Intro to problem solving

What is problem solving?

Problem solving in competitive programming means reading a well-defined problem, understanding its constraints, designing an algorithm, and writing code that produces the correct output for all valid inputs — within time and memory limits.

The problem-solving process

Every problem follows the same workflow:

Read and understand

Read the problem statement carefully. Identify the input format, output format, and constraints. Re-read if anything is unclear.

Work through examples

Trace through the sample test cases by hand. Make sure you understand why the expected output is correct.

Design your approach

Think about the algorithm before writing code. Ask yourself: what data structure do I need? What’s the time complexity?

Write the code

Implement your solution. Keep it simple and clean.

Test and debug

Test with sample cases first, then think of edge cases (minimum input, maximum input, special cases).

Input and output in C++

The most basic skill — reading input and writing output efficiently.

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

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);

    // Reading a single integer
    int n;
    cin >> n;

    // Reading multiple values
    int a, b;
    cin >> a >> b;
    cout << a + b << endl;

    // Reading n integers into a loop
    for (int i = 0; i < n; i++) {
        int x;
        cin >> x;
        cout << x * 2 << "\n";
    }

    return 0;
}

Always use "\n" instead of endl — it’s significantly faster because endl flushes the output buffer.

Data types and their limits

Choosing the right data type prevents overflow bugs:

Type	Size	Range	When to use
`int`	4 bytes	≈ ±2.1 × 10⁹	Most problems
`long long`	8 bytes	≈ ±9.2 × 10¹⁸	When n > 10⁹ or products/sums can overflow
`double`	8 bytes	~15 decimal digits	Floating point problems
`char`	1 byte	-128 to 127	Single characters
`bool`	1 byte	true/false	Flags

Integer overflow is the #1 beginner mistake. If the problem says n ≤ 10⁹, then n * n overflows int. Use long long!

Basic math operations

// Division (integer)
int a = 7, b = 2;
cout << a / b;     // 3 (truncated)
cout << a % b;     // 1 (remainder)

// Min and max
cout << min(a, b); // 2
cout << max(a, b); // 7

// Absolute value
cout << abs(-5);   // 5

// Power (for integers, write your own)
// Don't use pow() for integers — it returns double and has precision issues
long long power(long long base, long long exp) {
    long long result = 1;
    while (exp > 0) {
        if (exp % 2 == 1) result *= base;
        base *= base;
        exp /= 2;
    }
    return result;
}

Simple problem patterns

Pattern 1: Process and output

Read input, do some calculation, print the result.

// Example: Is a number even or odd?
int n;
cin >> n;
if (n % 2 == 0) cout << "Even";
else cout << "Odd";

Pattern 2: Count something

Count how many elements satisfy a condition.

int n, count = 0;
cin >> n;
for (int i = 0; i < n; i++) {
    int x;
    cin >> x;
    if (x > 0) count++;
}
cout << count;

Pattern 3: Find min/max

Track the minimum or maximum as you iterate.

int n;
cin >> n;
int mn = INT_MAX, mx = INT_MIN;
for (int i = 0; i < n; i++) {
    int x;
    cin >> x;
    mn = min(mn, x);
    mx = max(mx, x);
}
cout << mn << " " << mx;

Practice

Head over to Sheet 1 — Intro to PS to practice these concepts with curated problems.

Sheet 1: Intro to PS

Practice problems for this tutorial.

Level 0 Training

Practice Sheets

What is problem solving?

The problem-solving process

Input and output in C++

Data types and their limits

Basic math operations

Simple problem patterns

Pattern 1: Process and output

Pattern 2: Count something

Pattern 3: Find min/max

Practice

Sheet 1: Intro to PS

​What is problem solving?

​The problem-solving process

​Input and output in C++

​Data types and their limits

​Basic math operations

​Simple problem patterns

​Pattern 1: Process and output

​Pattern 2: Count something

​Pattern 3: Find min/max

​Practice

Sheet 1: Intro to PS

What is problem solving?

The problem-solving process

Input and output in C++

Data types and their limits

Basic math operations

Simple problem patterns

Pattern 1: Process and output

Pattern 2: Count something

Pattern 3: Find min/max

Practice