beautiful number

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 801    Accepted Submission(s): 518

Problem Description

Let A=∑ni=1ai?10n?i(1≤ai≤9)(n is the number of A‘s digits). We call A as “beautiful number” if and only if a[i]≥a[i+1] when 1≤i<n and a[i] mod a[j]=0 when 1≤i≤n,i<j≤n(Such as 931 is a "beautiful number" while 87 isn‘t).
Could you tell me the number of “beautiful number” in the interval [L,R](including L and R)?

Input

The fist line contains a single integer T(about 100), indicating the number of cases.
Each test case begins with two integers L,R(1≤L≤R≤109).

Output

For each case, output an integer means the number of “beautiful number”.

Sample Input

2

1 11

999999993 999999999

Sample Output

10

2

Source

BestCoder Round #31

Recommend

hujie

题意：

　　要你输出 [L, R] 范围内的满足高位大于等于地位而且高位mod低位的数要等于0 的数的个数。

题解：

　　1）离线暴力打表

　　　　我们跑[1,1e9] 的所有满足这个条件的数。

 1 #include <iostream>
 2 #include <cstdio>
 3 #include <cstring>
 4 #include <string>
 5 #include <algorithm>
 6 #include <cmath>
 7 #include <vector>
 8 #include <queue>
 9 #include <map>
10 #include <stack>
11 #include <set>
12 using namespace std;
13 typedef long long LL;
14 typedef unsigned long long uLL;
15 #define ms(a, b) memset(a, b, sizeof(a))
16 #define pb push_back
17 #define mp make_pair
18 #define eps 0.0000000001
19 const LL INF = 0x7fffffff;
20 const int inf = 0x3f3f3f3f;
21 const int mod = 10000007;
22 const int maxn = 500+10;
23 int a[1300] ={1,2,3,4,5,6,7,8,9,11,21,22,31,33,41,42,44,51,55,61,62,63,66,71,77,81,82,84,88,91,93,99,111,211,221,222,311,331,333,411,421,422,441,442,444,511,551,555,611,621,622,631,633,661,662,663,666,711,771,777,811,821,822,841,842,844,881,882,884,888,911,931,933,991,993,999,1111,2111,2211,2221,2222,3111,3311,3331,3333,4111,4211,4221,4222,4411,4421,4422,4441,4442,4444,5111,5511,5551,5555,6111,6211,6221,6222,6311,6331,6333,6611,6621,6622,6631,6633,6661,6662,6663,6666,7111,7711,7771,7777,8111,8211,8221,8222,8411,8421,8422,8441,8442,8444,8811,8821,8822,8841,8842,8844,8881,8882,8884,8888,9111,9311,9331,9333,9911,9931,9933,9991,9993,9999,11111,21111,22111,22211,22221,22222,31111,33111,33311,33331,33333,41111,42111,42211,42221,42222,44111,44211,44221,44222,44411,44421,44422,44441,44442,44444,51111,55111,55511,55551,55555,61111,62111,62211,62221,62222,63111,63311,63331,63333,66111,66211,66221,66222,66311,66331,66333,66611,66621,66622,66631,66633,66661,66662,66663,66666,71111,77111,77711,77771,77777,81111,82111,82211,82221,82222,84111,84211,84221,84222,84411,84421,84422,84441,84442,84444,88111,88211,88221,88222,88411,88421,88422,88441,88442,88444,88811,88821,88822,88841,88842,88844,88881,88882,88884,88888,91111,93111,93311,93331,93333,99111,99311,99331,99333,99911,99931,99933,99991,99993,99999,111111,211111,221111,222111,222211,222221,222222,311111,331111,333111,333311,333331,333333,411111,421111,422111,422211,422221,422222,441111,442111,442211,442221,442222,444111,444211,444221,444222,444411,444421,444422,444441,444442,444444,511111,551111,555111,555511,555551,555555,611111,621111,622111,622211,622221,622222,631111,633111,633311,633331,633333,661111,662111,662211,662221,662222,663111,663311,663331,663333,666111,666211,666221,666222,666311,666331,666333,666611,666621,666622,666631,666633,666661,666662,666663,666666,711111,771111,777111,777711,777771,777777,811111,821111,822111,822211,822221,822222,841111,842111,842211,842221,842222,844111,844211,844221,844222,844411,844421,844422,844441,844442,844444,881111,882111,882211,882221,882222,884111,884211,884221,884222,884411,884421,884422,884441,884442,884444,888111,888211,888221,888222,888411,888421,888422,888441,888442,888444,888811,888821,888822,888841,888842,888844,888881,888882,888884,888888,911111,931111,933111,933311,933331,933333,991111,993111,993311,993331,993333,999111,999311,999331,999333,999911,999931,999933,999991,999993,999999,1111111,2111111,2211111,2221111,2222111,2222211,2222221,2222222,3111111,3311111,3331111,3333111,3333311,3333331,3333333,4111111,4211111,4221111,4222111,4222211,4222221,4222222,4411111,4421111,4422111,4422211,4422221,4422222,4441111,4442111,4442211,4442221,4442222,4444