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Pattern Programs in Python

Master Python pattern programs using nested loops — stars, pyramids, diamonds, number triangles, alphabets, and special patterns. 15+ complete patterns with code, output, logic diagrams, and Hindi explanations.

Introduction (परिचय)

Pattern programs Python में nested loops की समझ को test करते हैं। ये interview में बहुत पूछे जाते हैं।

Pattern बनाने का secret: - Outer loop → rows (पंक्तियाँ) control करता है - Inner loop → columns (स्तंभ) control करता है - Pattern के shape को देखो → space और symbol के count को analyze करो

Pattern 1: Right Triangle (दाएँ त्रिभुज)

text example

*
* *
* * *
* * * *
* * * * *

Code

python example

n = 5

for i in range(1, n + 1):
    for j in range(i):
        print("*", end=" ")
    print()

Short Version

python example

n = 5
for i in range(1, n + 1):
    print("* " * i)

Logic Table

text example

i=1: j goes 0     → 1 star
i=2: j goes 0,1   → 2 stars
i=3: j goes 0,1,2 → 3 stars
...
i=n: j goes 0..n-1 → n stars

Pattern 2: Inverted Right Triangle (उल्टा दाएँ त्रिभुज)

text example

* * * * *
* * * *
* * *
* *
*

Code

python example

n = 5

for i in range(n, 0, -1):
    for j in range(i):
        print("*", end=" ")
    print()

Logic

text example

i=5: 5 stars
i=4: 4 stars
i=3: 3 stars
i=2: 2 stars
i=1: 1 star
(i decreases from n to 1)

Pattern 3: Full Pyramid (पूर्ण पिरामिड)

text example

        *
      * * *
    * * * * *
  * * * * * * *
* * * * * * * * *

Code

python example

n = 5

for i in range(1, n + 1):
    # Print spaces
    spaces = n - i
    print(" " * spaces, end="")
    
    # Print stars
    stars = 2 * i - 1
    print("* " * stars)

Cleaner Version

python example

n = 5
for i in range(1, n + 1):
    print(" " * (n - i) + "* " * (2 * i - 1))

Logic Table

text example

Row i | Spaces (n-i) | Stars (2i-1)
  1   |      4       |     1
  2   |      3       |     3
  3   |      2       |     5
  4   |      1       |     7
  5   |      0       |     9

Pattern 4: Inverted Pyramid (उल्टा पिरामिड)

text example

* * * * * * * * *
  * * * * * * *
    * * * * *
      * * *
        *

Code

python example

n = 5

for i in range(n, 0, -1):
    spaces = n - i
    stars = 2 * i - 1
    print(" " * spaces + "* " * stars)

Pattern 5: Diamond (हीरा / Diamond)

text example

        *
      * * *
    * * * * *
  * * * * * * *
* * * * * * * * *
  * * * * * * *
    * * * * *
      * * *
        *

Code

python example

n = 5

# Upper half (including middle row)
for i in range(1, n + 1):
    print(" " * (n - i) + "* " * (2 * i - 1))

# Lower half
for i in range(n - 1, 0, -1):
    print(" " * (n - i) + "* " * (2 * i - 1))

Logic

text example

Upper half: rows 1 to n (pyramid)
Lower half: rows n-1 to 1 (inverted pyramid, no middle row)

Pattern 6: Hollow Square (खाली वर्ग)

text example

* * * * *
*       *
*       *
*       *
* * * * *

Code

python example

n = 5

for i in range(1, n + 1):
    for j in range(1, n + 1):
        # First/last row OR first/last column
        if i == 1 or i == n or j == 1 or j == n:
            print("*", end=" ")
        else:
            print(" ", end=" ")
    print()

Pattern 7: Number Triangle (संख्या त्रिभुज)

text example

Code

python example

n = 5

for i in range(1, n + 1):
    for j in range(1, i + 1):
        print(j, end=" ")
    print()

Pattern 8: Repeated Number Triangle

text example

Code

python example

n = 5

for i in range(1, n + 1):
    for j in range(i):
        print(i, end=" ")
    print()

Pattern 9: Floyd's Triangle (फ्लॉयड का त्रिभुज)

text example

1
2  3
4  5  6
7  8  9  10
11 12 13 14 15

Code

python example

n = 5
num = 1

for i in range(1, n + 1):
    for j in range(i):
        print(num, end="\t")
        num += 1
    print()

