题意
将所有每位满足递减的整数排序，问第 \(k\) 大的是多少，不包括 \(0\)。
思路
我们发现最大的满足要求的整数是 \(9876543210\) ，只有 \(1e10\) 的大小，\(k\) 只有不到 \(3000\) 的大小，可以从小到大枚举所有的数，从 T1 粘来判断函数打一个表就解决了。
打表程序
#include<iostream>
#include<algorithm>
using namespace std;
#define int long long
int k,sum=1;
int ans[100010],num,an;
bool check(int x){
int tmp=-1;
while(x){
if(x%10<=tmp) return 0;
tmp=x%10;
x/=10;
}
return 1;
}
signed main(){
//cin>>k;
freopen("11.out","w",stdout);
while(1){
if(check(sum)){
num++;
printf("%lld,",sum);
}
if(sum==9876543210){
return 0;
}
sum++;
}
return 0;
}
最终程序
#include<iostream>
using namespace std;
long long ans[10000]={0,1,2,3,4,5,6,7,8,9,10,20,21,30,31,32,40,41,42,43,50,51,52,53,54,60,61,62,63,64,65,70,71,72,73,74,75,76,80,81,82,83,84,85,86,87,90,91,92,93,94,95,96,97,98,210,310,320,321,410,420,421,430,431,432,510,520,521,530,531,532,540,541,542,543,610,620,621,630,631,632,640,641,642,643,650,651,652,653,654,710,720,721,730,731,732,740,741,742,743,750,751,752,753,754,760,761,762,763,764,765,810,820,821,830,831,832,840,841,842,843,850,851,852,853,854,860,861,862,863,864,865,870,871,872,873,874,875,876,910,920,921,930,931,932,940,941,942,943,950,951,952,953,954,960,961,962,963,964,965,970,971,972,973,974,975,976,980,981,982,983,984,985,986,987,3210,4210,4310,4320,4321,5210,5310,5320,5321,5410,5420,5421,5430,5431,5432,6210,6310,6320,6321,6410,6420,6421,6430,6431,6432,6510,6520,6521,6530,6531,6532,6540,6541,6542,6543,7210,7310,7320,7321,7410,7420,7421,7430,7431,7432,7510,7520,7521,7530,7531,7532,7540,7541,7542,7543,7610,7620,7621,7630,7631,7632,7640,7641,7642,7643,7650,7651,7652,7653,7654,8210,8310,8320,8321,8410,8420,8421,8430,8431,8432,8510,8520,8521,8530,8531,8532,8540,8541,8542,8543,8610,8620,8621,8630,8631,8632,8640,8641,8642,8643,8650,8651,8652,8653,8654,8710,8720,8721,8730,8731,8732,8740,8741,8742,8743,8750,8751,8752,8753,8754,8760,8761,8762,8763,8764,8765,9210,9310,9320,9321,9410,9420,9421,9430,9431,9432,9510,9520,9521,9530,9531,9532,9540,9541,9542,9543,9610,9620,9621,9630,9631,9632,9640,9641,9642,9643,9650,9651,9652,9653,9654,9710,9720,9721,9730,9731,9732,9740,9741,9742,9743,9750,9751,9752,9753,9754,9760,9761,9762,9763,9764,9765,9810,9820,9821,9830,9831,9832,9840,9841,9842,9843,9850,9851,9852,9853,9854,9860,9861,9862,9863,9864,9865,9870,9871,9872,9873,9874,9875,9876,43210,53210,54210,54310,54320,54321,63210,64210,64310,64320,64321,65210,65310,65320,65321,65410,65420,65421,65430,65431,65432,73210,74210,74310,74320,74321,75210,75310,75320,75321,75410,75420,75421,75430,75431,75432,76210,76310,76320,76321,76410,76420,76421,76430,76431,76432,76510,76520,76521,76530,76531,76532,76540,76541,76542,76543,83210,84210,84310,84320,84321,85210,85310,85320,85321,85410,85420,85421,85430,85431,85432,86210,86310,86320,86321,86410,86420,86421,86430,86431,86432,86510,86520,86521,86530,86531,86532,86540,86541,86542,86543,87210,87310,87320,87321,87410,87420,87421,87430,87431,87432,87510,87520,87521,87530,87531,87532,87540,87541,87542,87543,87610,87620,87621,87630,87631,87632,87640,87641,87642,87643,87650,87651,87652,87653,87654,93210,94210,94310,94320,94321,95210,95310,95320,95321,95410,95420,95421,95430,95431,95432,96210,96310,96320,96321,96410,96420,96421,96430,96431,96432,96510,96520,96521,96530,96531,96532,96540,96541,96542,96543,97210,97310,97320,97321,97410,97420,97421,97430,97431,97432,97510,97520,97521,97530,97531,97532,97540,97541,97542,97543,97610,97620,97621,97630,97631