111,4444211,4444221,4444222,4444411,4444421,4444422,4444441,4444442,4444444,5111111,5511111,5551111,5555111,5555511,5555551,5555555,6111111,6211111,6221111,6222111,6222211,6222221,6222222,6311111,6331111,6333111,6333311,6333331,6333333,6611111,6621111,6622111,6622211,6622221,6622222,6631111,6633111,6633311,6633331,6633333,6661111,6662111,6662211,6662221,6662222,6663111,6663311,6663331,6663333,6666111,6666211,6666221,6666222,6666311,6666331,6666333,6666611,6666621,6666622,6666631,6666633,6666661,6666662,6666663,6666666,7111111,7711111,7771111,7777111,7777711,7777771,7777777,8111111,8211111,8221111,8222111,8222211,8222221,8222222,8411111,8421111,8422111,8422211,8422221,8422222,8441111,8442111,8442211,8442221,8442222,8444111,8444211,8444221,8444222,8444411,8444421,8444422,8444441,8444442,8444444,8811111,8821111,8822111,8822211,8822221,8822222,8841111,8842111,8842211,8842221,8842222,8844111,8844211,8844221,8844222,8844411,8844421,8844422,8844441,8844442,8844444,8881111,8882111,8882211,8882221,8882222,8884111,8884211,8884221,8884222,8884411,8884421,8884422,8884441,8884442,8884444,8888111,8888211,8888221,8888222,8888411,8888421,8888422,8888441,8888442,8888444,8888811,8888821,8888822,8888841,8888842,8888844,8888881,8888882,8888884,8888888,9111111,9311111,9331111,9333111,9333311,9333331,9333333,9911111,9931111,9933111,9933311,9933331,9933333,9991111,9993111,9993311,9993331,9993333,9999111,9999311,9999331,9999333,9999911,9999931,9999933,9999991,9999993,9999999,11111111,21111111,22111111,22211111,22221111,22222111,22222211,22222221,22222222,31111111,33111111,33311111,33331111,33333111,33333311,33333331,33333333,41111111,42111111,42211111,42221111,42222111,42222211,42222221,42222222,44111111,44211111,44221111,44222111,44222211,44222221,44222222,44411111,44421111,44422111,44422211,44422221,44422222,44441111,44442111,44442211,44442221,44442222,44444111,44444211,44444221,44444222,44444411,44444421,44444422,44444441,44444442,44444444,51111111,55111111,55511111,55551111,55555111,55555511,55555551,55555555,61111111,62111111,62211111,62221111,62222111,62222211,62222221,62222222,63111111,63311111,63331111,63333111,63333311,63333331,63333333,66111111,66211111,66221111,66222111,66222211,66222221,66222222,66311111,66331111,66333111,66333311,66333331,66333333,66611111,66621111,66622111,66622211,66622221,66622222,66631111,66633111,66633311,66633331,66633333,66661111,66662111,66662211,66662221,66662222,66663111,66663311,66663331,66663333,66666111,66666211,66666221,66666222,66666311,66666331,66666333,66666611,66666621,66666622,66666631,66666633,66666661,66666662,66666663,66666666,71111111,77111111,77711111,77771111,77777111,77777711,77777771,77777777,81111111,82111111,82211111,82221111,82222111,82222211,82222221,82222222,84111111,84211111,84221111,84222111,84222211,84222221,84222222,84411111,84421111,84422111,84422211,84422221,84422222,84441111,84442111,84442211,84442221,84442222,84444111,84444211,84444221,84444222,84444411,84444421,84444422,84444441,84444442,84444444,88111111,88211111,88221111,88222111,88222211,88222221,88222222,88411111,88421111,88422111,88422211,88422221,88422222,88441111,88442111,88442211,88442221,88442222,88444111,88444211,88444221,88444222,88444411,88444421,88444422,88444441,88444442,88444444,88811111,88821111,88822111,88822211,88822221,88822222,88841111,88842111,88842211,88842221,88842222,88844111,88844211,88844221,88844222,88844411,88844421,88844422,88844441,88844442,88844444,88881111,88882111,88882211,88882221,88882222,88884111,88884211,88884221,88884222,88884411,88884421,88884422,88884441,88884442,88884444,88888111,88888211,88888221,88888222,88888411,88888421,88888422,88888441,88888442,88888444,88888811,88888821,88888822,88888841,88888842,88888844,88888881,88888882,88888884,88888888,91111111,93111111,93311111,93331111,93333111,93333311,93333331,93333333,99111111,99311111,99331111,99333111,99333311,99333331,99333333,99911111,99931111,99933111,99933311,99933331,99933333,99991111,99993111,99993311,99993331,99993333,99999111,99999311,99999331,99999333,99999911,99999931,99999933,99999991,99999993,99999999,111111111,211111111,221111111,222111111,222211111,222221