diff --git a/5_practice.c b/5_practice.c
index 70d6651..1c4b351 100644
--- a/5_practice.c
+++ b/5_practice.c
@@ -2,38 +2,87 @@
 #include <stdlib.h>	// for memory allocation
 #include <time.h>	// for time calculation
 #include <math.h>	// for sine and cosine functions
+
 int main() {
 	// Declare all the variables
-	int k, n, N;
+	int k, n, N, i;
 	double *x, *yr, *yi;
-	time_t t;
-
-	// Input the number N
+	double *yr1,*yi1;
+	double an,bn,a0,b0,a,b;
+	double temp,dr,di;
+	time_t t,t1;
 	
-	
-	// Locate the memory for x, yr, yi;
+	// Input the number N
+	printf("Input the number N :");
+	scanf("%d",&N);
 
-	// Initial setting for x, for example, x[k] = k
-	
-	
+	// Locate the memory for x, yr, yi;
+	x = (double *) malloc(N*sizeof(double));
+	yr = (double *) malloc(N*sizeof(double));
+	yi = (double *) malloc(N*sizeof(double));
+	yr1 = (double *) malloc(N*sizeof(double));
+	yi1 = (double *) malloc(N*sizeof(double));
 	
+	// Initial setting for x, for example, x[k] = k
+	for(k=0;k<N;k++){
+		x[k] = k;
+	}
 	
 	t = clock();	
 	// yr[n]+i*yi[n] = sum(exp(-i 2 Pi k n / N)*x[k], k=0..N-1), n=0..N-1 
-
-
-
-
-
-
-
+	// Method 1 : ª½±µ­pºâ 
+	for(n=0;n<N;n++){
+		yr[n] = 0.0;
+		yi[n] = 0.0;
+		for(k=0;k<N;k++){
+			yr[n] += cos(2.0*M_PI*k*n/N)*x[k];
+			yi[n] -= sin(2.0*M_PI*k*n/N)*x[k];
+		} 
+		
+	}
 	// output the results
 	t = clock() - t;
-	printf("%d ms for discrete Fourier Transform of %d elements\n", t, N);
-
-	// free the memory located by x, yr, yi
-	
 	
+	// Method 2
+	a = cos(2.0*M_PI*k/N);
+	b = -sin(2.0*M_PI*k/N);
+	an = 1.0;
+	bn = 0.0;
+	t1 = clock();
+	for(n=0;n<N;n++){
+		yr1[n] = 0.0;
+		yi1[n] = 0.0;
+		a0 = 1.0;
+		b0 = 0.0;
+		for(k=0;k<N;k++){
+			yr1[n] += a0*x[k];
+			yi1[n] -= b0*x[k];
+			temp = an*a0-bn*b0;
+			b0 = an*b0+bn*a0;
+			a0 = temp;
+		}
+		temp = an*a - bn*b;
+		bn = an*b + bn*a;  
+		an = temp;
+	}
+	// output the results
+	t1 = clock() - t1;
+	printf("Method 1 : %e ms for discrete Fourier Transform of %d elements\n", t, N);
+	printf("Method 2 : %e ms for discrete Fourier Transform of %d elements\n", t1, N);
+	dr = 0.0;
+	di = 0.0;
+	for(i=0;i<N;i++){
+		dr += pow(yr1[i]-yr[i],2);
+		di += pow(yi1[i]-yi[i],2);
+	}
+	printf("the difference of real number for two methods: %e\n",sqrt(dr));
+	printf("the difference of imaginary numberfor two methods: %e\n",sqrt(di));
+	// free the memory located by x, yr, yi	
+	free(yr);
+	free(yi);
+	free(yr1);
+	free(yi1);
+	free(x);
 	
