N is a positive integer divisible by 7, and N does NOT contain the digit 9.
Devise an algorithm to lexicographically list all valid values of N ≤ 2022.
"Lexicographically" might mean merely to do the sort with leftmost digit primary regardless of whether that's the tens position or the thousands position, etc., so that for example 1400 precedes 805 (by many positions). Or, it implies we're using words rather than digits.
The key part is that the numbers have to be converted to strings for the sort to proceed lexicographically rather than numerically, regardless of whether you let the programming language do the sort behind the scenes as done here, or whether you write your own sort using comparison operators. Writing to a file and then sorting the file would work also, if the numbers are written left justified with no leading zeros.
So the program does both, first digits, then words:
clc,clearvars
a=string(7:7:2022);
b=a(~contains(a,'9'));
for i=1:length(b)
wordList(i)=words(str2double(b(i)));
end
c=sort(b);
wordList=sort(wordList);
for i=1:length(c)
fprintf('%-5d \n',str2double(c(i)))
end
for i=1:length(wordList)
fprintf('%-5s \n', wordList(i))
end
function w=words(n)
major=["" " thousand" " million" " trillion"];
w=""; ns=char(string(n));
for i=0:3
ns=['000',ns];
piece=ns(end-2-3*i:end-3*i);
if length(piece)>0
piecePlus=['000' piece];
piece=(piecePlus(end-2:end));
if isequal(piece,'000')
continue
end
part=procPiece(piece);
w=strcat(part,major(i+1),w);
end
end
function p=procPiece(s)
unitsTeens=["","one","two","three","four","five", ...
"six","seven","eight","nine","ten", ...
"eleven","twelve","thirteen","fourteen", ...
"fifteen","sixteen","seventeen", ...
"eighteen","nineteen"];
tens=["","twenty","thirty","forty","fifty", ...
"sixty","seventy","eighty","ninety"];
a="";
if s(1)>'0'
a=strcat(a," ", unitsTeens(str2num(s(1))+1) ," hundred");
end
lastPart=str2double(s(2:3));
if lastPart<20
a=strcat(a," ",unitsTeens(lastPart+1));
else
a=strcat(a," ",tens(str2double(s(2)))," ",unitsTeens(str2double(s(3))+1));
end
p=a;
end
end
1001
1008
1015
1022
1036
1043
105
1050
1057
1064
1071
1078
1085
1106
1113
112
1120
1127
1134
1141
1148
1155
1162
1176
1183
1204
1211
1218
1225
1232
1246
1253
126
1260
1267
1274
1281
1288
1302
1316
1323
133
1330
1337
1344
1351
1358
1365
1372
1386
14
140
1400
1407
1414
1421
1428
1435
1442
1456
1463
147
1470
1477
1484
1505
1512
1526
1533
154
1540
1547
1554
1561
1568
1575
1582
1603
161
1610
1617
1624
1631
1638
1645
1652
1666
1673
168
1680
1687
1701
1708
1715
1722
1736
1743
175
1750
1757
1764
1771
1778
1785
1806
1813
182
1820
1827
1834
1841
1848
1855
1862
1876
1883
2002
2016
203
21
210
217
224
231
238
245
252
266
273
28
280
287
301
308
315
322
336
343
35
350
357
364
371
378
385
406
413
42
420
427
434
441
448
455
462
476
483
504
511
518
525
532
546
553
56
560
567
574
581
588
602
616
623
63
630
637
644
651
658
665
672
686
7
70
700
707
714
721
728
735
742
756
763
77
770
777
784
805
812
826
833
84
840
847
854
861
868
875
882
eight hundred eighty two
eight hundred fifty four
eight hundred five
eight hundred forty
eight hundred forty seven
eight hundred seventy five
eight hundred sixty eight
eight hundred sixty one
eight hundred thirty three
eight hundred twelve
eight hundred twenty six
eighty four
fifty six
five hundred eighteen
five hundred eighty eight
five hundred eighty one
five hundred eleven
five hundred fifty three
five hundred forty six
five hundred four
five hundred seventy four
five hundred sixty
five hundred sixty seven
five hundred thirty two
five hundred twenty five
forty two
four hundred eighty three
four hundred fifty five
four hundred forty eight
four hundred forty one
four hundred seventy six
four hundred six
four hundred sixty two
four hundred thirteen
four hundred thirty four
four hundred twenty
four hundred twenty seven
fourteen
one hundred eighty two
one hundred fifty four
one hundred five
one hundred forty
one hundred forty seven
one hundred seventy five
one hundred sixty eight
one hundred sixty one
one hundred thirty three
one hundred twelve
one hundred twenty six
one thousand eight
one thousand eight hundred eighty three
one thousand eight hundred fifty five
one thousand eight hundred forty eight
one thousand eight hundred forty one
one thousand eight hundred seventy six
one thousand eight hundred six
one thousand eight hundred sixty two
one thousand eight hundred thirteen
one thousand eight hundred thirty four
one thousand eight hundred twenty
