1. 1 //humanity is a very illusive quality
2
3 /*
4 Name:
5 OJ:
6 Link:
7 Algorithm:
8 Type:
9 Difficulty:
10 Interest:
11 Additional:
12 */
13 #include<cstdio>
14 #include<cstring>
15 #include<cstdlib>
16 #include<cctype>
17
18 #include<cmath>
19 #include<iostream>
20 #include<fstream>
21
22 #include<string>
23 #include<vector>
24 #include<queue>
25 #include<map>
26 #include<algorithm>
27 #include<set>
28 #include<sstream>
29 #include<stack>
30 #include <ctime>
31 using namespace std;
32
33 class TimeLogger {
34 clock_t st, nd; double elapsed;
35 public:
36 TimeLogger() { st = clock(); }
37 ~TimeLogger() {
38 nd = clock(); elapsed = (nd - st)/(double)CLOCKS_PER_SEC;
39 printf("nYour program took %.3lf secondsn", elapsed);
40 }
41 };
42
43 const int inf = (1<<28);
44 const double pi = (2.0*acos(0.0));
45 const double eps = 1e-9;
46 const double eps2 = 1e-12; // printf rounder
47 const double sensitiveEPS = 1e-14;// depends on digits after . ex 7
digit
48
49 typedef long long lli;
50 //typedef __int64 lli;
51 //typedef unsigned long long llu;
52 //typedef unsigned __int64 llu;
53 //typedef pair < int , int > pii;
54 //typedef vector < int > vi;
55 //typedef vector < string > vs;
56
57 #define isp2( a ) (!(a & (a-1)))
58 #define CLR( a ) memset(a , 0 , sizeof (a))
59 #define SET( a , b) memset(a , b , sizeof (a))
60 #define SZ( a ) ((int)a.size())
61 #define all( a ) a.begin(),a.end()
62
63
64 //#define _rep( i, a, b, x ) for( __typeof(b) i = ( a ); i <= ( b );
i += x )

2. 65 #define _rep( i, a, b, x ) for( i = ( a ) ; i <= ( b ) ; i += x )
66 #define rep( i, n ) _rep( i, 0, n - 1, 1 )
67 #define _rrep( i, a, b, x ) for( i = (a) ; i >= (b) ; i -= x )
68 #define rrep( i, a, b) _rrep( i, a, b, 1)
69 #define xrep( i, a, b) _rep( i, a, b, 1)
70
71 #define SD( a ) scanf("%d",&a)
72 #define SL( a ) scanf("%lld",&a)
73 #define SI( a ) scanf("%I64d",&a)
74 #define SS( a ) scanf("%s",a)
75 #define SF( a ) scanf("%lf",&a)
76
77 #define pb push_back
78 #define ff first
79 #define ss second
80 ///Comparision macros
81 #define _aEb(a,b) (fabs((a)-(b))<eps)
82 #define _aGb(a,b) ((a)>(b)+eps)
83 #define _aLb(a,b) ((a)+eps<(b))
84 #define _aLEb(a,b) (_aLb(a,b) || _aEb(a,b))
85 #define _aGEb(a,b) (_aGb(a,b) || _aEb(a,b))
86 #define _minf(a,b) ((a)+eps<(b)?(a):(b))
87 #define _maxf(a,b) ((a)+eps<(b)?(b):(a))
88 #define _sq(x) ((x)*(x))
89
90 const int MX = 1000;
91 struct RKFMY
92 {
93 double t[ MX + 10 ];
94 double y[ MX + 10 ];
95 double w[ MX + 10 ];
96 double ww[ MX + 10 ];
97 double h[ MX + 10 ];
98 double R[ MX + 10 ];
99 double a , b , alpha , hmax, hmin;
100 double TOL;
101 bool flag;
102
103 double k[7];
104
105 double f( double T , double Y )
106 {
107 return ( Y - T*T + 1 );
108 }
109 void init()
110 {
111 hmax = .25;
112 hmin = .01;
113 a = 0.;
114 b = 2.;
115 alpha = .5;
116 t[ 0 ] = a;
117 w[ 0 ] = alpha;
118 h[ 0 ] = hmax;
119 flag = true;
120 TOL = 1.e-5;
121 }
122 double runIt()
123 {
124 int i = 0,j;
125 while( flag && i<200 )
126 {
127 k[1] = h[i] * f( t[i] , w[i] );
128 k[2] = h[i] * f( t[i] + (1./4.) * h[i] , w[i] + (1./4.) *
k[1] );
129 k[3] = h[i] * f( t[i] + (3./8.) * h[i] , w[i] + (3./32.)*

3. k[1] + (9/32.)*k[2] );
130 k[4] = h[i] * f( t[i] + (12./13.)*h[i] , w[i] + (1932./
2197.)*k[1]
131 - (7200./2197)*k[2] + (7296./
2197)*k[3] );
132 k[5] = h[i] * f( t[i] + h[i] , w[i] + (439./
216.)*k[1] - 8.*k[2]
133 + (3680./513)*k[3] - (845./
4104)*k[4] ) ;
134 k[6] = h[i] * f( t[i] + .5*h[i] , w[i] - (8./27.)*
k[1] + 2.*k[2]
135 - (3544./2565.)*k[3] + (1859./
4104.)*k[4] - (11./40.)*k[5] );
136 i++;
137
138 R[i] = (1./h[i-1]) * fabs( (1./360.)*k[1] - (128./4275.)*
k[3] - (2197./75240.)*k[4]
139 + (1./50.)*k[5]
+ (2./55.)*k[6] );
140
141 if( _aLEb(R[i],TOL) )
142 {
143 t[i] = t[i-1] + h[i-1];
144 w[i] = w[i-1] + (25./216.)*k[1] + (1408./2565.)*k[3]
+ (2197./4104.)*k[4] - (1./5.)*k[5];
145 printf("%.12lf %.12lf %.12lf %.12lfn",t[i],w[i],h[
i-1],R[i]);
146 }
147
148 double del = .84 * pow( double(TOL / R[i]) , double(1./4.
) );
149
150 if( _aLb( del , .1 ) ) h[i] = .1 *h[i-1];
151 else if ( _aGb( del , 4. ) ) h[i] = 4 *h[i-1];
152 else h[i] = del*h[i-1];
153
154 if( _aGb( h[i] , hmax ) ) h[i] = hmax ;
155 if( _aGb( t[i] , b ) ) flag = 0;
156 else if( _aGb( t[i] + h[i] , b ) ) h[i] = b-t[i];
157 else if( _aLb( h[i] , hmin ) )
158 {
159 flag = 0;
160 printf("min h exceededn");
161 }
162 }
163 }
164
165 };
166 RKFMY rk;
167 int main(void)
168 {
169 //freopen("in.txt","r",stdin);
170 //freopen("out.txt","w",stdout);
171 //TimeLogger tm;
172 int i,j,k,kase=0;
173
174 rk.init();
175 rk.runIt();
176
177 return 0;
178 }