Pattern 10: Pascal's Triangle (पास्कल का त्रिभुज)

text example

        1
      1   1
    1   2   1
  1   3   3   1
1   4   6   4   1

Code

python example

n = 5

for i in range(n):
    # Print leading spaces
    print(" " * (n - i - 1), end="")
    
    # Calculate and print values using combination formula
    val = 1
    for j in range(i + 1):
        print(f"{val:3d}", end="")
        val = val * (i - j) // (j + 1)
    print()

Logic (Pascal's Triangle Rule)

text example

Each number = sum of two numbers directly above it
     1
    1 1
   1 2 1
  1 3 3 1
 1 4 6 4 1

C(row, col) = row! / (col! * (row-col)!)

Pattern 11: Alphabet Triangle (वर्णमाला त्रिभुज)

text example

A
A B
A B C
A B C D
A B C D E

Code

python example

n = 5

for i in range(n):
    for j in range(i + 1):
        print(chr(65 + j), end=" ")  # chr(65) = 'A'
    print()

Same-Letter Triangle

text example

A
B B
C C C
D D D D
E E E E E

python example

n = 5
for i in range(n):
    letter = chr(65 + i)
    print((letter + " ") * (i + 1))

Pattern 12: Butterfly Pattern (तितली)

text example

*         *
* *     * *
* * *   * *  * 
* * * * * * * *
* * * * * * * *
* * *   * * *
* *     * *
*         *

Code

python example

n = 4

# Upper half
for i in range(1, n + 1):
    # Left stars
    print("* " * i, end="")
    # Middle spaces
    print("  " * (2 * (n - i)), end="")
    # Right stars
    print("* " * i)

# Lower half
for i in range(n, 0, -1):
    print("* " * i, end="")
    print("  " * (2 * (n - i)), end="")
    print("* " * i)

Pattern 13: Number Pyramid (संख्या पिरामिड)

text example

        1
      2 1 2
    3 2 1 2 3
  4 3 2 1 2 3 4
5 4 3 2 1 2 3 4 5

Code

python example

n = 5

for i in range(1, n + 1):
    # Spaces
    print("  " * (n - i), end="")
    # Decreasing numbers
    for j in range(i, 0, -1):
        print(j, end=" ")
    # Increasing numbers (skip center)
    for j in range(2, i + 1):
        print(j, end=" ")
    print()

Pattern 14: Hollow Diamond (खोखला हीरा)

text example

    *
   * *
  *   *
 *     *
*       *
 *     *
  *   *
   * *
    *

Code

python example

n = 5

# Upper half
for i in range(1, n + 1):
    for j in range(1, n + 1):
        if j == n - i + 1 or j == n + i - 1:
            print("*", end="")
        else:
            print(" ", end="")
    print()

# Lower half
for i in range(n - 1, 0, -1):
    for j in range(1, n + 1):
        if j == n - i + 1 or j == n + i - 1:
            print("*", end="")
        else:
            print(" ", end="")
    print()

Pattern 15: Cross / Plus Pattern (क्रॉस / प्लस)

text example

*   *
  * *
    *
  * *
*   *

X Pattern

python example

n = 5

for i in range(n):
    for j in range(n):
        if i == j or i + j == n - 1:
            print("*", end="")
        else:
            print(" ", end="")
    print()

Output:

Example

* * * * * * * * *

Pattern 16: Spiral Number Pattern (संख्या सर्पिल — Simulated)

text example

1  2  3  4  5
16 17 18 19  6
15 24 25 20  7
14 23 22 21  8
13 12 11 10  9

Code (Snail/Spiral Fill)

Example

n = 5 matrix = [[0]*n for _ in range(n)] top, bottom, left, right = 0, n-1, 0, n-1 num = 1 while top <= bottom and left <= right: for i in range(left, right+1): matrix[top][i] = num; num += 1 top += 1 for i in range(top, bottom+1): matrix[i][right] = num; num += 1 right -= 1 for i in range(right, left-1, -1): matrix[bottom][i] = num; num += 1 bottom -= 1 for i in range(bottom, top-1, -1): matrix[i][left] = num; num += 1 left += 1 for row in matrix: print(" ".join(f"{x:2d}" for x in row))

