Solve a Smaller Version
Solve a Smaller Version
A recursive function calls itself with a smaller problem and stops at a base case.
Summing the first three roll numbers makes the repeated reduction visible.
Before this lesson, review Choose by Parameter Types when needed.
What you’ll learn
- Use recursion to solve a Smaller Version.
- Explain how the complete example produces 6.
- Make the practice change and explain why the result changes or stays the same.
Follow a complete C++ example
Summing the first three roll numbers makes the repeated reduction visible.
Read the declarations above main before tracing its statements. Each declared name supplies the value, type or operation used later. The std:: prefix selects a name from the standard library, and cout << sends a value to the output stream.
C++17 · main.cpp · complete program
#include <iostream>
int rollSum(int roll) {
if (roll <= 0) return 0;
return roll + rollSum(roll - 1);
}
int main() {
std::cout << rollSum(3) << '\n';
return 0;
}
Expected output
6Connect the code to its result
C++17 · source used in this explanation
#include <iostream>
int rollSum(int roll) {
if (roll <= 0) return 0;
return roll + rollSum(roll - 1);
}
int main() {
std::cout << rollSum(3) << '\n';
return 0;
}
Expected output
6A recursive function calls itself with a smaller problem and stops at a base case. Summing the first three roll numbers makes the repeated reduction visible.
Trace the result: Read the complete program below from its starting values to the output operations. Each std::cout statement displays the value supplied at that point; \n begins the next line. The resulting lines, in order, are 6. In this example, distinguish what the program calculates or changes from what it actually displays.
Important mistakes and boundaries
Each call uses resources. Missing termination or very deep recursion can exhaust the call stack; this small example is not a scalable guarantee.
Change the school example
C++17 · edit this complete example
#include <iostream>
int rollSum(int roll) {
if (roll <= 0) return 0;
return roll + rollSum(roll - 1);
}
int main() {
std::cout << rollSum(3) << '\n';
return 0;
}
Your task: Call rollSum(4). Before running your edited program, predict the new output and explain which stored value, condition or object changes. Keep the rest of the example intact.
Use the complete source repeated here; this task does not depend on remembering code from another section.
Worked answer and reasoning
Worked variation: Call rollSum(4). The result is 4 + 3 + 2 + 1, which is 10.
A recursive function calls itself with a smaller problem and stops at a base case. Summing the first three roll numbers makes the repeated reduction visible.
Each call uses resources. Missing termination or very deep recursion can exhaust the call stack; this small example is not a scalable guarantee.
For a baseline run, save this source as main.cpp and use clang++ -std=c++17 -Wall -Wextra -pedantic main.cpp -o school, or equivalent g++ flags. Recompile after editing so that you run the updated executable.
The source and output below belong to the edited program. Compare them with the original example to see the consequence of this single change.
C++17 · worked variation · complete program
#include <iostream>
int rollSum(int roll) {
if (roll <= 0) return 0;
return roll + rollSum(roll - 1);
}
int main() {
std::cout << rollSum(4) << '\n';
return 0;
}
Expected output
10Check your understanding
C++17 · original program for this question
#include <iostream>
int rollSum(int roll) {
if (roll <= 0) return 0;
return roll + rollSum(roll - 1);
}
int main() {
std::cout << rollSum(3) << '\n';
return 0;
}
What to remember
A recursive function calls itself with a smaller problem and stops at a base case. Each call uses resources. Missing termination or very deep recursion can exhaust the call stack; this small example is not a scalable guarantee.
Useful connections: Choose by Parameter Types, Give a Task a Name.
Language and design guidance: C++ Core Guidelines and C++ working draft. The draft describes an evolving language; these examples deliberately target C++17.
Reaching the recap and completing the quizzes are separate milestones.