 	return 100;
 }
diff --git a/6_sorting.c b/6_sorting.c
new file mode 100644
index 0000000..8c815d1
--- /dev/null
+++ b/6_sorting.c
@@ -0,0 +1,205 @@
+#include <stdio.h>	// for printf function
+#include <stdlib.h>	// for memory allocation
+#include <time.h>	// for time calculation
+#include <math.h>	// for sine and cosine functions
+int quick_sort(double *x, int L, int R);
+double quick_sort_median(double *x, int L, int R, int M1,int bl);
+double quick_sort_median1(double *x, int L, int R, int M1);
+int main() {
+	// Declare all the variables
+	int k, m, n, N;
+	double *x, *y, z, p , med, med1, med2,q1,q3;
+	time_t t,t1,t2;
+
+	// Input the number N
+	printf("Input N: ");
+	scanf("%d",&N);
+	
+	// Locate the memory for x and y;
+	x = (double *) malloc(N*sizeof(double));
+	y = (double *) malloc(N*sizeof(double));
+	// Initial setting for x, for example, x[k] = 1.0*rand()/RAND_MAX
+
+	srand( time(NULL) );
+	for(k=0;k<N;k++){
+		x[k] = y[k] = 1.0*rand()/RAND_MAX;
+	}	
+	// sorting x;  
+	for(n=0;n<N;n++) {
+		for(k=n+1;k<N;k++) {
+			if (x[n] > x[k]) {
+				z = x[n];
+				x[n] = x[k];
+				x[k] = z;
+			}
+		}
+	}
+	for(k=0;k<N;++k){
+		x[k] = y[k];
+	}
+	
+	quick_sort(x,0,N);
+	
+	if(N<=20) {
+		printf("y \t\t x\n");
+		for(k=0;k<N;++k) {
+			printf("%d %f\t%f\n",k,y[k],x[k]);
+		}
+	}
+	
+	if( N % 2 != 0){
+		med = x[N/2];
+	}
+	else{
+		med = (x[(N/2)-1]+x[N/2])/2.0;
+	}
+
+	for(k=0;k<N;++k){
+		x[k] = y[k];
+	}
+	t = clock();
+	if( N % 2 != 0){
+		med1 = quick_sort_median(x,0,N,(N-1)/2,1);
+	}
+	else{
+		med1 = quick_sort_median(x,0,N,(N-1)/2,0);
+	}
+	t = clock() - t;
+	
+	t2 = clock();
+	if( (((N-1)/2)%2 != 0 && N%2 != 0) || (N % 2 ==0 && (N/2)%2 != 0)){
+		q1 = quick_sort_median(x,0,N/2,((N/2)-1)/2,1); 
+		q3 = quick_sort_median(x,N/2+1,N,3*N/4,1); 
+	}
+	else{
+		q1 = quick_sort_median(x,0,N/2,((N/2)-1)/2,0);
+		q3 = quick_sort_median(x,(N-1)/2+1,N,(3*N-1)/4,0);
+	}
+	t2 = t2-clock();
+	
+	for(k=0;k<N;++k){
+		x[k] = y[k];
+	}
+	
+	t1 = clock();
+	if( N % 2 != 0){
+	med2 = quick_sort_median1(x,0,N,(N-1)/2);
+	  }
+	else{
+	  	med2 = quick_sort_median1(x,0,N,(N-1)/2);
+	   	med2 = med2 + quick_sort_median1(x,0,N,N/2);
+	   	med2 = med2/2.0;
+	}
+	t1 = t1-clock();
+
+	printf("quick_sort_median spends : %e s\n", N, 1.0*t/CLOCKS_PER_SEC);
+	printf("quick_sort_median1 spends : %e s\n", N, 1.0*t1/CLOCKS_PER_SEC);
+	printf("The error with quick_sort_median is %f \n",med-med1);
+	printf("The error with quick_sort_median1 is %f \n",med-med2);
+	printf("q1 = %f q3 = %f time : %e \n", q1,q3,1.0*t2/CLOCKS_PER_SEC);
+	// free the memory located by x, y
+	free(x);
+	free(y);	
+
+	return 100;
+}
+
+int quick_sort(double *x, int L, int R){
+	int k, n;
+	double z, p;
+	if(L >= R){
+		return 0;
+	}
+	p = x[R-1];
+	n = L;
+	
+	for(k=L;k<R-1;k++) {
+		// put all elements smaller than p from the beginning
+		if (x[k] < p) {
+			z = x[n];
+			x[n] = x[k];
+			x[k] = z;
+			n++;
+		}
+	}
+	z = x[n];
+	x[n] = x[R-1];
+	x[R-1] = z;
+
+	quick_sort(x,L,n);
+	quick_sort(x,n+1,R);
+	return 0;
+}
+
+double quick_sort_median(double *x, int L, int R, int M1,int bl){
+	int k, n,m;
+	double z, p;
+	if(L >= R){
+		return 0;
+	}
+
+	p = x[R-1];
+	n = L;
+	for(k=L;k<R-1;k++) {
+		// put all elements smaller than p from the beginning
+		if (x[k] < p) {
+			z = x[n];
+			x[n] = x[k];
+			x[k] = z;
+			n++;
+		}
+	}
+	z = x[n];
+	x[n] = x[R-1];
+	x[R-1] = z;
+
+	if(n > M1){
+		quick_sort_median(x,L,n,M1,bl);
+	}
+	else if(n < M1){
+		quick_sort_median(x,n+1,R,M1,bl);
+	}
+	else{
+		if(bl){
+			return x[n];
+		}
+		else{
+			quick_sort_median(x,n+1,R,M1+1,bl);
+			return (x[n]+x[n+1])/2.0;
+		}
+	}
+}
+
+double quick_sort_median1(double *x, int L, int R, int M1){
+	int k, n,m;
+	double z, p;
+	if(L >= R){
+		return 0;
+	}
+
+	p = x[R-1];
+	n = L;
+	for(k=L;k<R-1;k++) {
+		// put all elements smaller than p from the beginning
+		if (x[k] < p) {
+			z = x[n];
+			x[n] = x[k];
+			x[k] = z;
+			n++;
+		}
+	}
+	z = x[n];
+	x[n] = x[R-1];
+	x[R-1] = z;
+
+	if(n > M1){
+		quick_sort_median1(x,L,n,M1);
+	}
+	else if(n < M1){
+		quick_sort_median1(x,n+1,R,M1);
+	}
+	else{
+		return x[n];
+	}
+	
+}