Pattern Summary Table (पैटर्न सारांश तालिका)

#	Pattern Name	Key Formula
1	Right Triangle	`print("* " * i)`
2	Inverted Triangle	`range(n, 0, -1)`
3	Full Pyramid	Spaces: `n-i`, Stars: `2i-1`
4	Inverted Pyramid	Reverse of pyramid
5	Diamond	Pyramid + Inverted Pyramid
6	Hollow Square	Check border condition
7	Number Triangle	`print(j)` for j in range(1, i+1)
8	Repeated Number	`print(i)` i times
9	Floyd's Triangle	Running counter
10	Pascal's Triangle	Combination formula
11	Alphabet Triangle	`chr(65 + j)`
12	Butterfly	Left stars + spaces + right stars
13	Number Pyramid	Descend then ascend
14	Hollow Diamond	Border condition
15	X Pattern	`i==j or i+j==n-1`
16	Spiral	Layer-by-layer fill

Quick Pattern Cheat Sheet (त्वरित संदर्भ)

Example

# ─── PATTERN BUILDING BLOCKS ─── # Spaces before content print(" " * (n - i), end="") # Stars print("* " * i) # Numbers ascending for j in range(1, i + 1): print(j, end=" ") # Numbers descending for j in range(i, 0, -1): print(j, end=" ") # Alphabet print(chr(65 + j), end=" ") # A=65, B=66, ... # New line after each row print() # or print("\n", end="")

Common Mistakes in Patterns (सामान्य गलतियाँ)

❌ Mistake 1: Off-by-one in range

python example

# WRONG — prints 0..n-1 (0 is not useful for row count)
for i in range(n):        # i = 0, 1, 2, ..., n-1

# CORRECT — prints 1..n
for i in range(1, n + 1): # i = 1, 2, 3, ..., n

❌ Mistake 2: Not using `end=""`

python example

# WRONG — each star on new line!
for j in range(i):
    print("*")      # Newline after every star

# CORRECT — all stars on same line
for j in range(i):
    print("*", end=" ")
print()             # Move to next line after row

❌ Mistake 3: Forgetting to print newline

python example

n = 5
for i in range(1, n + 1):
    for j in range(i):
        print("*", end=" ")
    # Missing print() here!
    # All rows print on same line!

# CORRECT
for i in range(1, n + 1):
    for j in range(i):
        print("*", end=" ")
    print()   # ← Don't forget this!

❌ Mistake 4: Wrong space calculation

python example

n = 5

# WRONG — spaces don't decrease properly
for i in range(1, n+1):
    print(" " * n, end="")   # Always n spaces!
    print("* " * i)

# CORRECT — spaces = n - i
for i in range(1, n+1):
    print(" " * (n - i), end="")
    print("* " * i)

Practice Exercises (अभ्यास प्रश्न)

Exercise 1 — Easy

Print this pattern (n=5):

Example

* * * * * * * * * * * * * * *

Exercise 2 — Easy

Print this number pattern:

Example

1 2 3 4 5 1 2 3 4 1 2 3 1 2 1

Exercise 3 — Medium

Print zigzag pattern:

Example

* * * * * * * * * * * * *

Exercise 4 — Medium

Print this hollow triangle:

Example

* * * * * * * * * * * *

Exercise 5 — Hard

Print the following (hourglass):

Example

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

Exercise 6 — Hard

Print numbers in a spiral pattern for n=4:

Example

1 2 3 4 12 13 14 5 11 16 15 6 10 9 8 7

Solutions (हल)

Solution 1 — Inverted Right Triangle

python example

n = 5
for i in range(n, 0, -1):
    print("* " * i)

Solution 2 — Inverted Number Triangle

python example

n = 5
for i in range(n, 0, -1):
    for j in range(1, i + 1):
        print(j, end=" ")
    print()

Solution 4 — Hollow Triangle

python example

n = 5
for i in range(1, n + 1):
    for j in range(1, i + 1):
        if j == 1 or j == i or i == n:
            print("*", end=" ")
        else:
            print(" ", end=" ")
    print()

