For Loops — The Counter Loop

Real-world analogy

What is it?

A for loop is a compact loop structure that combines initialization, condition checking, and updating into a single line. It is the most commonly used loop in competitive programming because it neatly handles counted repetition — when you know exactly how many times to repeat.

Real-world relevance

For loops dominate competitive programming. Reading N numbers, processing each element of an array, generating patterns, computing sums, products, and powers — nearly every CP problem uses at least one for loop. Once you master for loops, you can solve hundreds of basic problems.

Key points

• The For Loop Syntax — A for loop has three parts in one line: for(init; condition; update) { body }. First the init runs once. Then before each repetition, the condition is checked. After each repetition, the update runs. It is a while loop with everything organized in one place.
• Breaking Down the Three Parts — init: usually declares and sets a counter like int i = 0. condition: checked before each iteration like i < n. update: runs after each iteration like i++. If the condition is false from the start, the body never executes.
• Counting Up — for(int i = 1; i <= 10; i++) counts from 1 to 10. The variable i starts at 1, goes up by 1 each time, and the loop stops when i exceeds 10. This is the most common loop pattern in CP.
• Counting Down — for(int i = 10; i >= 1; i--) counts from 10 down to 1. Use i-- to decrease by 1 each time. Useful for reversing arrays or counting backwards.
• Running Sum with For — To sum 1 to N: int sum = 0; for(int i = 1; i <= n; i++) sum += i; This is cleaner than a while loop because the counter setup is all in the for line. The variable i is only visible inside the loop.
• Factorial with For — Factorial of N (written N!) means multiply 1 × 2 × 3 × ... × N. Use: long long fact = 1; for(int i = 1; i <= n; i++) fact *= i; We use long long because factorials grow extremely fast — 20! is already over 2 quintillion.
• For vs While — When to Use Which — Use a for loop when you know how many times to repeat (count from 1 to N, process N items). Use a while loop when you do not know in advance (read until end of input, repeat until a condition changes). In CP, for loops are used about 80% of the time.
• Loop Variable Scope — When you declare a variable inside the for statement like for(int i = 0; ...), that variable only exists inside the loop. After the loop ends, i is gone. This prevents accidental reuse and keeps your code clean.

Code example

#include <bits/stdc++.h>
using namespace std;

int main() {
    int n;
    cin >> n;

    // Sum from 1 to n
    int sum = 0;
    for (int i = 1; i <= n; i++) {
        sum += i;
    }
    cout << "Sum = " << sum << endl;

    // Factorial of n
    long long fact = 1;
    for (int i = 1; i <= n; i++) {
        fact *= i;
    }
    cout << n << "! = " << fact << endl;

    // Count down from n to 1
    for (int i = n; i >= 1; i--) {
        cout << i << " ";
    }
    cout << endl;

    // Print even numbers from 2 to 20
    for (int i = 2; i <= 20; i += 2) {
        cout << i << " ";
    }
    cout << endl;

    return 0;
}

Line-by-line walkthrough

1. 1. We read n from the user to know how many numbers to work with.
2. 2. int sum = 0; — Start with a sum of zero.
3. 3. for (int i = 1; i <= n; i++) — Start i at 1, keep going while i is at most n, add 1 to i after each round.
4. 4. sum += i; — Each time through the loop, add the current i to sum.
5. 5. After the loop, sum holds 1 + 2 + 3 + ... + n.
6. 6. For factorial, we start fact at 1 (not 0, because we are multiplying).
7. 7. fact *= i; means fact = fact * i. After the loop, fact = 1 × 2 × 3 × ... × n.
8. 8. The countdown loop starts i at n and decreases: i-- subtracts 1 each time.
9. 9. The even numbers loop uses i += 2 to skip by 2 each time, starting from 2.
10. 10. All four examples show different ways to use the three parts of a for loop.

Spot the bug

#include <bits/stdc++.h>
using namespace std;

int main() {
    int n = 5;
    int fact = 1;
    for (int i = 1; i <= n; i++) {
        fact *= i;
    }
    cout << n << "! = " << fact << endl;
    return 0;
}

Explain like I'm 5

Fun fact

Hands-on challenge

More resources

• C++ For Loops for Beginners (YouTube)
• For Loop — cppreference (cppreference.com)
• Loop Problems — CSES (CSES Problem Set)