A left-shifted descending triangle prints digits i..rows on each row — so the starting digit climbs and the row shrinks from the left.
Rule: for i = 1..rows
print i..rows
12345
2345
345
45
5 ← rows = 5Unlike Program 1’s 1..i with a descending outer loop, this one counts up and starts each row at i.
Walk i from 1 to rows; print digits from i through rows.
| Method | Idea | Best for |
|---|---|---|
| Nested loops | Outer = start i; inner prints i..rows | Learning, interviews |
| input() rows | Same loops; read rows at runtime | Interactive practice |
"".join | Build the row string, then print once | Compact style |
for i from 1 to rows:
for j from i to rows:
print j (no newline)
print newline| Goal | Pattern |
|---|---|
| Set rows | rows = 5 |
| Outer loop | for i in range(1, rows + 1): |
| Inner loop | for j in range(i, rows + 1): print(j, end="") |
| End row | print() |
| Digits per row | rows - i + 1 |
| Join shortcut | print("".join(str(j) for j in range(i, rows + 1))) |
| vs Program 1 | Print i..rows vs 1..i with descending outer |
| API | Effect | Use for |
|---|---|---|
print(j, end="") | Stays on the same line | Each digit |
print() | Ends the current line | After the inner loop |
Print digits with end="", then break once with print(). Putting print() inside the inner loop prints one digit per line.
Change the row count and the left-shifted triangle updates instantly.
rows = 3Trace each outer i, the inner j range, and the printed row.
i | Inner j | Printed row |
|---|---|---|
1 | 1..3 | 123 |
2 | 2..3 | 23 |
3 | 3..3 | 3 |
Digits per row = rows - i + 1. Total = 6 = 3×4/2.
Three complete programs: fixed rows = 5, input() rows, and a "".join shortcut. Use View Output for sample results.
rows = 5Hard-coded height — inner loop starts at i and runs through rows.
rows = 5
for i in range(1, rows + 1):
for j in range(i, rows + 1):
print(j, end="")
print()1. Outer loop. i is the starting digit of that row (1, then 2, then 3…).
2. Inner loop. Print j from i to rows with end="".
3. Newline. print() after the inner loop starts the next shorter row.
Read rows at runtime with input() and int().
rows = int(input("Enter the number of rows: "))
for i in range(1, rows + 1):
for j in range(i, rows + 1):
print(j, end="")
print()1. Read rows. Convert the prompt answer with int().
2. Same shape. Inner start is still i — only the height changes.
3. Safer input tip. Bare int(input()) raises ValueError on letters. Prefer:
raw = input("Enter the number of rows: ").strip()
try:
rows = int(raw)
except ValueError:
print("Enter a positive whole number.")
raise SystemExit(1)
if rows < 1:
print("Enter a positive whole number.")
raise SystemExit(1)"".join ShortcutBuild each row as one string, then print once — same shape, fewer print calls.
rows = 5
for i in range(1, rows + 1):
print("".join(str(j) for j in range(i, rows + 1)))1. Same range. range(i, rows + 1) still produces digits i..rows.
2. Join once. Convert each digit to a string, join them, then print the whole row.
3. When to use it. Prefer nested print(j, end="") while learning; use join when you want a shorter style.
Check these before calling the solution done.
If the inner loop starts at 1, every row prints 1..rows — a rectangle, not this shift.
If print() is inside the inner loop, each digit lands on its own line.
range(rows, 0, -1) with 1..i is Program 1. Keep range(1, rows + 1) with i..rows here.
Output is just 1 — a good sanity check.
When rows > 9, cells become two characters. Keep demos at rows ≤ 9 or add spaces.
Letters crash bare int(input()) — wrap in try/except and require rows >= 1.
| Program | Time | Extra space |
|---|---|---|
| Examples 1–2 | O(n²) | O(1) |
| Join shortcut (Example 3) | O(n²) | O(n) for the row string |
Digits per pattern = n + (n-1) + … + 1 = n(n+1)/2 → O(n²).
i, print digits i..rows.i, not 1.print() advances after each row.n(n+1)/2 → O(n²).One line: raise the start digit each row and print straight through to rows.
Each row starts at i and prints through rows, so the left edge shifts right each line — still O(n²) total prints for n rows.
Continue with the next pattern in the Python number-pattern series.
12 people found this page helpful