A reverse row number triangle grows one digit per row, but each row prints digits downward from the row index to 1 — 1, 21, 321, and so on.
Rule: for i from 1 to rows
for j from i down to 1: print j (no space)
1
21
321
4321
54321 ← rows = 5Follows the reverse ascending triangle in Program 6; next is the reverse left-growing triangle in Program 8.
Outer loop counts up from 1 to rows. Inner loop counts down from i to 1. End each row with a bare print().
| Method | Idea | Best for |
|---|---|---|
| Ascending outer + descending inner | Outer i = 1..rows; inner j = i..1; print j | Learning, interviews, exams |
| Spaced digits | print(str(j) + " ", end="") instead of print(j, end="") | Easier reading on each row |
for i from 1 to rows:
for j from i down to 1:
print j
print newline| Goal | Pattern |
|---|---|
| Pick each row | for i in range(1, rows + 1): |
| Print digits | for j in range(i, 0, -1): print(j, end="") |
| End of row | print() |
| Spaced form | print(str(j) + " ", end="") |
| vs Program 5 / 6 | 5: 1..i; 6: i..rows; 7: i..1 |
| API | Effect | Use for |
|---|---|---|
print(j, end="") | Stays on the same line | Each digit on the row |
print() | Ends the current line | After the inner loop finishes |
Digits use end=""; a bare print() ends the row once.
Change the row count and the reverse-row triangle updates instantly — capped at 9 for readable single-digit demos.
rows = 5Trace how a descending inner loop reverses each row while the outer loop grows the width.
i | Inner j | Prints |
|---|---|---|
1 | 1..1 | 1 |
2 | 2..1 | 21 |
3 | 3..1 | 321 |
5 | 5..1 | 54321 |
Total digits = n(n+1)/2 → O(n²). Compare with Program 5 (1..i) and Program 6 (i..rows).
Three complete programs: fixed rows = 5, user-input rows, and a compact rows = 3 demo. Use View Output to reveal sample results.
rows = 5Hard-coded height — outer counts up, inner prints i..1 with no spaces.
rows = 5
for i in range(1, rows + 1):
for j in range(i, 0, -1):
print(j, end="")
print()1. Outer up. i grows from 1 to 5, so each row is one digit wider.
2. Inner down. range(i, 0, -1) starts at i and steps to 1 — that reverses the digits.
3. Newline. Call bare print() only after the inner loop finishes the row.
Read rows safely, validate, then run the same nested loops.
try:
rows = int(input("Enter the number of rows: "))
except ValueError:
print("Please enter a positive integer.")
raise SystemExit
if rows <= 0:
print("Please enter a positive integer.")
raise SystemExit
for i in range(1, rows + 1):
for j in range(i, 0, -1):
print(j, end="")
print()1. Prompt and validate. Catch ValueError; reject non-positive values before looping.
2. Same core. Outer up / inner i..1 matches Example 1 — only rows comes from the user.
3. Safer input tip. Cap demos for readable single-digit output:
try:
rows = int(input("Enter the number of rows: "))
except ValueError:
print("Enter a whole number from 1 to 9.")
raise SystemExit
if rows < 1 or rows > 9:
print("Enter a whole number from 1 to 9.")
raise SystemExitrows = 3Same structure with only three rows — easy to trace on paper.
rows = 3
for i in range(1, rows + 1):
for j in range(i, 0, -1):
print(j, end="")
print()1. Three rows. i = 1 → 1; i = 2 → 21; i = 3 → 321.
2. Trace on paper. Confirm each new digit is prepended on the left of the descending sequence.
3. Scale up next. Once the small demo is clear, use Examples 1–2 for five rows or user input.
Check these before calling the solution done.
If the inner loop counts up from 1 to i, you get 1, 12, 123… Keep range(i, 0, -1).
A descending outer with inner i..rows is Program 6. Program 7 needs outer 1..rows and inner i..1.
If bare print() sits inside the inner loop, each digit lands on its own line. Call it only after the row finishes.
Output is just 1 — a good sanity check for input validation.
Digits 10+ make tight rows hard to read. Cap demos at 9 or switch to spaced print(str(j) + " ", end="").
Use try/except ValueError and require rows > 0 before looping — bad input should not crash.
| Program | Time | Extra space |
|---|---|---|
| Fixed / input (Examples 1–2) | O(n²) | O(1) |
| Compact rows = 3 (Example 3) | O(n²) | O(1) |
Total digits printed = 1 + 2 + … + n = n(n+1)/2 → O(n²) time. Only a few loop variables are needed.
1..rows, inner i..1.print(j, end="") in the inner loop; bare print() after it.O(n²) time from n(n+1)/2 digits; O(1) extra space.One line: count i up to rows, print j from i down to 1, then newline.
Each row prints digits in reverse order — outer i runs 1..rows, inner j counts down from i to 1 — producing 1, 21, 321, and so on. Total prints grow as O(n²).
Continue with rows like 5, 54, 543 that count down from the peak.
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