Solution 5 — Hourglass

python example

n = 4  # half height
# Upper half (inverted pyramid)
for i in range(n, 0, -1):
    print(" " * (n - i) + "* " * (2 * i - 1))
# Lower half (pyramid, skip middle)
for i in range(2, n + 1):
    print(" " * (n - i) + "* " * (2 * i - 1))

Interview Tips (Interview की तैयारी)

text example

Pattern Interview Checklist:
□ Start with the easy right triangle
□ Always analyze rows vs columns first
□ Draw the table: i, spaces, stars
□ Use end="" to print on same line
□ Use print() at end of each row
□ Test with n=3 or n=4 first
□ Common questions: pyramid, diamond, Floyd's
□ Know how chr(65) = 'A' works for alphabets
□ Practice without seeing the solution

Final Summary (अंतिम सारांश)

Pattern programs आपकी loop thinking test करते हैं:

Right Triangle — Basic nested loop
Pyramid — Add spaces before stars
Diamond — Pyramid + Inverted
Floyd's Triangle — Running counter
Pascal's Triangle — Math + loops
Alphabet patterns — chr() function
Hollow patterns — Border condition
Number patterns — Inner loop value

Practice करो: एक pattern बनाओ, समझो, फिर बिना देखे लिखो। यही interview में काम आएगा।

Previous Topic (पिछला विषय)

⬅️ Break, Continue & Pass

Next Section (अगला खंड)

➡️ Functions — Code को reusable बनाओ

📤 Output Examples (Pattern Outputs with Code)

यहाँ कुछ key patterns के outputs verify करें:

Right Triangle Output

python example

n = 5
for i in range(1, n + 1):
    print("* " * i)

Output

*
* *
* * *
* * * *
* * * * *

Full Pyramid Output

python example

n = 5
for i in range(1, n + 1):
    print(" " * (n - i) + "* " * (2 * i - 1))

Output

        *
      * * *
    * * * * *
  * * * * * * *
* * * * * * * * *

Diamond Output

python example

n = 5
for i in range(1, n + 1):
    print(" " * (n - i) + "* " * (2 * i - 1))
for i in range(n - 1, 0, -1):
    print(" " * (n - i) + "* " * (2 * i - 1))

Output

        *
      * * *
    * * * * *
  * * * * * * *
* * * * * * * * *
  * * * * * * *
    * * * * *
      * * *
        *

Number Triangle Output

python example

n = 5
for i in range(1, n + 1):
    for j in range(1, i + 1):
        print(j, end=" ")
    print()

Output

Floyd's Triangle Output

python example

n = 5
num = 1
for i in range(1, n + 1):
    for j in range(i):
        print(num, end="\t")
        num += 1
    print()

Output

1
2	3
4	5	6
7	8	9	10
11	12	13	14	15

Alphabet Triangle Output

python example

n = 5
for i in range(n):
    for j in range(i + 1):
        print(chr(65 + j), end=" ")
    print()

Output

A
A B
A B C
A B C D
A B C D E

✅ Key Takeaways

🔁 Nested loops = Pattern programs — Outer loop rows handle करता है, inner loop columns print करता है
📐 Spaces matter — Pyramid और diamond patterns में " " * (n - i) spaces center alignment देते हैं
🖨️ end="" is essential — Same line पर print करने के लिए end=" " या end="" ज़रूरी है
🔢 Formula find करो — हर pattern में row number (i) से spaces और symbols का count derive होता है
💎 Diamond = Pyramid + Inverted Pyramid — Complex patterns को simple patterns combine करके बनाओ
📊 Table बनाओ — Row, spaces, और stars का table बनाकर formula discover करो
🔤 chr(65) = 'A' — Alphabet patterns के लिए ASCII values use करो (chr(65 + j))
🧱 Hollow patterns — Border condition check करो: first/last row OR first/last column
🧮 Pascal's Triangle — Math formula C(n, r) use करता है — loops + math combination
🎯 Practice without looking — Interview में pattern देखकर 2 min में code लिखने की ability चाहिए

❓ FAQ

Q1: Pattern programs क्यों important हैं? 🤔

Answer: Pattern programs loop logic, nested loops, और problem decomposition test करते हैं। Interview में ये commonly पूछे जाते हैं क्योंकि ये prove करते हैं कि आप loops को deeply समझते हो। साथ ही ये matrix manipulation और 2D array problems की foundation हैं।