111,222222111,222222211,222222221,222222222,311111111,331111111,333111111,333311111,333331111,333333111,333333311,333333331,333333333,411111111,421111111,422111111,422211111,422221111,422222111,422222211,422222221,422222222,441111111,442111111,442211111,442221111,442222111,442222211,442222221,442222222,444111111,444211111,444221111,444222111,444222211,444222221,444222222,444411111,444421111,444422111,444422211,444422221,444422222,444441111,444442111,444442211,444442221,444442222,444444111,444444211,444444221,444444222,444444411,444444421,444444422,444444441,444444442,444444444,511111111,551111111,555111111,555511111,555551111,555555111,555555511,555555551,555555555,611111111,621111111,622111111,622211111,622221111,622222111,622222211,622222221,622222222,631111111,633111111,633311111,633331111,633333111,633333311,633333331,633333333,661111111,662111111,662211111,662221111,662222111,662222211,662222221,662222222,663111111,663311111,663331111,663333111,663333311,663333331,663333333,666111111,666211111,666221111,666222111,666222211,666222221,666222222,666311111,666331111,666333111,666333311,666333331,666333333,666611111,666621111,666622111,666622211,666622221,666622222,666631111,666633111,666633311,666633331,666633333,666661111,666662111,666662211,666662221,666662222,666663111,666663311,666663331,666663333,666666111,666666211,666666221,666666222,666666311,666666331,666666333,666666611,666666621,666666622,666666631,666666633,666666661,666666662,666666663,666666666,711111111,771111111,777111111,777711111,777771111,777777111,777777711,777777771,777777777,811111111,821111111,822111111,822211111,822221111,822222111,822222211,822222221,822222222,841111111,842111111,842211111,842221111,842222111,842222211,842222221,842222222,844111111,844211111,844221111,844222111,844222211,844222221,844222222,844411111,844421111,844422111,844422211,844422221,844422222,844441111,844442111,844442211,844442221,844442222,844444111,844444211,844444221,844444222,844444411,844444421,844444422,844444441,844444442,844444444,881111111,882111111,882211111,882221111,882222111,882222211,882222221,882222222,884111111,884211111,884221111,884222111,884222211,884222221,884222222,884411111,884421111,884422111,884422211,884422221,884422222,884441111,884442111,884442211,884442221,884442222,884444111,884444211,884444221,884444222,884444411,884444421,884444422,884444441,884444442,884444444,888111111,888211111,888221111,888222111,888222211,888222221,888222222,888411111,888421111,888422111,888422211,888422221,888422222,888441111,888442111,888442211,888442221,888442222,888444111,888444211,888444221,888444222,888444411,888444421,888444422,888444441,888444442,888444444,888811111,888821111,888822111,888822211,888822221,888822222,888841111,888842111,888842211,888842221,888842222,888844111,888844211,888844221,888844222,888844411,888844421,888844422,888844441,888844442,888844444,888881111,888882111,888882211,888882221,888882222,888884111,888884211,888884221,888884222,888884411,888884421,888884422,888884441,888884442,888884444,888888111,888888211,888888221,888888222,888888411,888888421,888888422,888888441,888888442,888888444,888888811,888888821,888888822,888888841,888888842,888888844,888888881,888888882,888888884,888888888,911111111,931111111,933111111,933311111,933331111,933333111,933333311,933333331,933333333,991111111,993111111,993311111,993331111,993333111,993333311,993333331,993333333,999111111,999311111,999331111,999333111,999333311,999333331,999333333,999911111,999931111,999933111,999933311,999933331,999933333,999991111,999993111,999993311,999993331,999993333,999999111,999999311,999999331,999999333,999999911,999999931,999999933,999999991,999999993,999999999};
24 int main() {
25 #ifdef LOCAL
26     freopen("input.txt", "r", stdin);
27 //        freopen("output.txt", "w", stdout);
28 #endif
29     ios::sync_with_stdio(0);cin.tie(0);
30     int t;
31     cin >> t;
32     while(t--){
33         int L, R;
34         cin >> L >> R;
35         int ans = 0;
36         for(int i=0;i<1299;i++){
37             if(a[i]>=L&&a[i]<=R)    ans++;
38         }
39         cout << ans << endl;
40     }
41     return 0;
42 }

