Arrays — A Row of Boxes

Real-world analogy

What is it?

An array is a data structure that stores a fixed-size list of elements of the same type. Each element is accessed by its position number (index), starting from 0. Arrays are the foundation of almost every CP problem.

Real-world relevance

Arrays are everywhere! A class roster is an array of student names. A playlist is an array of songs. A scoreboard is an array of scores. In CP, nearly every problem gives you an array of numbers and asks you to do something with them — find the biggest, sort them, count something, etc.

Key points

• What is an Array? — An array is a way to store many values of the same type in a single variable. Instead of creating 100 separate variables like a1, a2, a3... you create one array that holds all 100 values. Think of it as a row of boxes — each box has a number (called an index) and holds one value.
• Declaring an Array — In C++, you declare an array like this: int arr[5]; — this creates 5 boxes that can each hold an integer. You can also declare with initial values: int arr[5] = {10, 20, 30, 40, 50}; The number in the square brackets tells C++ how many boxes to create.
• Indexing Starts at 0 — The first box in an array is box number 0, not box number 1! This is super important. So if you have int arr[5] = {10, 20, 30, 40, 50}, then arr[0] is 10, arr[1] is 20, arr[2] is 30, arr[3] is 40, and arr[4] is 50. The last index is always size minus 1.
• Reading an Array with a Loop — In CP, you almost always read array values from the user using a for loop. First read n (how many values), then loop from i = 0 to i < n and read each arr[i]. This is one of the most common patterns you will write in every single contest!
• Printing an Array — To print all values in an array, use a for loop from 0 to n-1 and print each element. You can print them on one line separated by spaces: cout << arr[i] << ' '; Or each on a new line: cout << arr[i] << '\n'; Choosing the right format depends on the problem.
• Accessing Individual Elements — You can read or change any box at any time using its index. arr[2] = 99; changes the third box to 99. You can also use arr[i] where i is a variable — this is what makes arrays so powerful with loops. The computer can jump to any box instantly!
• Array Size Limits — In CP, arrays can be very large — sometimes up to 1,000,000 elements or more. When you need a big array, declare it outside main() (as a global variable) so it doesn't cause a stack overflow. Inside main(), arrays bigger than about 100,000 can crash your program.
• Common Beginner Mistake — The #1 beginner mistake is going out of bounds — trying to access arr[5] when the array only has 5 elements (indices 0-4). This is called 'array index out of bounds' and can cause wrong answers or crashes. Always remember: if the array has n elements, valid indices are 0 to n-1.

Code example

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

int main() {
    int n;
    cin >> n;  // How many numbers?
    
    int arr[n];  // Create an array of n boxes
    
    // Read n numbers into the array
    for (int i = 0; i < n; i++) {
        cin >> arr[i];
    }
    
    // Print the array in reverse order
    cout << "Reversed: ";
    for (int i = n - 1; i >= 0; i--) {
        cout << arr[i] << " ";
    }
    cout << endl;
    
    // Access a specific element
    cout << "First element: " << arr[0] << endl;
    cout << "Last element: " << arr[n - 1] << endl;
    
    return 0;
}
// Input:  5
//         10 20 30 40 50
// Output: Reversed: 50 40 30 20 10
//         First element: 10
//         Last element: 50

Line-by-line walkthrough

1. 1. We include bits/stdc++.h to get all the tools we need.
2. 2. We read n — how many numbers the user will give us.
3. 3. int arr[n] creates an array with n boxes, numbered 0 to n-1.
4. 4. The first for loop reads numbers from the user into each box: arr[0], arr[1], ... arr[n-1].
5. 5. The second for loop prints in reverse — it starts at n-1 (the last box) and goes down to 0.
6. 6. arr[0] always gives us the first element, arr[n-1] always gives us the last element.
7. 7. We use endl or '\n' to move to the next line after printing.

Spot the bug

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

int main() {
    int n;
    cin >> n;
    int arr[n];
    
    for (int i = 1; i <= n; i++) {
        cin >> arr[i];
    }
    
    for (int i = 1; i <= n; i++) {
        cout << arr[i] << " ";
    }
    
    return 0;
}
// Input: 3
//        10 20 30
// Expected: 10 20 30
// But this code has a sneaky bug!

Explain like I'm 5

Fun fact

Hands-on challenge

More resources

• Arrays in C++ — Complete Tutorial (The Cherno)
• Arrays — USACO Guide (USACO Guide)
• Array Practice Problems (Codeforces)