one thousand eight hundred twenty seven
one thousand eighty five
one thousand fifteen
one thousand fifty
one thousand fifty seven
one thousand five hundred eighty two
one thousand five hundred fifty four
one thousand five hundred five
one thousand five hundred forty
one thousand five hundred forty seven
one thousand five hundred seventy five
one thousand five hundred sixty eight
one thousand five hundred sixty one
one thousand five hundred thirty three
one thousand five hundred twelve
one thousand five hundred twenty six
one thousand forty three
one thousand four hundred
one thousand four hundred eighty four
one thousand four hundred fifty six
one thousand four hundred forty two
one thousand four hundred fourteen
one thousand four hundred seven
one thousand four hundred seventy
one thousand four hundred seventy seven
one thousand four hundred sixty three
one thousand four hundred thirty five
one thousand four hundred twenty eight
one thousand four hundred twenty one
one thousand one
one thousand one hundred eighty three
one thousand one hundred fifty five
one thousand one hundred forty eight
one thousand one hundred forty one
one thousand one hundred seventy six
one thousand one hundred six
one thousand one hundred sixty two
one thousand one hundred thirteen
one thousand one hundred thirty four
one thousand one hundred twenty
one thousand one hundred twenty seven
one thousand seven hundred eight
one thousand seven hundred eighty five
one thousand seven hundred fifteen
one thousand seven hundred fifty
one thousand seven hundred fifty seven
one thousand seven hundred forty three
one thousand seven hundred one
one thousand seven hundred seventy eight
one thousand seven hundred seventy one
one thousand seven hundred sixty four
one thousand seven hundred thirty six
one thousand seven hundred twenty two
one thousand seventy eight
one thousand seventy one
one thousand six hundred eighty
one thousand six hundred eighty seven
one thousand six hundred fifty two
one thousand six hundred forty five
one thousand six hundred seventeen
one thousand six hundred seventy three
one thousand six hundred sixty six
one thousand six hundred ten
one thousand six hundred thirty eight
one thousand six hundred thirty one
one thousand six hundred three
one thousand six hundred twenty four
one thousand sixty four
one thousand thirty six
one thousand three hundred eighty six
one thousand three hundred fifty eight
one thousand three hundred fifty one
one thousand three hundred forty four
one thousand three hundred seventy two
one thousand three hundred sixteen
one thousand three hundred sixty five
one thousand three hundred thirty
one thousand three hundred thirty seven
one thousand three hundred twenty three
one thousand three hundred two
one thousand twenty two
one thousand two hundred eighteen
one thousand two hundred eighty eight
one thousand two hundred eighty one
one thousand two hundred eleven
one thousand two hundred fifty three
one thousand two hundred forty six
one thousand two hundred four
one thousand two hundred seventy four
one thousand two hundred sixty
one thousand two hundred sixty seven
one thousand two hundred thirty two
one thousand two hundred twenty five
seven
seven hundred
seven hundred eighty four
seven hundred fifty six
seven hundred forty two
seven hundred fourteen
seven hundred seven
seven hundred seventy
seven hundred seventy seven
seven hundred sixty three
seven hundred thirty five
seven hundred twenty eight
seven hundred twenty one
seventy
seventy seven
six hundred eighty six
six hundred fifty eight
six hundred fifty one
six hundred forty four
six hundred seventy two
six hundred sixteen
six hundred sixty five
six hundred thirty
six hundred thirty seven
six hundred twenty three
six hundred two
sixty three
thirty five
three hundred eight
three hundred eighty five
three hundred fifteen
three hundred fifty
three hundred fifty seven
three hundred forty three
three hundred one
three hundred seventy eight
three hundred seventy one
three hundred sixty four
three hundred thirty six
three hundred twenty two
twenty eight
twenty one
two hundred eighty
two hundred eighty seven
two hundred fifty two
two hundred forty five
two hundred seventeen
two hundred seventy three
two hundred sixty six
two hundred ten
two hundred thirty eight
two hundred thirty one
two hundred three
two hundred twenty four
two thousand sixteen
two thousand two
|
|
Posted by Charlie
on 2022-05-29 13:34:23 |
solution
