A palindromic number pyramid is centered with leading spaces. Row i prints 1..i ascending, then i-1..1 descending — so every line reads the same both ways.
Unlike Program 55 (column-wise 2D fill) or Program 52 (left-aligned, starts at i), this shape always starts at 1 and uses spacing to center the pyramid.
Approach
How to Solve It
Outer loop over rows. For each row: print leading spaces, count up to i, count down from i-1, then end the line.
Method
Idea
Best for
Three loops
Spaces + ascending + descending
Learning, interviews, demos
Compact trace
Same logic with rows = 3
Quick dry-runs on paper
Pseudocode
Pseudocode
for i from 1 to rows:
for s from 1 to (rows - i):
print " "
for k from 1 to i:
print k and a space
for k from (i - 1) down to 1:
print k and a space
print newline
Cheat sheet
Goal
Pattern
Outer row loop
for (i = 1; i <= rows; i++)
Leading spaces
for (s = 1; s <= rows - i; s++) cout << " ";
Ascending half
for (k = 1; k <= i; k++) cout << k << " ";
Descending half
for (k = i - 1; k >= 1; k--) cout << k << " ";
End the row
cout << "\n";
Digits on row i
2 * i - 1
Printing Numbers vs Starting a New Line
API
Effect
Use for
cout << k << " " / cout << " "
Stays on the same line
Spaces and digits
cout << "\n"
Ends the line
After both number loops
Print spaces and digits without a newline, then end the row once.
Try it
Live Preview
Change the row count and the centered palindromic pyramid updates instantly.
Use rows from 1 to 9. Tap a chip or type a value — the preview redraws as you go.
Live result5 rows · 25 digits
1
1 2 1
1 2 3 2 1
1 2 3 4 3 2 1
1 2 3 4 5 4 3 2 1
Trace
Worked Walkthrough
Trace row i = 3 when rows = 5 — spaces, ascending, then descending.
Step
Loop
Prints
1
Spaces: s = 1..2
(2 pairs)
2
Ascending: k = 1..3
1 2 3
3
Descending: k = 2..1
2 1
Result
Full row 3
1 2 3 2 1
The descending loop starts at i - 1 so the peak digit is printed only once.
Code
C++ Programs
Three complete programs: fixed rows = 5, cin input, and a compact rows = 3 demo. Use View Output to reveal sample results.
Example 1 — Fixed rows = 5
Hard-coded height — spaces, ascending 1..i, then descending i-1..1.
C++
#include <iostream>
using namespace std;
int main()
{
int rows = 5;
int i, s, k;
for (i = 1; i <= rows; i++)
{
for (s = 1; s <= rows - i; s++)
cout << " ";
for (k = 1; k <= i; k++)
cout << k << " ";
for (k = i - 1; k >= 1; k--)
cout << k << " ";
cout << "\n";
}
return 0;
}
Output
1
1 2 1
1 2 3 2 1
1 2 3 4 3 2 1
1 2 3 4 5 4 3 2 1
How It Works
1. Center with spaces. Print (rows - i) pairs of " " before any digit on row i.
2. Ascend to the peak.k = 1..i prints the left half including the middle digit.
3. Descend without a double peak.k = i-1..1 mirrors the left half, then "\n" ends the row.
Example 2 — User Input Rows
Read the row count at runtime with a simple validation check.
C++
#include <iostream>
using namespace std;
int main()
{
int rows, i, s, k;
cout << "Enter the number of rows: ";
cin >> rows;
for (i = 1; i <= rows; i++)
{
for (s = 1; s <= rows - i; s++)
cout << " ";
for (k = 1; k <= i; k++)
cout << k << " ";
for (k = i - 1; k >= 1; k--)
cout << k << " ";
cout << "\n";
}
return 0;
}
Output (when user enters 4)
Enter the number of rows: 4
1
1 2 1
1 2 3 2 1
1 2 3 4 3 2 1
How It Works
1. Same loop core. Only the source of rows changes from a literal to cin.
2. Entering 4 stops early. You get four centered rows ending at 1 2 3 4 3 2 1.
3. Validate in real apps. Prefer checking cin failure and requiring a positive height (tip below).
Safer input tip
if (!(cin >> rows) || rows < 1)
{
cout << "Please enter a positive integer.\n";
return 1;
}
Example 3 — Compact rows = 3
Smaller height for quick tracing of spaces and both number loops.
C++
#include <iostream>
using namespace std;
int main()
{
int rows = 3;
int i, s, k;
for (i = 1; i <= rows; i++)
{
for (s = 1; s <= rows - i; s++)
cout << " ";
for (k = 1; k <= i; k++)
cout << k << " ";
for (k = i - 1; k >= 1; k--)
cout << k << " ";
cout << "\n";
}
return 0;
}
Output
1
1 2 1
1 2 3 2 1
How It Works
1. Only three rows. Easy to dry-run every space pair and digit on paper.
2. Same formula. Nothing changes except rows — proving the pattern scales.
3. Peak still once. Row 3 prints 1 2 3 2 1 — ascending includes 3; descending starts at 2.
Edge Cases & Pitfalls
Check these before calling the solution done.
Double peak
Start descending at i - 1
Starting at i prints the middle digit twice (e.g. 1 2 3 3 2 1).
Spacing
Use two spaces per indent step
One space per step looks left-skewed once digits and their trailing spaces are printed.
Alignment
View output in a monospace font
Proportional fonts hide the pyramid shape even when the spaces are correct.
Bad cin
Validate input
Check cin >> rows and require rows >= 1 before the loops.
Analysis
Time and Space Complexity
Program
Time
Extra space
Pyramid (Examples 1–3)
O(n²)
O(1)
Digits printed are 1 + 3 + 5 + … + (2n - 1) = n². Leading spaces add the same order of work. Extra memory is only a few loop variables.
Remember
Key Takeaways
Rule: spaces (rows - i), then 1..i, then i-1..1.
Palindrome: each row reads the same left-to-right and right-to-left.
Break the row: call cout << "\n" only after both number loops finish.
Complexity:O(n²) time, O(1) extra space.
One line: center with spaces, count up to i, count down from i-1.
Frequently Asked Questions
Each row reads the same forward and backward: 1, 1 2 1, 1 2 3 2 1, and so on.
Print (rows - i) pairs of two spaces before the numbers on row i — more spaces on upper rows, fewer on lower rows.
A centered pyramid where row i shows 1..i ascending then i-1..1 descending. For rows=5, the bottom row is 1 2 3 4 5 4 3 2 1.
Program 55 fills a 2D array column-wise. Program 56 prints palindromic digits directly with spaces, ascending, and descending loops.
Program 52 is left-aligned and starts each row at i (e.g. 34543). Program 56 is centered and always starts at 1 (e.g. 1 2 3 2 1).
Row i already printed the peak in the ascending loop. Starting at i-1 avoids repeating that digit.
Printing a digit (and space) stays on the same line. Printing a newline ends the current row. Digits use cout without a newline; the row break uses cout << "\n" after both number loops.
O(n²) for n rows because each row prints O(n) spaces and digits, and 1+3+5+...+(2n-1) = n² digits.
🤔
Did you know?
Each row prints 1..i..1 with leading spaces for centering. Row i has 2i-1 digits — total prints grow as O(n²) for n rows.
