#include <stdio.h>
#include <stdlib.h>
#include <math.h>


void differentiate(double* f, double** df, int D, int K){
	df[0] = f;
	int i;
	for(int k=1; k<=K; k++){
		for(i=0; i<D-k; i++){
			df[k][i] = df[k-1][i+1] - df[k-1][i];
		}
	}
}

double integrate(double* f, double p, int D){
	double sum = 0.0;
	for(int i=0;i<D;i++){
		sum += pow(fabs(f[i]),p);
	}
	return pow(sum,1/p);
}

double compute_derivatives(int* f, int** Sf, double** Af, double* Mf, double** df, double** dMf, double p, double* intdf, double* intdMf, int N, int D, int K){

for(int i=0;i<D;i++) df[0][i] = (double) f[i];

int r=0;
for(int i=0;i<D;i++) {
	Sf[i][i] = f[i];
	Af[i][i] = 1.0*Sf[i][i];
}
for(int n=1;n<D;n++){
	for(int i=0;i+n<D;i++){
		Sf[i][i+n] = Sf[i][i+n-1]+f[i+n];
		Sf[i+n][i] = Sf[i][i+n];

		Af[i][i+n] = 1.0*Sf[i][i+n]/(n+1);
		Af[i+n][i] = Af[i][i+n];
	}
}

for(int i=0;i<D;i++){
	Mf[i] = Af[i][i];
	for(int j=0;j<D;j++){
		if(Af[i][j] > Mf[i]) Mf[i] = Af[i][j];
	}
}

//printf("Mf    ");
//for(int i=0;i<D;i++) printf("%+0.1f ",Mf[i]);
//printf("\n");
for(int i=0;i<D;i++){
	//for(int j=0;j<D;j++) printf("%0.1f ",Af[i][j]);
	//printf("\n");
}

differentiate(df[0],df,D,K);
differentiate(dMf[0],dMf,D,K);

//for(int k=0;k<=K;k++){
	//printf("f  %d: ",k);
	//for(int i=0;i<D;i++) printf("%+0.1f ",df[k][i]);
	//printf("\n");
	//printf("Mf %d: ",k);
	//for(int i=0;i<D;i++) printf("%+0.1f ",dMf[k][i]);
	//printf("\n");
//}

//for(int k=0;k<=K;k++){
int k=K;
	intdf[k] = integrate(df[k],p,D);
	intdMf[k] = integrate(dMf[k],p,D);
	//printf("%d: %f / %f = %f\n",k,intdMf[k],intdf[k],intdMf[k]/intdf[k]);

return intdMf[k]/intdf[k];
//}

}

int main() {

int N=16;
int D=5*N;
int K=3;
double p = 1.0;

int* f = malloc(D*sizeof(int));
int** Sf = malloc(D*sizeof(int*));
double** Af = malloc(D*sizeof(double*));
double* Mf = malloc(D*sizeof(double));
for(int i=0;i<D;i++){
	Sf[i] = malloc(D*sizeof(int));
	Af[i] = malloc(D*sizeof(double));
}

double** df = malloc(D*sizeof(double*));
double** dMf = malloc(D*sizeof(double*));

for(int k=0;k<=K;k++){
	df[k] = malloc(D*sizeof(double));
	dMf[k] = malloc(D*sizeof(double));
	for(int i=0;i<D;i++){
		df[k][i] = 0;
		dMf[k][i] = 0;
	}
}
dMf[0] = Mf;

double* intdf = malloc(sizeof(double)*K);
double* intdMf = malloc(sizeof(double)*K);
double r = 0.0;

for(int t=1; t<=(1 << N)-1; t++){
	for(int i=0;i<D;i++) f[i]=0;
	//for(int i=0;i<N;i++) f[N+i] = rand() %2;
	for(int i=0;i<N;i++){
		f[2*N+i+K/2] = (t >> i) & 1;
		//if(i%3==0) f[2*N+i+K/2] = 1;
	}
	r = compute_derivatives(f, Sf, Af, Mf, df, dMf, p, intdf, intdMf, N, D, K);
	//printf("%.3d: %.3f  \n",t,r);
	if(r>.4997){
		printf("f: ");
		for(int i=0;i<D;i++) printf("%.1d ",f[i]);
		printf("\n");
		printf("%.4f\n",r);
	}
}

return 0;
}