Q2: Outer loop और Inner loop में क्या difference है? 🔄

Answer: Outer loop = rows (पंक्तियाँ) control करता है — कितनी lines print होंगी। Inner loop = columns (स्तंभ) control करता है — एक line में क्या-क्या print होगा। Pattern programs में outer loop हमेशा row number decide करता है, inner loop content decide करता है।

Q3: `end=""` और `end=" "` में क्या अंतर है? 🖨️

Answer: end="" means print के बाद कुछ भी add मत करो (no space, no newline)। end=" " means print के बाद एक space add करो। Default end="\n" होता है जो newline add करता है। Pattern programs में same line पर multiple characters print करने के लिए end parameter ज़रूरी है।

Q4: Pyramid pattern में spaces कैसे calculate करें? 📐

Answer: Formula simple है: Spaces = n - i (जहाँ n = total rows, i = current row number 1 से शुरू)।

Row 1: n-1 spaces (4 spaces for n=5)
Row 2: n-2 spaces (3 spaces)
Row n: 0 spaces

Stars formula: 2*i - 1 (odd numbers: 1, 3, 5, 7, 9)

Q5: Floyd's Triangle और Pascal's Triangle में क्या difference है? 🔢

Answer: Floyd's Triangle — Simply 1 से शुरू होकर continuous numbers fill करता है (1, 2, 3, 4...)। Logic simple है — एक counter बढ़ाते जाओ। Pascal's Triangle — Mathematical combination formula use करता है C(row, col)। हर number ऊपर के दो numbers का sum होता है। Pascal ज़्यादा complex है।

Q6: Diamond pattern कैसे बनाएं easily? 💎

Answer: Diamond = Upper pyramid + Lower inverted pyramid (without repeating middle row)।

python example

# Upper: range(1, n+1) — rows 1 to n
# Lower: range(n-1, 0, -1) — rows n-1 to 1

इसे divide and conquer approach कहते हैं — complex pattern को 2 simple patterns में तोड़ो।

Q7: Pattern programs को solve करने का best approach क्या है? 🎯

Answer: 5-step approach follow करो:

Observe — Pattern को ध्यान से देखो
Table बनाओ — Row number, spaces count, symbols count लिखो
Formula find करो — i के terms में express करो
Code लिखो — Outer loop (rows), inner loops (spaces + symbols)
Test करो — Small n (3 or 4) से verify करो

Q8: Hollow patterns कैसे बनाते हैं? 🧱

Answer: Hollow patterns में border condition check करो — star सिर्फ तभी print करो जब:

First row (i == 1) या Last row (i == n)
First column (j == 1) या Last column (j == n)

Baaki सब positions पर space print करो। यही logic hollow square, hollow triangle, hollow diamond सबमें apply होता है।

🎯 Interview Questions

Q1: Write a program to print a right-angled triangle with numbers instead of stars.

Answer:

python example

n = 5
for i in range(1, n + 1):
    for j in range(1, i + 1):
        print(j, end=" ")
    print()

Output

Explanation: Outer loop rows control करता है (1 to n)। Inner loop range(1, i+1) — current row number तक numbers print करता है। end=" " same line पर print करता है, print() row end करता है।

Q2: How would you print a hollow pyramid? Explain the logic.

Answer:

python example

n = 5
for i in range(1, n + 1):
    for j in range(n - i):
        print(" ", end="")
    for j in range(1, 2 * i):
        if j == 1 or j == 2 * i - 1 or i == n:
            print("*", end="")
        else:
            print(" ", end="")
    print()

Explanation: Normal pyramid logic + hollow condition। Star सिर्फ first column (j==1), last column (j==2*i-1), या last row (i==n) पर print होता है। बाकी सब positions पर space print करते हैं।

Q3: What is the time complexity of printing a pattern of size n?

Answer: Most basic patterns O(n²) time complexity रखते हैं क्योंकि nested loops हैं — outer loop n times, inner loop average n/2 times चलता है। Spiral pattern भी O(n²) है लेकिन single loop से fill होता है। Pascal's triangle O(n²) है but mathematical computation extra cost add करता है।

Q4: How do you print a diamond pattern using minimum lines of code?

