 1174.[79, 93] 1175.[79, 97] 1176.[80, 84] 1177.[80, 88] 1178.[80, 92] 1179.[80, 96] 1180.[80, 100] 1181.[81, 83] 1182.[81, 87] 1183.[81, 91] 1184.[81, 95] 1185.[81, 99] 1186.[82, 86] 1187.[82, 90] 1188.[82, 94] 1189.[82, 98] 1190.[83, 85] 1191.[83, 89] 1192.[83, 93] 1193.[83, 97] 1194.[84, 88] 1195.[84, 92] 1196.[84, 96] 1197.[84, 100] 1198.[85, 87] 1199.[85, 91] 1200.[85, 95] 1201.[85, 99] 1202.[86, 90] 1203.[86, 94] 1204.[86, 98] 1205.[87, 89] 1206.[87, 93] 1207.[87, 97] 1208.[88, 92] 1209.[88, 96] 1210.[88, 100] 1211.[89, 91] 1212.[89, 95] 1213.[89, 99] 1214.[90, 94] 1215.[90, 98] 1216.[91, 93] 1217.[91, 97] 1218.[92, 96] 1219.[92, 100] 1220.[93, 95] 1221.[93, 99] 1222.[94, 98] 1223.[95, 97] 1224.[96, 100] 1225.[97, 99]
程序输出和数学计算的结果相互可以印证！
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