HDU 3271-SNIBB（数位dp）

题意：给一个数q，

q=1时求给定区间，给定进制，各数位和等于m的数字的个数

q=2时求给定区间，给定进制，各数位和等于m的数字中的第k大的数字

分析：dp[i][sum][j],表示长度为i当前数位和是sum,进制是j的个数，q=2时用二分求出k大数

题意给的区间[x,y]，x不一定小于y，给定区间没k大数，则输出 Could not find the Number!

#include <map>

#include <set>

#include <list>

#include <cmath>

#include <queue>

#include <stack>

#include <cstdio>

#include <vector>

#include <string>

#include <cctype>

#include <complex>

#include <cassert>

#include <utility>

#include <cstring>

#include <cstdlib>

#include <iostream>

#include <algorithm>

using namespace std;

typedef pair<int,int> PII;

typedef long long ll;

#define lson l,m,rt<<1

#define pi acos(-1.0)

#define rson m+1,r,rt<<11

#define All 1,N,1

#define read freopen("in.txt", "r", stdin)

const ll  INFll = 0x3f3f3f3f3f3f3f3fLL;

const int INF= 0x7ffffff;

const int mod =  1000000007;

ll dp[50][500][65],x,y,k;

int b,m,bit[50];

ll dfs(int i,int s,int j,int e){

    if(i==0)return (s==m);

    if(!e&&dp[i][s][j]!=-1)return dp[i][s][j];

    int u=e?bit[i]:b-1;

    ll num=0;

    for(int v=0;v<=u;++v){

        num+=dfs(i-1,s+v,j,e&&(v==u));

    }

    return e?num:dp[i][s][j]=num;

}

ll solve1(ll a){

    int len=0;

    if(a<0)return 0;

    while(a){

        bit[++len]=a%b;

        a/=b;

    }

    return dfs(len,0,b,1);

}

ll solve2(){

    ll l=x,r=y;

    ll num=solve1(x-1);

    if(solve1(y)-num<k)return -1;

    while(l<=r){

        ll mid=(l+r)>>1;

        if(solve1(mid)-num<k)l=mid+1;

        else r=mid-1;

    }

    return l;

}

int main()

{

    int q,cas=0;

    while(~scanf("%d",&q)){

        memset(dp,-1,sizeof(dp));

        printf("Case %d:\n",++cas);

        if(q==1){

            scanf("%I64d%I64d%d%d",&x,&y,&b,&m);

            if(x>y)swap(x,y);

            printf("%I64d\n",solve1(y)-solve1(x-1));

        }

        else{

            scanf("%I64d%I64d%d%d%I64d",&x,&y,&b,&m,&k);

            if(x>y)swap(x,y);

            ll tmp=solve2();

            if(tmp!=-1)

            printf("%I64d\n",tmp);

            else

            printf("Could not find the Number!\n");

        }

    }

return 0;

}