Answer:

python example

n = 5
for i in range(1, n + 1):
    print(" " * (n - i) + "* " * (2 * i - 1))
for i in range(n - 1, 0, -1):
    print(" " * (n - i) + "* " * (2 * i - 1))

Explanation: सिर्फ 4 lines of actual code! String multiplication (" " * count और "* " * count) use करके concise code लिखा। Upper half और lower half दो separate loops में handle किया।

Q5: Explain the difference between `range(n)`, `range(1, n+1)`, and `range(n, 0, -1)`.

Answer:

range(n) → 0, 1, 2, ..., n-1 (n elements, 0 से start)
range(1, n+1) → 1, 2, 3, ..., n (n elements, 1 से start)
range(n, 0, -1) → n, n-1, n-2, ..., 1 (reverse order, 0 excluded)

Pattern programs में: ascending patterns (growing triangle) → range(1, n+1), descending patterns (inverted triangle) → range(n, 0, -1) use करो।

Q6: Write a program to print Pascal's Triangle. Explain the mathematical formula.

Answer:

python example

n = 5
for i in range(n):
    val = 1
    print(" " * (n - i - 1), end="")
    for j in range(i + 1):
        print(f"{val:3d}", end="")
        val = val * (i - j) // (j + 1)
    print()

Explanation: Pascal's Triangle में हर element C(row, col) = combination formula use करता है। Instead of calculating factorial हर बार, हम previous value से next value derive करते हैं: val = val * (i - j) // (j + 1)। यह efficient approach है — O(1) per element।

Q7: How would you print a pattern using recursion instead of loops?

Answer:

python example

def print_triangle(n, current=1):
    if current > n:
        return
    print("* " * current)
    print_triangle(n, current + 1)

print_triangle(5)

Output

*
* *
* * *
* * * *
* * * * *

Explanation: Recursion में function खुद को call करता है — base case current > n पर stop। हर call एक row print करती है और current + 1 pass करती है। यह approach interviews में recursion understanding demonstrate करता है, but loops ज़्यादा efficient हैं।

Q8: What is the approach to solve any unknown pattern in an interview?

Answer: 5-step systematic approach:

Pattern observe करो — Rows count करो, हर row में क्या है लिखो
Table बनाओ — | Row (i) | Spaces | Symbols | Formula |
Formula derive करो — Spaces और symbols को i के terms में express करो
Code structure — Outer loop = rows, Inner loop(s) = spaces + content
Edge cases handle करो — First/last row, hollow conditions

Pro tip: Always start with n=3 for verification — less computation, easy to trace mentally।

Q9: Print a sandglass (hourglass) pattern. What's the trick?

Answer:

python example

n = 4
# Upper inverted pyramid
for i in range(n, 0, -1):
    print(" " * (n - i) + "* " * (2 * i - 1))
# Lower pyramid (skip middle)
for i in range(2, n + 1):
    print(" " * (n - i) + "* " * (2 * i - 1))

Output

* * * * * * *
  * * * * *
    * * *
      *
    * * *
  * * * * *
* * * * * * *

Explanation: Hourglass = Inverted Pyramid (top) + Normal Pyramid (bottom, starting from row 2 to avoid duplicate middle row)। Same formula " " * (n-i) और "* " * (2*i-1) — बस direction change होती है।

Q10: How do you optimize pattern programs for large values of n?

Answer: Optimization techniques:

String multiplication — "* " * n is faster than loop-based printing
List comprehension + join — print("".join(["* " for _ in range(i)])) avoids multiple I/O calls
Buffer output — Store all rows in list, then print("\n".join(rows)) — single I/O operation
Avoid repeated calculations — Pre-calculate spaces/stars formulas

Example

# Optimized pyramid rows = [" " * (n - i) + "* " * (2 * i - 1) for i in range(1, n + 1)] print("\n".join(rows))

Key insight: For n > 1000, I/O bottleneck matters more than loop computation। Buffer everything, print once।

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Python Notes

Pattern Programs in Python

Introduction (परिचय)

Pattern programs Python में nested loops की समझ को test करते हैं। ये interview में बहुत पूछे जाते हैं।

Pattern बनाने का secret: - Outer loop → rows (पंक्तियाँ) control करता है - Inner loop → columns (स्तंभ) control करता है - Pattern के shape को देखो → space और symbol के count को analyze करो

