Solutions

sheet1/C/.vscode/settings.json

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+{
+    "files.associations": {
+        "iostream": "cpp",
+        "ostream": "cpp"
+    }
+}

sheet1/C/Makefile

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+#
+# use GNU-Compiler tools
+COMPILER=GCC_
+# alternatively from the shell
+# export COMPILER=GCC_
+# or, alternatively from the shell
+# make COMPILER=GCC_
+
+# use Intel compilers
+#COMPILER=ICC_
+
+# use PGI compilers
+# COMPILER=PGI_
+
+
+SOURCES = main.cpp 
+OBJECTS = $(SOURCES:.cpp=.o)
+
+PROGRAM	= main.${COMPILER}
+
+# uncomment the next to lines for debugging and detailed performance analysis
+CXXFLAGS += -g
+LINKFLAGS += -g
+# do not use -pg with PGI compilers
+
+ifndef COMPILER
+  COMPILER=GCC_
+endif
+
+include ../${COMPILER}default.mk

sheet1/C/main.cpp

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+#include <iostream>
+#include "timing.h"
+
+using namespace std;
+
+
+unsigned long  multiplesOf3Or5(unsigned int n)
+{
+    unsigned long sum = 0;
+    for(unsigned int i=1; i<=n; i++)
+    {
+        if(i % 3 == 0 || i % 5 == 0)
+        {
+            sum += i;
+        }
+    }
+    return sum;
+}
+
+unsigned long gauss_sum(unsigned long n)
+{
+    return n*(n+1)/2;
+}
+
+unsigned long multiplesOf3Or5_noLoop(unsigned int n)
+{
+    /*for n there are floor(n/3) multiples of 3 and floor(n/5) multiples of 5. Calculate them using Gauss summation and subtract the 
+    multiples of 15 (counted twice)*/
+    unsigned long multiples3 = gauss_sum(n/3)*3;
+    unsigned long multiples5 = gauss_sum(n/5)*5;
+    unsigned long multiples15 = gauss_sum(n/15)*15;
+
+    return multiples3 + multiples5 - multiples15;
+
+}
+
+
+int main() {
+
+    unsigned long mA,mB,mC,mD,mE,mF;
+
+    tic();
+    for(unsigned int i = 0; i< 10000; i++)
+    {
+        mA = multiplesOf3Or5(15);
+        mB = multiplesOf3Or5(1001);
+        mC = multiplesOf3Or5(1432987);
+    }
+    double timeA = toc();
+
+    tic();
+    for(unsigned int i = 0; i< 10000; i++)
+    {
+        mD = multiplesOf3Or5_noLoop(15);
+        mE = multiplesOf3Or5_noLoop(1001);
+        mF = multiplesOf3Or5_noLoop(1432987);
+    }
+    double timeB = toc();
+
+    cout << "n = 15, result = " << mA << endl;
+    cout << "n = 1001, result = " << mB << endl;
+    cout << "n = 1432987, result = " << mC << endl;
+    cout << "time: " << timeA << endl;
+    cout << "--------------------------------------------------------------" <<endl;
+    cout << "n = 15, result = " << mD << endl;
+    cout << "n = 1001, result = " << mE << endl;
+    cout << "n = 1432987, result = " << mF << endl;
+    cout << "time: " << timeB << endl;
+    return 0;
+}

sheet1/C/timing.h

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+//
+//    Gundolf Haase, Oct 18 2024
+//
+#pragma once
+#include <chrono>                  // timing
+#include <stack>
+
+//using Clock = std::chrono::system_clock;   //!< The wall clock timer chosen
+using Clock = std::chrono::high_resolution_clock;
+using TPoint= std::chrono::time_point<Clock>;
+
+// [Galowicz, C++17 STL Cookbook, p. 29]
+ 
+std::stack<TPoint> MyStopWatch; //!< starting time of stopwatch
+
+/** Starts stopwatch timer.
+ *  Use as @code tic(); myfunction(...) ; double tsec = toc();  @endcode
+ * 
+ *  The timining can be nested and the recent time point is stored on top of the stack.
+ * 
+ *  @return recent time point
+ *  @see toc
+ */
+auto tic()
+{
+    MyStopWatch.push(Clock::now());
+    return MyStopWatch.top();
+}
+ 
+/** Returns the elapsed time from stopwatch. 
+ * 
+ * The time point from top of the stack is used
+ * if time point @p t_b is not passed as input parameter.
+ * Use as @code tic(); myfunction(...) ; double tsec = toc();  @endcode
+ * or as @code auto t_b = tic(); myfunction(...) ; double tsec = toc(t_b);  @endcode
+ * The last option is to be used in the case of 
+ * non-nested but overlapping time measurements.
+ * 
+ * @param[in]  t_b start time of some stop watch
+ * @return elapsed time in seconds.
+ *
+*/ 
+double toc(TPoint const &t_b = MyStopWatch.top())
+{
+    // https://en.cppreference.com/w/cpp/chrono/treat_as_floating_point
+    using Unit      = std::chrono::seconds;
+    using FpSeconds = std::chrono::duration<double, Unit::period>;        
+    auto t_e = Clock::now();
+    MyStopWatch.pop();
+    return FpSeconds(t_e-t_b).count();
+}