# Solution to the Calculation of P1028 Number in Luogu--Zhgjun

#### Title Description

We want to find the number of natural numbers (nnn containing the input) that have the following properties:

Enter a natural number n n n (n < 1000n \le 1000n < 1000) first, and then process the natural number as follows:

Do nothing;

Add a natural number to its left, but it cannot exceed half of the original number.

After adding a number, continue processing according to this rule until no more natural numbers can be added.

#### Input Format

111 natural numbers n n n (n < 1000n \le 1000n < 1000)

#### Output Format

111 integers representing the number of numbers with this property.

```6
```
```6
```

#### Instructions/Tips

The number that meets the criteria is

6，16，26，126，36，136

## thinking

Unexpectedly, I used to type tables recursively using functions
The code is as follows:

```#include<bits/stdc++.h>
using namespace std;
long long f[1001]{0,1,2,2,4,4,6,6,10,10,14,14,20,20,26,26,36,36,46,46,60,60,74,74,94,94,114,114,140,140,166,166,202,202,238,238,284,284,330,330,390,390,450,450,524,524,598,598,692,692,786,786,900,900,1014,1014,1154,1154,1294,1294,1460,1460,1626,1626,1828,1828,2030,2030,2268,2268,2506,2506,2790,2790,3074,3074,3404,3404,3734,3734,4124,4124,4514,4514,4964,4964,5414,5414,5938,5938,6462,6462,7060,7060,7658,7658,8350,8350,9042,9042,9828,9828,10614,10614,11514,11514,12414,12414,13428,13428,14442,14442,15596,15596,16750,16750,18044,18044,19338,19338,20798,20798,22258,22258,23884,23884,25510,25510,27338,27338,29166,29166,31196,31196,33226,33226,35494,35494,37762,37762,40268,40268,42774,42774,45564,45564,48354,48354,51428,51428,54502,54502,57906,57906,61310,61310,65044,65044,68778,68778,72902,72902,77026,77026,81540,81540,86054,86054,91018,91018,95982,95982,101396,101396,106810,106810,112748,112748,118686,118686,125148,125148,131610,131610,138670,138670,145730,145730,153388,153388,161046,161046,169396,169396,177746,177746,186788,186788,195830,195830,205658,205658,215486,215486,226100,226100,236714,236714,248228,248228,259742,259742,272156,272156,284570,284570,297998,297998,311426,311426,325868,325868,340310,340310,355906,355906,371502,371502,388252,388252,405002,405002,423046,423046,441090,441090,460428,460428,479766,479766,500564,500564,521362,521362,543620,543620,565878,565878,589762,589762,613646,613646,639156,639156,664666,664666,692004,692004,719342,719342,748508,748508,777674,777674,808870,808870,840066,840066,873292,873292,906518,906518,942012,942012,977506,977506,1015268,1015268,1053030,1053030,1093298,1093298,1133566,1133566,1176340,1176340,1219114,1219114,1264678,1264678,1310242,1310242,1358596,1358596,1406950,1406950,1458378,1458378,1509806,1509806,1564308,1564308,1618810,1618810,1676716,1676716,1734622,1734622,1795932,1795932,1857242,1857242,1922286,1922286,1987330,1987330,2056108,2056108,2124886,2124886,2197788,2197788,2270690,2270690,2347716,2347716,2424742,2424742,2506282,2506282,2587822,2587822,2673876,2673876,2759930,2759930,2850948,2850948,2941966,2941966,3037948,3037948,3133930,3133930,3235326,3235326,3336722,3336722,3443532,3443532,3550342,3550342,3663090,3663090,3775838,3775838,3894524,3894524,4013210,4013210,4138358,4138358,4263506,4263506,4395116,4395116,4526726,4526726,4665396,4665396,4804066,4804066,4949796,4949796,5095526,5095526,5248914,5248914,5402302,5402302,5563348,5563348,5724394,5724394,5893790,5893790,6063186,6063186,6240932,6240932,6418678,6418678,6605466,6605466,6792254,6792254,6988084,6988084,7183914,7183914,7389572,7389572,7595230,7595230,7810716,7810716,8026202,8026202,8252302,8252302,8478402,8478402,8715116,8715116,8951830,8951830,9200058,9200058,9448286,9448286,9708028,9708028,9967770,9967770,10239926,10239926,10512082,10512082,10796652,10796652,11081222,11081222,11379220,11379220,11677218,11677218,11988644,11988644,12300070,12300070,12625938,12625938,12951806,12951806,13292116,13292116,13632426,13632426,13988332,13988332,14344238,14344238,14715740,14715740,15087242,15087242,15475494,15475494,15863746,15863746,16268748,16268748,16673750,16673750,17096796,17096796,17519842,17519842,17960932,17960932,18402022,18402022,18862450,18862450,19322878,19322878,19802644,19802644,20282410,20282410,20782974,20782974,21283538,21283538,21804900,21804900,22326262,22326262,22869882,22869882,23413502,23413502,23979380,23979380,24545258,24545258,25135020,25135020,25724782,25724782,26338428,26338428,26952074,26952074,27591230,27591230,28230386,28230386,28895052,28895052,29559718,29559718,30251722,30251722,30943726,30943726,31663068,31663068,32382410,32382410,33130918,33130918,33879426,33879426,34657100,34657100,35434774,35434774,36243644,36243644,37052514,37052514,37892580,37892580,38732646,38732646,39605938,39605938,40479230,40479230,41385748,41385748,42292266,42292266,43234278,43234278,44176290,44176290,45153796,45153796,46131302,46131302,47146570,47146570,48161838,48161838,49214868,49214868,50267898,50267898,51361196,51361196,52454494,52454494,53588060,53588060,54721626,54721626,55897966,55897966,57074306,57074306,58293420,58293420,59512534,59512534,60777212,60777212,62041890,62041890,63352132,63352132,64662374,64662374,66020970,66020970,67379566,67379566,68786516,