Pattern 1: Right Triangle (दाएँ त्रिभुज)

text example

*
* *
* * *
* * * *
* * * * *

Code

python example

n = 5

for i in range(1, n + 1):
    for j in range(i):
        print("*", end=" ")
    print()

Short Version

python example

n = 5
for i in range(1, n + 1):
    print("* " * i)

Logic Table

text example

i=1: j goes 0     → 1 star
i=2: j goes 0,1   → 2 stars
i=3: j goes 0,1,2 → 3 stars
...
i=n: j goes 0..n-1 → n stars

Pattern 2: Inverted Right Triangle (उल्टा दाएँ त्रिभुज)

text example

* * * * *
* * * *
* * *
* *
*

Code

python example

n = 5

for i in range(n, 0, -1):
    for j in range(i):
        print("*", end=" ")
    print()

Logic

text example

i=5: 5 stars
i=4: 4 stars
i=3: 3 stars
i=2: 2 stars
i=1: 1 star
(i decreases from n to 1)

Pattern 3: Full Pyramid (पूर्ण पिरामिड)

text example

        *
      * * *
    * * * * *
  * * * * * * *
* * * * * * * * *

Code

python example

n = 5

for i in range(1, n + 1):
    # Print spaces
    spaces = n - i
    print(" " * spaces, end="")
    
    # Print stars
    stars = 2 * i - 1
    print("* " * stars)

Cleaner Version

python example

n = 5
for i in range(1, n + 1):
    print(" " * (n - i) + "* " * (2 * i - 1))

Logic Table

text example

Row i | Spaces (n-i) | Stars (2i-1)
  1   |      4       |     1
  2   |      3       |     3
  3   |      2       |     5
  4   |      1       |     7
  5   |      0       |     9

Pattern 4: Inverted Pyramid (उल्टा पिरामिड)

text example

* * * * * * * * *
  * * * * * * *
    * * * * *
      * * *
        *

Code

python example

n = 5

for i in range(n, 0, -1):
    spaces = n - i
    stars = 2 * i - 1
    print(" " * spaces + "* " * stars)

Pattern 5: Diamond (हीरा / Diamond)

text example

        *
      * * *
    * * * * *
  * * * * * * *
* * * * * * * * *
  * * * * * * *
    * * * * *
      * * *
        *

Code

python example

n = 5

# Upper half (including middle row)
for i in range(1, n + 1):
    print(" " * (n - i) + "* " * (2 * i - 1))

# Lower half
for i in range(n - 1, 0, -1):
    print(" " * (n - i) + "* " * (2 * i - 1))

Logic

text example

Upper half: rows 1 to n (pyramid)
Lower half: rows n-1 to 1 (inverted pyramid, no middle row)

Pattern 6: Hollow Square (खाली वर्ग)

text example

* * * * *
*       *
*       *
*       *
* * * * *

Code

python example

n = 5

for i in range(1, n + 1):
    for j in range(1, n + 1):
        # First/last row OR first/last column
        if i == 1 or i == n or j == 1 or j == n:
            print("*", end=" ")
        else:
            print(" ", end=" ")
    print()

Pattern 7: Number Triangle (संख्या त्रिभुज)

text example

Code

python example

n = 5

for i in range(1, n + 1):
    for j in range(1, i + 1):
        print(j, end=" ")
    print()

Pattern 8: Repeated Number Triangle

text example

Code

python example

n = 5

for i in range(1, n + 1):
    for j in range(i):
        print(i, end=" ")
    print()

Pattern 9: Floyd's Triangle (फ्लॉयड का त्रिभुज)

text example

1
2  3
4  5  6
7  8  9  10
11 12 13 14 15

Code

python example

n = 5
num = 1

for i in range(1, n + 1):
    for j in range(i):
        print(num, end="\t")
        num += 1
    print()

Pattern 10: Pascal's Triangle (पास्कल का त्रिभुज)

text example

        1
      1   1
    1   2   1
  1   3   3   1
1   4   6   4   1

Code

python example

n = 5

for i in range(n):
    # Print leading spaces
    print(" " * (n - i - 1), end="")
    
    # Calculate and print values using combination formula
    val = 1
    for j in range(i + 1):
        print(f"{val:3d}", end="")
        val = val * (i - j) // (j + 1)
    print()

Logic (Pascal's Triangle Rule)

text example

Each number = sum of two numbers directly above it
     1
    1 1
   1 2 1
  1 3 3 1
 1 4 6 4 1

C(row, col) = row! / (col! * (row-col)!)

