The 10th ACM Programming Competition of Zhengzhou Institute of Light Industry and Henan University Invitational Competition (official competition) I. number (hash, binary)

Topic description

Someone just learned digital DP, and he suddenly thought about the following questions one day:

Given n, ask how many pairs <x, y> satisfy:

x, y∈[1, n], x < y

The numbers of [0, 9] appearing in x, y are the same

enter

an integer n (n <= 107)

output

output a number as the answer

sample input

30

Sample output

3

hint

<1, 11> <2, 22> <12, 21>

ideas

The number has a total of 0~910 numbers. For the given number, nwe can traverse it once 1~n. For each number, split the current number into decimal, and then use binary bit pressing to compress it into a state, and mark the current number with an array. The state appeared several times, and finally found$C_n^2$The sum will do.

When the binary bit is pressed, when this bit exists, it isnum|=(1<<i)

code

#include <bits/stdc++.h>
using namespace std;
#define mem(a,b) memset(a,b,sizeof(a))
#define lson l,m,rt<<1
#define rson m+1,r,rt<<1|1
typedef long long ll;
const ll N=1e7+20;
ll vis[15];
ll mp[1025];
int main()
{
    ll n,len=0,num=0;
    scanf("%lld",&n);
    for(ll i=1; i<=n; i++)
    {
        mem(vis,0);
        ll x=i;
        while(x)
        {
            vis[x%10]=1;
            x/=10;
        }
        ll num=0;
        for(ll j=0; j<=9; j++)
            if(vis[j])
                num|=(1<<j);
        mp[num]++;
    }
    ll sum=0;
    for(ll i=1; i<=1025; i++)
        if(mp[i])
            sum+=(mp[i])*(mp[i]-1)/2;
    printf("%lld\n",sum);
    return 0;
}