Codeforces Round #460 (Div. 2) B Perfect Number（二分+数位dp）

Posted 2021-01-11 zhgyki

题目传送门

B. Perfect Number

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

We consider a positive integer perfect, if and only if the sum of its digits is exactly $\mathrm{1010.\; Given\; a\; positive\; integer kk,\; your\; task\; is\; to\; find\; the kk-th\; smallest\; perfect\; positive\; integer.}$

Input

A single line with a positive integer $\mathrm{kk (1\le k\le 100001\le k\le 10000).}$

Output

A single number, denoting the $\mathrm{kk-th\; smallest\; perfect\; integer.}$

Examples

input

Copy

1

output

Copy

19

input

Copy

2

output

Copy

28

Note

The first perfect integer is $\mathrm{1919 and\; the\; second\; one\; is 2828.}$

题意：求出第k个各位数和为10的数

题解：本题k的范围比较小，所以暴力可以解决

但是当范围大的时候，就要用数位dp了

数位dp记录的是小于某个数的符合条件的数有多少个

用二分去枚举

代码：

#include<iostream>
#include<string.h>
#include<algorithm>
#include<stdio.h>
#include<queue>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef long long ll;
typedef pair<int,int> PII;
#define mod 1000000007
#define pb push_back
#define mp make_pair
#define all(x) (x).begin(),(x).end()
#define fi first
#define se second
//head
int k;
ll a[10005];
bool check(ll x)
{
    ll ans=0;
    while(x){
       ans+=x%10;
       x/=10;
    }
    return ans==10;
}
int main()
{
    scanf("%d",&k);
    int p=0;
   for(int i=0;i<11000006;i++)
   {
       if(check(i))
          {
              a[++p]=i;
          }
   }
   printf("%lld
",a[k]);
    return 0;
}

枚举 873 ms 300 KB

#include<bits/stdc++.h>
using namespace std;
int k;
bool check(int x)
{
    int ans=0;
    while(x){
       ans+=x%10;
       x/=10;
    }
    return ans==10;
}
int main()
{
    scanf("%d",&k);
    int p=0;
   for(int i=0;i<11000006;i++)
   {
       if(check(i))
          {
              p++;
              if(p==k)
              {
                    printf("%d
",i);
              }
          }
   }

    return 0;
}

枚举 140 ms 0 KB

 

#include<iostream>
#include<string.h>
#include<algorithm>
#include<stdio.h>
#include<queue>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef long long ll;
typedef pair<int,int> PII;
#define mod 1000000007
#define INF 0x3f3f3f3f
#define pb push_back
#define mp make_pair
#define all(x) (x).begin(),(x).end()
#define fi first
#define se second
//head
int k;
int bit[11];
int dp[20][11];//表示到第i位，数位和为j的个数
int dfs(int pos,int sum,bool limit)
{
    if(pos==-1) return sum==10;
    if(sum>10)return 0;
    if(!limit&&dp[pos][sum]!=-1)return dp[pos][sum];
    int ans=0;
    int up=limit?bit[pos]:9;
    for(int i=0;i<=up;i++)
    {
        ans+=dfs(pos-1,sum+i,limit&&(i==up));
    }
    if(!limit) dp[pos][sum]=ans;
    return ans;
}
int calc(int x)
{
    int len=0;
    while(x)
    {
        bit[len++]=x%10;
        x/=10;
    }
    return dfs(len-1,0,true);
}
int main()
{
    memset(dp,-1,sizeof(dp));
    while(~scanf("%d",&k))
    {
        int lb=0,ub=INF;
        int ans=0;
        while(ub-lb>1){
            int mid=(lb+ub)/2;
            if(calc(mid)<k) lb=mid;
            else ans=mid,ub=mid;
        }
        printf("%d
",ans);
    }

    return 0;
}

二分+数位dp 31 ms 0 KB