unfinished ex0 and finished ex1

README.md

-# PT1_2021
+:q# PT1_2021
 
-Submission of Junpeng's exercise
\ No newline at end of file
+Submission of Junpeng's exercise

ex1/pb3/.gitignore

-.DS_Store
-*.out
-*~
-*.a
-*.aux
-*.dat
-*.log
-*.o
-*.out
-*.synctex.gz
-*.pyc
-build/
-install/
-*.swp
-

hw0/ex1.cpp

+#include <iostream>
+
+int recur_gcd(int a, int b){
+  if (b == 0){
+    return a;
+  }
+  else{
+    return recur_gcd(b, a % b);
+  }
+}
+
+int loop_gcd(int a, int b){
+  int t;
+  while (b != 0){
+    t = b;
+    b = a % b;
+    a = t;
+  }
+  return a;
+}
+
+int main(){
+  int a,b;
+  a = recur_gcd(18,12);
+  b = loop_gcd(18,12);
+
+  printf("%i \n %i\n", a,b);
+  return 0;
+}
+  

hw0/ex2.cpp

+#include <iostream>
+
+int recur_Fibo(int m){
+  if (m == 0){
+    return 0;
+  } else if (m == 1){
+    return 1;
+  } else{
+    return recur_Fibo(m-1) + recur_Fibo(m-2);
+  }
+}
+
+int loop_Fibo(int m){
+  int k = 0;
+  int a = 0; // F_{n-2}
+  int b = 1; // F_{n-1}
+  if (m == 0){
+    k = 0;
+  } else if (m == 1){
+    k = 1;
+  } else{
+    for (int i = 1; i < m; i++){
+    a = b;
+    b = a;
+    k = a + b;
+    }
+  }
+  return k;
+}
+
+int main(){
+  int a, b;
+  a = recur_Fibo(82);
+  b = loop_Fibo(82);
+  printf("%i \n %i \n", a, b);
+  return 0;
+}

hw1/ex5.cpp

+#include <iostream>
+
+float machine_precision(){
+
+  float epsilon = 1.0;
+  while (1.0 + 0.5*epsilon != 1.0) {
+    epsilon = 0.5 * epsilon;
+  }
+
+  return epsilon;
+}
+
+int main(){
+  
+  float a;
+  a = machine_precision();
+
+  std::cout << a << std::endl;
+  return a;
+}
+

hw1/ex6.cpp

+#include <stdio.h>
+#include <math.h> 
+#include <iostream>
+
+int simpson_integrate(double a, double b){
+  int N = 200;
+  double x = a;
+  double delta = (b-a)/N;
+  double integ = 0;
+  for (int i = 0; i < N; i++){
+    integ += delta/6*(sin(x) + 4*sin(x+delta/2) + sin(x+delta));
+    x += delta;
+
+  }
+
+  return integ;
+}
+
+int main(){
+
+  double integ = simpson_integrate(0.0, M_PI);
+  printf("%f\n" ,integ);
+
+  return integ; 
+}
+
+
+