[hdu1028]整数拆分,生成函数
题意:给一个正整数n,求n的拆分方法数(不考虑顺序)
思路:不妨考虑用1~n来构成n。用多项式表示单个数所有能构成的数,用多项式表示,就相当于卷积运算了。
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 | #include <map> #include <set> #include <cmath> #include <ctime> #include <deque> #include <queue> #include <vector> #include <cstdio> #include <string> #include <cstdlib> #include <cstring> #include <iostream> #include <algorithm> using namespace std; #define X first #define Y second #define pb push_back #define mp make_pair #define all(a) (a).begin(), (a).end() #define fillchar(a, x) memset(a, x, sizeof(a)) typedef long long ll; typedef pair< int , int > pii; typedef unsigned long long ull; #ifndef ONLINE_JUDGE void RI(vector< int >&a, int n){a.resize(n); for ( int i=0;i<n;i++) scanf ( "%d" ,&a[i]);} void RI(){} void RI( int &X){ scanf ( "%d" ,&X);} template < typename ...R> void RI( int &f,R&...r){RI(f);RI(r...);} void RI( int *p, int *q){ int d=p<q?1:-1; while (p!=q){ scanf ( "%d" ,p);p+=d;}} void print(){cout<<endl;} template < typename T> void print( const T t){cout<<t<<endl;} template < typename F, typename ...R> void print( const F f, const R...r){cout<<f<< ", " ;print(r...);} template < typename T> void print(T*p, T*q){ int d=p<q?1:-1; while (p!=q){cout<<*p<< ", " ;p+=d;}cout<<endl;} #endif template < typename T> bool umax(T&a, const T&b){ return b<=a? false :(a=b, true );} template < typename T> bool umin(T&a, const T&b){ return b>=a? false :(a=b, true );} template < typename T> void V2A(T a[], const vector<T>&b){ for ( int i=0;i<b.size();i++)a[i]=b[i];} template < typename T> void A2V(vector<T>&a, const T b[]){ for ( int i=0;i<a.size();i++)a[i]=b[i];} const double PI = acos (-1.0); const int INF = 1e9 + 7; /* -------------------------------------------------------------------------------- */ int a[123], b[123]; int main() { #ifndef ONLINE_JUDGE freopen ( "in.txt" , "r" , stdin); //freopen("out.txt", "w", stdout); #endif // ONLINE_JUDGE int n; while (cin >> n) { for ( int i = 0; i <= n; i ++) a[i] = 1; for ( int i = 2; i <= n; i ++) { fillchar(b, 0); for ( int j = 0; j <= n; j ++) { for ( int k = 0; k <= n / i; k ++) { if (j + k * i > n) break ; b[j + k * i] += a[j]; } } memcpy (a, b, sizeof (b)); } cout << a[n] << endl; } return 0; } |