Let's introduce a number system which is based on a roman digits. There are digits I, V, X, L which correspond to the numbers 11, 55, 1010and 5050 respectively. The use of other roman digits is not allowed.
Numbers in this system are written as a sequence of one or more digits. We define the value of the sequence simply as the sum of digits in it.
For example, the number XXXV evaluates to 3535 and the number IXI — to 1212.
Pay attention to the difference to the traditional roman system — in our system any sequence of digits is valid, moreover the order of digits doesn't matter, for example IX means 1111, not 99.
One can notice that this system is ambiguous, and some numbers can be written in many different ways. Your goal is to determine how many distinct integers can be represented by exactly nn roman digits I, V, X, L.
The only line of the input file contains a single integer nn (1≤n≤1091≤n≤109) — the number of roman digits to use.
Output a single integer — the number of distinct integers which can be represented using nn roman digits exactly.
1
4
2
10
10
244
In the first sample there are exactly 44 integers which can be represented — I, V, X and L.
In the second sample it is possible to represent integers 22 (II), 66 (VI), 1010 (VV), 1111 (XI), 1515 (XV), 2020 (XX), 5151 (IL), 5555 (VL), 6060 (XL) and 100100 (LL).
打表找规律
下面为打表程序
#include <cstdio> #include <cstring> #include <queue> #include <cmath> #include <algorithm> #include <set> #include <iostream> #include <map> #include <stack> #include <string> #include <vector> #include <bits/stdc++.h> #define pi acos(-1.0) #define eps 1e-6 #define fi first #define se second #define lson l,m,rt<<1 #define rson m+1,r,rt<<1|1 #define bug printf("******\n") #define mem(a,b) memset(a,b,sizeof(a)) #define fuck(x) cout<<"["<<x<<"]"<<endl #define f(a) a*a #define sf(n) scanf("%d", &n) #define sff(a,b) scanf("%d %d", &a, &b) #define sfff(a,b,c) scanf("%d %d %d", &a, &b, &c) #define sffff(a,b,c,d) scanf("%d %d %d %d", &a, &b, &c, &d) #define pf printf #define FRE(i,a,b) for(i = a; i <= b; i++) #define FREE(i,a,b) for(i = a; i >= b; i--) #define FRL(i,a,b) for(i = a; i < b; i++) #define FRLL(i,a,b) for(i = a; i > b; i--) #define FIN freopen("DATA.txt","r",stdin) #define gcd(a,b) __gcd(a,b) #define lowbit(x) x&-x #pragma comment (linker,"/STACK:102400000,102400000") using namespace std; typedef long long LL; const int maxn = 1e6 + 10; set<int>st; int n,sum=0; int val[5]={1,5,10,50}; void dfs(int x) { if (x==n+1){ st.insert(sum); return ; } for (int i=0 ;i<4 ;i++){ sum+=val[i]; dfs(x+1); sum-=val[i]; } } int main() { for (int i=1 ;i<=60 ;i++) { n=i; sum=0; st.clear(); dfs(1); printf("%d ",st.size()); } return 0; }
1 #include <cstdio> 2 #include <cstring> 3 #include <queue> 4 #include <cmath> 5 #include <algorithm> 6 #include <set> 7 #include <iostream> 8 #include <map> 9 #include <stack> 10 #include <string> 11 #include <vector> 12 #define pi acos(-1.0) 13 #define eps 1e-6 14 #define fi first 15 #define se second 16 #define lson l,m,rt<<1 17 #define rson m+1,r,rt<<1|1 18 #define bug printf("******\n") 19 #define mem(a,b) memset(a,b,sizeof(a)) 20 #define fuck(x) cout<<"["<<x<<"]"<<endl 21 #define f(a) a*a 22 #define sf(n) scanf("%d", &n) 23 #define sff(a,b) scanf("%d %d", &a, &b) 24 #define sfff(a,b,c) scanf("%d %d %d", &a, &b, &c) 25 #define sffff(a,b,c,d) scanf("%d %d %d %d", &a, &b, &c, &d) 26 #define pf printf 27 #define FRE(i,a,b) for(i = a; i <= b; i++) 28 #define FREE(i,a,b) for(i = a; i >= b; i--) 29 #define FRL(i,a,b) for(i = a; i < b; i++) 30 #define FRLL(i,a,b) for(i = a; i > b; i--) 31 #define FIN freopen("DATA.txt","r",stdin) 32 #define gcd(a,b) __gcd(a,b) 33 #define lowbit(x) x&-x 34 #pragma comment (linker,"/STACK:102400000,102400000") 35 using namespace std; 36 typedef long long LL; 37 typedef unsigned long long ULL; 38 const int maxn = 1e5 + 10; 39 int ans[50]={0,4,10,20,35,56,83,116,155,198,244,292}; 40 int main() { 41 LL n; 42 scanf("%lld",&n); 43 if (n<=11) printf("%d\n",ans[n]); 44 else printf("%lld\n",292+(n-11)*49); 45 return 0; 46 }