An inverted center-aligned pyramid prints the widest odd-width star row first, then narrows to a single tip star — with leading spaces so each shorter row stays centered.
Remember
Rule: for i from rows down to 1,
print (rows - i) spaces, then (2 * i - 1) stars
*********
*******
*****
***
* ← 5 rows (base on top)
It is the flip of Program 5: keep the same space and star formulas, reverse only the outer loop. That mirrors how Program 2 inverts Program 1, but with odd-width centering.
Approach
How to Solve It
Two ways to emit the same shape — start with nested loops, then optionally shorten with string multiplication.
Method
Idea
Best for
Nested loops
Countdown i; spaces then odd stars via print(..., end="")
Learning, interviews, exams
"*" * n
Build margin and star run in one call
Shorter demos once formulas click
Pseudocode
Pseudocode
for i from rows down to 1:
print (rows - i) spaces (no newline)
print (2 * i - 1) stars (no newline)
print newline
Change the height and the inverted pyramid updates instantly — including the star total (n²).
Whole numbers from 1 to 14. Tap a chip or type a value — the preview redraws as you go.
Live result5 rows · 25 stars
*********
*******
*****
***
*
Trace
Worked Walkthrough — rows = 4
Trace spaces, stars, and the printed line as i counts down from 4 to 1.
i
Spaces rows - i
Stars 2*i - 1
Printed row
4
0
7
*******
3
1
5
*****
2
2
3
***
1
3
1
*
Star total: 7 + 5 + 3 + 1 = 16 = 4² — same as Program 5, only the print order differs. That square sum is why time is O(n²).
Code
Python Programs
Three complete programs: fixed rows, console input, and a string-multiplication shortcut. Use View Output to reveal sample results.
Example 1 — Fixed rows = 5
Hard-coded height — countdown outer loop with space and star inner loops.
Python
rows = 5
for i in range(rows, 0, -1):
for j in range(rows - i):
print(" ", end="")
for k in range(2 * i - 1):
print("*", end="")
print()
Output
*********
*******
*****
***
*
How It Works
1. Set height.rows = 5 means five lines from base to tip.
2. Outer loop counts down.range(rows, 0, -1) walks i from rows down to 1 — widest row first.
3. Spaces, then stars. Print rows - i spaces, then 2 * i - 1 stars with print(..., end="").
4. Break the line. Bare print() after both inner loops starts the next row.
When i = 5 you get 0 spaces and 9 stars; when i = 1 you get 4 spaces and 1 star.
Example 2 — User Input Version
Read the height at runtime. Prefer try/except ValueError in real apps (shown in the tip below).
Python
rows = int(input("Enter the number of rows: "))
for i in range(rows, 0, -1):
for j in range(rows - i):
print(" ", end="")
for k in range(2 * i - 1):
print("*", end="")
print()
Output (when user enters 4)
Enter the number of rows: 4
*******
*****
***
*
How It Works
1. Prompt and read. Ask for a row count, then convert the line with int(input(...)).
2. Same countdown core. Only the source of rows changes — the space and star logic matches Example 1.
3. Safer input tip. Bare int(input()) raises ValueError on letters. Prefer:
Safer input
try:
rows = int(input("Enter the number of rows: "))
except ValueError:
print("Enter a positive whole number.")
raise SystemExit(1)
if rows < 1:
print("Enter a positive whole number.")
raise SystemExit(1)
Example 3 — String Multiplication
Build each margin and odd star run in one call — same shape, no explicit character loops.
Python
rows = 5
for i in range(rows, 0, -1):
print(" " * (rows - i) + "*" * (2 * i - 1))
Output
*********
*******
*****
***
*
How It Works
1. Same countdown. Still walk i from rows down to 1.
2. Build each segment." " * (rows - i) is the margin; "*" * (2 * i - 1) is the star run.
3. Print and advance. One print(...) prints the full row and ends the line.
Learn the two-loop version first (Examples 1–2) so you can explain both bounds in an interview; treat this as a polish shortcut afterward.
Edge Cases & Pitfalls
Check these before calling the solution done.
range up
Upright pyramid by mistake
If you use range(1, rows + 1), you reprint Program 5. Use range(rows, 0, -1).
Tabs
Broken centering
Always print the space character " ", not tabs — tab width varies and skews the tip.
print() inside
Column of stars
If bare print("*") is inside either inner loop, each character lands on its own line. Use end="" for spaces and stars; print() only after both loops.
rows = 1
Single tip star
Output is just * — base and tip coincide. A good sanity check.
rows ≤ 0
Empty output
Outer loop never runs. Validate and re-prompt for interactive programs.
Bad input
Use try/except
int(input()) raises ValueError on letters — prefer try/except and require rows >= 1.
Analysis
Time and Space Complexity
Program
Time
Extra space
Nested loops (Examples 1–2)
O(rows²)
O(1)
String multiply (Example 3)
O(rows²)
O(rows) per temporary row string
Total stars = 1 + 3 + … + (2n - 1) = n², plus up to Θ(n) spaces per row — still quadratic in n. Same totals as Program 5.
Remember
Key Takeaways
Rule: countdown i; print rows - i spaces then 2 * i - 1 stars.
Flip of Program 5: same formulas — only reverse the outer loop.
Break the row: call bare print() only after both space and star loops.
Complexity:O(n²) time from n² stars; O(1) extra space for nested loops.
One line: for i from rows down to 1, print rows - i spaces and 2 * i - 1 stars, then print().
Frequently Asked Questions
The outer loop runs i from rows down to 1. Stars still use 2*i-1, so large i prints many stars first. As i shrinks, stars become 9,7,5,… and spaces (rows-i) grow from 0 upward. Same formulas as Program 5 — only the order of i changes.
Spaces use (rows-i). When i is rows, the margin is 0; when i is 1, the margin is rows-1. As i steps down, the margin grows while 2*i-1 shrinks, which keeps shorter rows centered under the wide top.
Program 5 uses for i in range(1, rows + 1) so stars grow. Program 6 uses for i in range(rows, 0, -1) with the same inner loops, so the base prints first and the tip last.
Program 2 is an inverted left-aligned triangle (i stars, no centering). Program 6 keeps (rows-i) spaces and odd star runs so the tip stays centered.
print("*", end="") stays on the same line. print() ends the current line. Spaces and stars use end=""; the row break uses print() after both inner loops.
O(n²) for n rows. Same totals as Program 5; only iteration order differs. Total stars equal n².
Yes. With the countdown outer loop: print(" " * (rows - i) + "*" * (2 * i - 1)).
Wrap int(input()) in try/except ValueError so bad input does not crash the script.
🤔
Did you know?
This inverted pyramid is exactly Program 5 with the outer loop reversed — same formulas, different print order. Total stars still equal n².
