URAL 2052 Physical Education（数位DP）

题目链接：https://vjudge.net/contest/254142#problem/G

参考题解：https://blog.csdn.net/zearot/article/details/47984379

#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define LL __int128
#define ull unsigned long long
#define mst(a,b) memset((a),(b),sizeof(a))
#define mp(a,b) make_pair(a,b)
#define pi acos(-1)
#define pii pair<int,int>
#define pb push_back
const int INF = 0x3f3f3f3f;
const double eps = 1e-6;
const int MAXN = 1e5 + 10;
const int MAXM = 2e6 + 10;
const ll mod = 1e9 + 7;

int f[15][100], dig[15];

void init() {
    mst(f, 0);
    f[0][0] = 1;
    for(int i = 1; i <= 10; i++)
        for(int j = 0; j <= i * 9; j++)
            for(int k = 0; k <= min(9, j); k++)
                f[i][j] += f[i - 1][j - k];
}

int findall(int pos,int sum,bool limit) {
    if(!limit || !pos) return f[pos][sum];
    int ans = 0, mx = min(dig[pos], sum);
    for(int i = 0; i <= mx; i++)
        ans += findall(pos - 1,sum - i,limit && i == dig[pos]);
    return ans;
}

int shu[15];

void findd(int pos,int sum,int rnk,bool limit) {
    if(!pos) return ;
    if(!limit) {
        int mx = min(9, sum);
        for(int i = 0; i <= mx; i++) {
            if(f[pos - 1][sum - i] < rnk) rnk -= f[pos - 1][sum - i];
            else {
                shu[pos] = i;
                findd(pos - 1,sum - i,rnk,limit);
                return ;
            }
        }
    } else {
        int mx = min(dig[pos], sum);
        for(int i = 0; i <= mx; i++) {
            int temp = findall(pos - 1,sum - i,i == dig[pos]);
            if(temp < rnk) rnk -= temp;
            else {
                shu[pos] = i;
                findd(pos - 1,sum - i,rnk,i == dig[pos]);
                return ;
            }
        }
    }
}

int main()
{
#ifdef local
    freopen("data.txt", "r", stdin);
//    freopen("data.txt", "w", stdout);
#endif
    init();
    int n,len = 0;
    scanf("%d",&n);
    while(n) {
        dig[++len] = n % 10;
        n /= 10;
    }
    int ans = 0,sum = 0;
    for(int i = 1; i <= len * 9; i++) {
        int num = findall(len,i,true);
        if(!num) continue;
        int l = 1, r = num, num1;
        bool flag = false;
        while(l <= r) {
            int mid = (l + r) >> 1;
            findd(len,i,mid,true);
            num1 = 0;
            for(int j = len; j >= 1; j--) {
                if(!num1 && !shu[j]) continue;
                num1 = num1 * 10 + shu[j];
            }
            if(sum + mid > num1) l = mid + 1;
            else if(sum + mid < num1) r = mid - 1;
            else {
                flag = true;
                break;
            }
        }
        if(flag) ans++;
        sum += num;
    }
    printf("%d
",ans);
    return 0;
}