　　2）dfs

　　　　最大也就10个位，暴力dfs每一个位。

 1 #include <iostream>
 2 #include <cstdio>
 3 #include <cstring>
 4 #include <string>
 5 #include <algorithm>
 6 #include <cmath>
 7 #include <vector>
 8 #include <queue>
 9 #include <map>
10 #include <stack>
11 #include <set>
12 using namespace std;
13 typedef long long LL;
14 typedef unsigned long long uLL;
15 #define ms(a, b) memset(a, b, sizeof(a))
16 #define pb push_back
17 #define mp make_pair
18 #define eps 0.0000000001
19 const LL INF = 0x7fffffff;
20 const int inf = 0x3f3f3f3f;
21 const int mod = 10000007;
22 const int maxn = 500+10;
23 int L, R;
24 int ans = 0;
25 void dfs(LL num, int pre)
26 {
27     if(num>R)   return;
28     if(num>=L)  ans++;
29     for(int i = 1;i<=pre;i++){
30         if(pre%i==0)
31             dfs(num*10+i, i);
32     }
33 }
34 int main() {
35 #ifdef LOCAL
36     freopen("input.txt", "r", stdin);
37 //        freopen("output.txt", "w", stdout);
38 #endif
39     ios::sync_with_stdio(0);cin.tie(0);
40     int t;
41     cin >> t;
42     while(t--){
43         ans = 0;
44         cin >> L >> R;
45         for(int i = 1;i<=9;i++){
46             dfs(i, i);
47         }
48         cout << ans << endl;
49     }
50     return 0;
51 }

　　3）数位dp

　　　　跟dfs很像，但是加上了记忆话搜索。

 1 #include <iostream>
 2 #include <cstdio>
 3 #include <cstring>
 4 #include <string>
 5 #include <algorithm>
 6 #include <cmath>
 7 #include <vector>
 8 #include <queue>
 9 #include <map>
10 #include <stack>
11 #include <set>
12 using namespace std;
13 typedef long long LL;
14 typedef unsigned long long uLL;
15 #define ms(a, b) memset(a, b, sizeof(a))
16 #define pb push_back
17 #define mp make_pair
18 #define eps 0.0000000001
19 const LL INF = 0x7fffffff;
20 const int inf = 0x3f3f3f3f;
21 const int mod = 10000007;
22 const int maxn = 500+10;
23 int L, R;
24 int ans = 0;
25 int a[15];
26 int dp[25][10];
27 int dfs(int pos, bool lead, bool limit, int pre)
28 {
29     if(pos == 0)    return 1;
30     if(!limit&&!lead&&dp[pos][pre]!=-1) return dp[pos][pre];
31     int up = limit?a[pos]:9;
32     LL ans = 0;
33     for(int i = 0;i<=up;i++){
34         if(lead||pre>=i&&i!=0&&pre%i==0){
35             ans +=dfs(pos-1, lead&&i==0, limit&&i==a[pos], i);
36         }
37     }
38     if(!limit&&!lead)   dp[pos][pre] = ans;
39     return ans;
40 }
41 int solve(int x)
42 {
43     int len = 0;
44     while(x){
45         a[++len] = x%10;
46         x/=10;
47     }
48     return dfs(len, true, true, 0);
49 }
50 int main() {
51 #ifdef LOCAL
52     freopen("input.txt", "r", stdin);
53 //        freopen("output.txt", "w", stdout);
54 #endif
55     ios::sync_with_stdio(0);cin.tie(0);
56     int t;
57     cin >> t;
58     ms(dp, -1);
59     while(t--){
60         cin >> L >> R;
61         cout << solve(R) - solve(L-1) << endl;
62     }
63     return 0;
64 }