68786516,70193466,70193466,71651844,71651844,73110222,73110222,74620028,74620028,76129834,76129834,77694142,77694142,79258450,79258450,80877260,80877260,82496070,82496070,84172786,84172786,85849502,85849502,87584124,87584124,89318746,89318746,91114678,91114678,92910610,92910610,94767852,94767852,96625094,96625094,98547380,98547380,100469666,100469666,102456996,102456996,104444326,104444326,106500434,106500434,108556542,108556542,110681428,110681428,112806314,112806314,115004102,115004102,117201890,117201890,119472580,119472580,121743270,121743270,124090986,124090986,126438702,126438702,128863444,128863444,131288186,131288186,133794468,133794468,136300750,136300750,138888572,138888572,141476394,141476394,144150270,144150270,146824146,146824146,149584076,149584076,152344006,152344006,155194954,155194954,158045902,158045902,160987868,160987868,163929834,163929834,166967782,166967782,170005730,170005730,173139660,173139660,176273590,176273590,179508916,179508916,182744242,182744242,186080964,186080964,189417686,189417686,192861218,192861218,196304750,196304750,199855092,199855092,203405434,203405434,207068524,207068524,210731614,210731614,214507452,214507452,218283290,218283290,222177814,222177814,226072338,226072338,230085548,230085548,234098758,234098758,238237116,238237116,242375474,242375474,246638980,246638980,250902486,250902486,255297602,255297602,259692718,259692718,264219444,264219444,268746170,268746170,273411566,273411566,278076962,278076962,282881028,282881028,287685094,287685094,292634890,292634890,297584686,297584686,302680212,302680212,307775738,307775738,313024652,313024652,318273566,318273566,323675868,323675868,329078170,329078170,334641518,334641518,340204866,340204866,345929260,345929260,351653654,351653654,357547444,357547444,363441234,363441234,369504420,369504420,375567606,375567606,381808538,381808538,388049470,388049470,394468148,394468148,400886826,400886826,407492292,407492292,414097758,414097758,420890012,420890012,427682266,427682266,434670350,434670350,441658434,441658434,448842348,448842348,456026262,456026262,463415834,463415834,470805406,470805406,478400636,478400636,485995866,485995866,493806582,493806582,501617298,501617298,509643500,509643500,517669702,517669702,525922004,525922004,534174306,534174306,542652708,542652708,551131110,551131110,559846226,559846226,568561342,568561342,577513172,577513172,586465002,586465002,595665060,595665060,604865118,604865118,614313404,614313404,623761690,623761690,633469718,633469718,643177746,643177746,653145516,653145516,663113286,663113286,673353212,673353212,683593138,683593138,694105220,694105220,704617302,704617302,715413954,715413954,726210606,726210606,737291828,737291828,748373050,748373050,759752270,759752270,771131490,771131490,782808708,782808708,794485926,794485926,806474570,806474570,818463214,818463214,830763284,830763284,843063354,843063354,855689292,855689292,868315230,868315230,881267036,881267036,894218842,894218842,907510958,907510958,920803074,920803074,934435500,934435500,948067926,948067926,962056258,962056258,976044590,976044590,990388828,990388828,1004733066,1004733066,1019448806,1019448806,1034164546,1034164546,1049251788,1049251788,1064339030,1064339030,1079814524,1079814524,1095290018,1095290018,1111153764,1111153764,1127017510,1127017510,1143286258,1143286258,1159555006,1159555006,1176228756,1176228756,1192902506,1192902506,1209999302,1209999302,1227096098,1227096098,1244615940,1244615940,1262135782,1262135782,1280096714,1280096714,1298057646,1298057646,1316459668,1316459668,1334861690,1334861690,1353724140,1353724140,1372586590,1372586590,1391909468,1391909468,1411232346,1411232346,1431034990,1431034990,1450837634,1450837634,1471120044,1471120044,1491402454,1491402454,1512185428,1512185428,1532968402,1532968402,1554251940,1554251940,1575535478,1575535478,1597340378,1597340378,1619145278,1619145278,1641471540,1641471540,1663797802,1663797802,1686667684,1686667684,1709537566,1709537566,1732951068,1732951068,1756364570,1756364570,1780343950,1780343950,1804323330,1804323330,1828868588,1828868588,1853413846,1853413846,1878548866,1878548866,1903683886,1903683886,1929408668,1929408668,1955133450,1955133450,1981471878};
int main()
{
int n;
scanf("%d",&n);
printf("%lld",f[n]);
return 0;
}
```

Later it seemed that you didn't need to open long long\long long

Okay, don't talk too much, just start explaining

First, this is a typical dynamic programming, where fif_ifi is used to indicate that iii can have at most a few splits.

Then, obviously f1=1f_1=1f1=1

If fif_ifi is required

Then we'll enumerate the numbers that it can split up for the first time, and after that, we'll have the answers for the remaining numbers, and then we'll put them all together.

## Code

```#include<bits/stdc++.h>
using namespace std;
int n;
int f[1001];
int main(){
cin>>n;
for(int i=1;i<=n;i++){
for(int j=1;j<=i/2;j++)//Can only split up to half of itself
f[i]+=f[j];
f[i]++;//Notice that it can be split into itself
}
cout<<f[n];
return 0;
}
```

It should not be difficult to understand

# Thank you - Zhgjun

39 original articles published, 39 praised, 1380 visits

Tags: Programming

Posted on Fri, 06 Mar 2020 19:30:52 -0800 by Monshery