Easy–medium · 2D arrays

Sum a Matrix

Read a rows x cols matrix and print the sum of all entries. First nested-loop problem where the shape of the input matters.

At a glanceRead rows and cols, then add every entry in a double loop — the inner loop must read cols numbers per row, not rows.

Problem

Input: First line: rows and cols. Then rows lines of cols integers.

Output: The sum of every entry.

Sample:

Input	Output
`2 3` `1 2 3` `4 5 6`	`21`

Your solution

main.cpp — your solution

Custom input for "Run my input"

Judging runs in your browser against hidden tests. A runaway loop is cut off after 3 seconds — still, make sure every loop has an exit. Your code is saved in this browser as you type.

Stuck? Hints

Hint 1 — You do not need a 2D array

To just sum, read each value into a temporary and add it. A 2D array is only needed if you revisit entries later.

Hint 2 — Nested loops, row-major

for (i < rows) for (j < cols) { cin >> v; sum += v; } — input arrives row by row.

Solution (try it first!)

#include <iostream>
using namespace std;

int main() {
    int rows, cols;
    cin >> rows >> cols;
    int sum = 0;
    for (int i = 0; i < rows; i++) {
        for (int j = 0; j < cols; j++) {
            int v;
            cin >> v;
            sum += v;
        }
    }
    cout << sum << endl;
    return 0;
}

Stretch goals: sum only the main diagonal, or transpose the matrix — both need the 2D array you skipped here.

Deep dive

Why this works

Nested loops matching the shape of the data — rows × cols — is the mental model for all two-dimensional work. C++ stores row-major, so loop order has a real cache cost.

The cost

O(r·c) time, O(1) extra space if you sum while reading.

Where it goes wrong

Swapping the bounds (columns outer, rows inner) is still correct but walks memory in the wrong order — several times slower on large matrices.
int m[100][100] on the stack is 40 KB. Bigger sizes overflow the stack instead of failing gracefully.

Next step

One-dimensional patterns you now combine: Array Maximum.

Two things to remember

Loop order should match memory order (row-major).
Sum while reading — you never need the matrix.

🐞 This version fails — open it and try

i < rows - 1 skips the last row

#include <iostream>
using namespace std;

int main() {
    int rows, cols;
    cin >> rows >> cols;
    int sum = 0;
    for (int i = 0; i < rows - 1; i++) {
        for (int j = 0; j < cols; j++) {
            int v;
            cin >> v;
            sum += v;
        }
    }
    cout << sum << endl;
    return 0;
}