Unlike Program 50 (fixed digit sequences), numbers stay continuous — total values = n(n+1)/2.
Approach
How to Solve It
Keep a counter nxt. On odd rows append ascending; on even rows start from end and descend.
Method
Idea
Best for
Odd/even + counter
i % 2 picks direction; nxt never resets
Classic zig-zag demos
Compact
Same logic with fewer rows (e.g. 3)
Quick dry-runs
Pseudocode
Pseudocode
nxt = 1
for i from 1 to rows:
end = nxt + i - 1
line = ""
repeat i times:
if i is odd:
append nxt
else:
append end; end -= 1
nxt += 1
print line
Cheat sheet
Goal
Pattern
Outer (rows)
for (let i = 1; i <= rows; i++)
Row end value
let end = nxt + i - 1;
Odd (ascending)
line += nxt + " ";
Even (descending)
line += end + " "; end--;
Advance counter
nxt++; once per printed value
End the row
console.log(line.trim());
Total numbers
rows * (rows + 1) / 2
Printing Numbers vs Starting a New Line
API
Effect
Use for
line += …
Stays on the same row
Each number on the row
console.log(line)
Ends the current row
After all i numbers finish
Append without a newline, then end the row once.
Try it
Live Preview
Change the row count and the alternating triangle updates instantly.
Whole numbers from 1 to 9. Tap a chip or type a value — the preview redraws as you go.
Live resultrows = 5 · 15 numbers
1
3 2
4 5 6
10 9 8 7
11 12 13 14 15
Trace
Worked Walkthrough
Trace three rows when rows = 5 — watch nxt, end, and direction.
Row i
Direction
nxt start
end
Printed row
1
Odd ↑
1
1
1
2
Even ↓
2
3
3 2
3
Odd ↑
4
6
4 5 6
After row 2, nxt is 4 — so row 3 starts at 4 and continues ascending.
Code
JavaScript Programs
Three complete programs: fixed rows = 5, prompt input, and a compact rows = 3 demo. Use View Output for samples, or Try It Yourself to edit and run live.
Example 1 — Fixed rows = 5
Odd rows ascend with nxt; even rows descend from end.
JavaScript
const rows = 5;
let nxt = 1;
for (let i = 1; i <= rows; i++) {
let end = nxt + i - 1;
let line = "";
for (let j = 0; j < i; j++) {
if (i % 2 === 1) {
line += nxt + " ";
} else {
line += end + " ";
end--;
}
nxt++;
}
console.log(line.trim());
}
1. Counter never resets.nxt starts at 1 and advances once per printed value across every row.
2. Odd rows ascend. Append nxt left-to-right — row 1 is 1, row 3 is 4 5 6.
3. Even rows descend. Set end = nxt + i - 1, then append while decrementing — row 2 is 3 2.
Example 2 — User Input Rows
Read rows with prompt and validate before drawing.
JavaScript
const rows = parseInt(prompt("Enter number of rows:"), 10);
if (!Number.isFinite(rows) || rows < 1) {
console.log("Please enter a positive integer.");
} else {
let nxt = 1;
for (let i = 1; i <= rows; i++) {
let end = nxt + i - 1;
let line = "";
for (let j = 0; j < i; j++) {
if (i % 2 === 1) {
line += nxt + " ";
} else {
line += end + " ";
end--;
}
nxt++;
}
console.log(line.trim());
}
}
1. Prompt and validate. Use parseInt and require rows >= 1.
2. Same odd/even core. Only the source of rows changes — counter and direction match Example 1.
3. Entering 4. Ten numbers total (4×5/2), last row 10 9 8 7.
Example 3 — Compact rows = 3
Same alternating logic with fewer rows for a quick visual check.
JavaScript
const rows = 3;
let nxt = 1;
for (let i = 1; i <= rows; i++) {
let end = nxt + i - 1;
let line = "";
for (let j = 0; j < i; j++) {
if (i % 2 === 1) {
line += nxt + " ";
} else {
line += end + " ";
end--;
}
nxt++;
}
console.log(line.trim());
}
1. Shrink the size. Only rows changes — still odd ascend / even descend.
2. Easier to trace. Six numbers total — useful while learning nxt and end.
3. Same continuity rule.nxt still never resets between rows.
Edge Cases & Pitfalls
Check these before calling the solution done.
Counter
Never reset nxt between rows
Resetting breaks continuity — row 3 would restart at 1 instead of 4.
Even rows
Compute end before the inner loop
Use end = nxt + i - 1, then decrement while appending.
rows = 1
Single-row case
Output is just 1 — one ascending value on an odd row.
Bad input
Validate parseInt
Check Number.isFinite(rows) and require rows >= 1 before the loops.
Analysis
Time and Space Complexity
Program
Time
Extra space
Fixed / compact (Examples 1, 3)
O(n²)
O(n) per row string
User input (Example 2)
O(n²)
O(n) per row string
Total printed numbers are 1 + 2 + … + n = n(n+1)/2 — still quadratic in n.
Remember
Key Takeaways
Rule: odd rows ascend, even rows descend — one continuous counter.
Even rows: start from end = nxt + i - 1, then decrement.
Break the row: call console.log only after all i numbers finish.
Complexity:O(n²) — triangular count of values.
One line: keep a running counter; print ascending on odd rows and descending on even rows.
Frequently Asked Questions
Row 2 is even, so it logs right-to-left. The numbers 2 and 3 belong on that row, but they appear as 3 2.
A running counter nxt increments once per printed value and is never reset between rows.
Before printing row i, end = nxt + i - 1. That is the rightmost value when logging in reverse.
line += appends on the same row. console.log(line) ends the row after all i numbers are appended.
Program 50 concatenates fixed digit sequences per row. Program 51 uses a continuous counter and alternates direction on odd/even rows.
O(n²) for n rows because total printed numbers are 1+2+…+n = n(n+1)/2.
Yes — build with a trailing space then trim, or join an array with spaces before console.log.
One row prints 1 — a single ascending value on the first odd row.
🤔
Did you know?
Numbers stay continuous via a running counter nxt. Odd rows append ascending; even rows append descending with end = nxt + i - 1. Row 2 shows 3 2 — total values = n(n+1)/2.
