C++ Sequential Number Triangle Pattern (Narrowing)
Beginner
6 min read
Updated: Sep 2026
3 programs
Live preview
Definition
What Is This Pattern?
A decreasing continuous number triangle prints numbers in one unbroken sequence from 1, while each row prints one fewer value than the row above — left-aligned, no leading spaces.
Remember
Rule: k starts at 1; row i prints (rows - i + 1) numbers
1 2 3 4 5
6 7 8 9
10 11 12
13 14
15 ← 5 rows (setw(3) columns)
Unlike Program 35 (same continuous counter, but right-aligned with leading spaces), this shape sits flush left and simply shortens each row.
Approach
How to Solve It
Keep one counter outside the loops, shrink the inner bound each row, and format with setw(3).
Method
Idea
Best for
Counter + nested loops
Outer = rows; inner = rows..i with k++
Learning, interviews, exams
setw(3) columns
Fixed width keeps 1-digit and 2-digit values aligned
Readable console output
Pseudocode
Pseudocode
k = 1
for i from 1 to rows:
for j from rows down to i:
print k in width 3 (no newline)
k = k + 1
print newline
Print numbers without a newline, then end the row once. cout << endl also ends the line and flushes; "\n" is enough for these demos.
Try it
Live Preview
Change the row count and the decreasing continuous triangle updates instantly — including the triangular number total.
Whole numbers from 1 to 12. Tap a chip or type a value — the preview redraws as you go.
Live result5 rows · 15 numbers
1 2 3 4 5
6 7 8 9
10 11 12
13 14
15
Trace
Worked Walkthrough — rows = 4
Trace each outer-loop value of i, the shrinking inner range, and the numbers taken from k.
i
Inner j
Count
k values
Printed row
1
4..1
4
1..4
1 2 3 4
2
4..2
3
5..7
5 6 7
3
4..3
2
8..9
8 9
4
4..4
1
10
10
Total prints: 4 + 3 + 2 + 1 = 10 = 4×5/2. Never reset k between rows or you get a restarting triangle instead.
Code
C++ Programs
Three complete programs: fixed rows, cin input, and a small trace demo. Use View Output to reveal sample results.
Example 1 — Fixed rows = 5
Hard-coded row count — ideal for first demos and screenshots.
C++
#include <iostream>
#include <iomanip>
using namespace std;
int main()
{
int rows = 5;
int i, j, k = 1;
for (i = 1; i <= rows; ++i)
{
for (j = rows; j >= i; --j)
cout << setw(3) << k++;
cout << "\n";
}
return 0;
}
Output
1 2 3 4 5
6 7 8 9
10 11 12
13 14
15
How It Works
1. Start the counter once.k = 1 lives outside both loops so the sequence never restarts.
2. Outer loop walks rows.i runs from 1 to rows — one shrinking line per iteration.
3. Inner loop shrinks.j runs from rows down to i, so row i prints rows - i + 1 numbers.
4. Format, then break the line.setw(3) keeps columns tidy; cout << "\n" only after the inner loop.
Example 2 — User Input Version
Read the row count at runtime. Prefer validating cin (shown in the tip below).
C++
#include <iostream>
#include <iomanip>
using namespace std;
int main()
{
int rows;
int i, j, k = 1;
cout << "Enter rows: ";
cin >> rows;
for (i = 1; i <= rows; ++i)
{
for (j = rows; j >= i; --j)
cout << setw(3) << k++;
cout << "\n";
}
return 0;
}
Output (when user enters 3)
Enter rows: 3
1 2 3
4 5
6
How It Works
1. Prompt and read. Ask for a row count, then store it in rows.
2. Same counter core. Only the source of rows changes — the print logic matches Example 1.
3. Safer input tip. Prefer:
Safer input
if (!(cin >> rows) || rows < 1)
{
cout << "Enter a whole number of rows (1 or more).\n";
return 1;
}
Example 3 — Compact rows = 3
Same counter and shrinking inner loop with a smaller row count for quick tracing on paper.
C++
#include <iostream>
#include <iomanip>
using namespace std;
int main()
{
int rows = 3;
int i, j, k = 1;
for (i = 1; i <= rows; ++i)
{
for (j = rows; j >= i; --j)
cout << setw(3) << k++;
cout << "\n";
}
return 0;
}
Output
1 2 3
4 5
6
How It Works
1. Only rows changes. The counter and inner loop stay identical to Example 1.
2. Trace on paper. For i = 1, 2, 3 the counts are 3, 2, 1 — easy to check by hand before scaling up.
3. Same formatting.setw(3) still applies; with single digits you mainly see the leading pad spaces.
Edge Cases & Pitfalls
Check these before calling the solution done.
k reset
Restarting triangle
If you set k = 1 inside the outer loop, each row restarts at 1. Keep k outside both loops.
j = 1..i
Growing width
An ascending inner bound prints a normal growing triangle. Use j = rows; j >= i; --j to shrink.
\n early
Column of numbers
If cout << "\n" is inside the inner loop, each number lands on its own line. End the row only after the inner loop.
No setw
Misaligned digits
Without setw(3), single-digit and two-digit values drift. Include <iomanip> and keep a fixed width.
rows = 1
Single number
Output is just 1 (padded to width 3). A good sanity check.
Bad cin
Validate rows
Check cin >> rows and require rows >= 1 before the outer loop.
Analysis
Time and Space Complexity
Program
Time
Extra space
Nested loops (Examples 1–3)
O(rows²)
O(1)
Total numbers printed = n + (n - 1) + … + 1 = n(n + 1)/2 — quadratic in n. Only a few integers of extra memory.
Remember
Key Takeaways
Rule: one counter k; row i prints rows - i + 1 values with setw(3).
vs Program 35: same continuous sequence — here left-aligned and shrinking; there right-aligned with pads.
Break the row: call cout << "\n" only after the inner loop.
Complexity:O(n²) time from the triangular print count; O(1) extra space.
One line: for i = 1..rows, print setw(3) << k++ while j runs rows..i, then end the line.
Frequently Asked Questions
Continuous numbers starting from 1, but each row has one fewer number: 5 on row 1, then 4, 3, 2, and 1 — totaling 15 numbers for 5 rows.
Counter k starts at 1 before the loops and increments with k++ each time a number prints — it is never reset inside the outer loop.
Row i prints rows - i + 1 numbers — the inner loop runs from j = rows down to i.
setw(3) reserves 3 columns per number (right-aligned), keeping columns aligned when values become two digits.
Program 35 is right-aligned with leading spaces. Program 38 is left-aligned with decreasing row width and the same continuous counter.
Printing with setw stays on the same line for each number. Printing a newline ends the current line. Numbers use cout without a newline; the row break uses cout << "\n" after the inner loop.
O(n²) for n rows because total prints are 1 + 2 + ... + n = n(n+1)/2.
After cin >> rows, check failure and require rows ≥ 1 before the outer loop.
🤔
Did you know?
A counter k starts at 1 and increments every time a number prints. Row i prints rows - i + 1 numbers with setw(3) — total prints = n(n+1)/2. Same continuous sequence as Program 35, but left-aligned with shrinking width.