,97632,97640,97641,97642,97643,97650,97651,97652,97653,97654,98210,98310,98320,98321,98410,98420,98421,98430,98431,98432,98510,98520,98521,98530,98531,98532,98540,98541,98542,98543,98610,98620,98621,98630,98631,98632,98640,98641,98642,98643,98650,98651,98652,98653,98654,98710,98720,98721,98730,98731,98732,98740,98741,98742,98743,98750,98751,98752,98753,98754,98760,98761,98762,98763,98764,98765,543210,643210,653210,654210,654310,654320,654321,743210,753210,754210,754310,754320,754321,763210,764210,764310,764320,764321,765210,765310,765320,765321,765410,765420,765421,765430,765431,765432,843210,853210,854210,854310,854320,854321,863210,864210,864310,864320,864321,865210,865310,865320,865321,865410,865420,865421,865430,865431,865432,873210,874210,874310,874320,874321,875210,875310,875320,875321,875410,875420,875421,875430,875431,875432,876210,876310,876320,876321,876410,876420,876421,876430,876431,876432,876510,876520,876521,876530,876531,876532,876540,876541,876542,876543,943210,953210,954210,954310,954320,954321,963210,964210,964310,964320,964321,965210,965310,965320,965321,965410,965420,965421,965430,965431,965432,973210,974210,974310,974320,974321,975210,975310,975320,975321,975410,975420,975421,975430,975431,975432,976210,976310,976320,976321,976410,976420,976421,976430,976431,976432,976510,976520,976521,976530,976531,976532,976540,976541,976542,976543,983210,984210,984310,984320,984321,985210,985310,985320,985321,985410,985420,985421,985430,985431,985432,986210,986310,986320,986321,986410,986420,986421,986430,986431,986432,986510,986520,986521,986530,986531,986532,986540,986541,986542,986543,987210,987310,987320,987321,987410,987420,987421,987430,987431,987432,987510,987520,987521,987530,987531,987532,987540,987541,987542,987543,987610,987620,987621,987630,987631,987632,987640,987641,987642,987643,987650,987651,987652,987653,987654,6543210,7543210,7643210,7653210,7654210,7654310,7654320,7654321,8543210,8643210,8653210,8654210,8654310,8654320,8654321,8743210,8753210,8754210,8754310,8754320,8754321,8763210,8764210,8764310,8764320,8764321,8765210,8765310,8765320,8765321,8765410,8765420,8765421,8765430,8765431,8765432,9543210,9643210,9653210,9654210,9654310,9654320,9654321,9743210,9753210,9754210,9754310,9754320,9754321,9763210,9764210,9764310,9764320,9764321,9765210,9765310,9765320,9765321,9765410,9765420,9765421,9765430,9765431,9765432,9843210,9853210,9854210,9854310,9854320,9854321,9863210,9864210,9864310,9864320,9864321,9865210,9865310,9865320,9865321,9865410,9865420,9865421,9865430,9865431,9865432,9873210,9874210,9874310,9874320,9874321,9875210,9875310,9875320,9875321,9875410,9875420,9875421,9875430,9875431,9875432,9876210,9876310,9876320,9876321,9876410,9876420,9876421,9876430,9876431,9876432,9876510,9876520,9876521,9876530,9876531,9876532,9876540,9876541,9876542,9876543,76543210,86543210,87543210,87643210,87653210,87654210,87654310,87654320,87654321,96543210,97543210,97643210,97653210,97654210,97654310,97654320,97654321,98543210,98643210,98653210,98654210,98654310,98654320,98654321,98743210,98753210,98754210,98754310,98754320,98754321,98763210,98764210,98764310,98764320,98764321,98765210,98765310,98765320,98765321,98765410,98765420,98765421,98765430,98765431,98765432,876543210,976543210,986543210,987543210,987643210,987653210,987654210,987654310,987654320,987654321,9876543210};
int main(){
int k;
cin>>k;
cout<<ans[k]<<endl;
return 0;
}