Pattern 11: Alphabet Triangle (वर्णमाला त्रिभुज)

text example

A
A B
A B C
A B C D
A B C D E

Code

python example

n = 5

for i in range(n):
    for j in range(i + 1):
        print(chr(65 + j), end=" ")  # chr(65) = 'A'
    print()

Same-Letter Triangle

text example

A
B B
C C C
D D D D
E E E E E

python example

n = 5
for i in range(n):
    letter = chr(65 + i)
    print((letter + " ") * (i + 1))

Pattern 12: Butterfly Pattern (तितली)

text example

*         *
* *     * *
* * *   * *  * 
* * * * * * * *
* * * * * * * *
* * *   * * *
* *     * *
*         *

Code

python example

n = 4

# Upper half
for i in range(1, n + 1):
    # Left stars
    print("* " * i, end="")
    # Middle spaces
    print("  " * (2 * (n - i)), end="")
    # Right stars
    print("* " * i)

# Lower half
for i in range(n, 0, -1):
    print("* " * i, end="")
    print("  " * (2 * (n - i)), end="")
    print("* " * i)

Pattern 13: Number Pyramid (संख्या पिरामिड)

text example

        1
      2 1 2
    3 2 1 2 3
  4 3 2 1 2 3 4
5 4 3 2 1 2 3 4 5

Code

python example

n = 5

for i in range(1, n + 1):
    # Spaces
    print("  " * (n - i), end="")
    # Decreasing numbers
    for j in range(i, 0, -1):
        print(j, end=" ")
    # Increasing numbers (skip center)
    for j in range(2, i + 1):
        print(j, end=" ")
    print()

Pattern 14: Hollow Diamond (खोखला हीरा)

text example

    *
   * *
  *   *
 *     *
*       *
 *     *
  *   *
   * *
    *

Code

python example

n = 5

# Upper half
for i in range(1, n + 1):
    for j in range(1, n + 1):
        if j == n - i + 1 or j == n + i - 1:
            print("*", end="")
        else:
            print(" ", end="")
    print()

# Lower half
for i in range(n - 1, 0, -1):
    for j in range(1, n + 1):
        if j == n - i + 1 or j == n + i - 1:
            print("*", end="")
        else:
            print(" ", end="")
    print()

Pattern 15: Cross / Plus Pattern (क्रॉस / प्लस)

text example

*   *
  * *
    *
  * *
*   *

X Pattern

python example

n = 5

for i in range(n):
    for j in range(n):
        if i == j or i + j == n - 1:
            print("*", end="")
        else:
            print(" ", end="")
    print()

Output:

Example

* * * * * * * * *

Pattern 16: Spiral Number Pattern (संख्या सर्पिल — Simulated)

text example

1  2  3  4  5
16 17 18 19  6
15 24 25 20  7
14 23 22 21  8
13 12 11 10  9

Code (Snail/Spiral Fill)

Example

Pattern Summary Table (पैटर्न सारांश तालिका)

#	Pattern Name	Key Formula
1	Right Triangle	`print("* " * i)`
2	Inverted Triangle	`range(n, 0, -1)`
3	Full Pyramid	Spaces: `n-i`, Stars: `2i-1`
4	Inverted Pyramid	Reverse of pyramid
5	Diamond	Pyramid + Inverted Pyramid
6	Hollow Square	Check border condition
7	Number Triangle	`print(j)` for j in range(1, i+1)
8	Repeated Number	`print(i)` i times
9	Floyd's Triangle	Running counter
10	Pascal's Triangle	Combination formula
11	Alphabet Triangle	`chr(65 + j)`
12	Butterfly	Left stars + spaces + right stars
13	Number Pyramid	Descend then ascend
14	Hollow Diamond	Border condition
15	X Pattern	`i==j or i+j==n-1`
16	Spiral	Layer-by-layer fill

Quick Pattern Cheat Sheet (त्वरित संदर्भ)

Example

Common Mistakes in Patterns (सामान्य गलतियाँ)

❌ Mistake 1: Off-by-one in range

python example

# WRONG — prints 0..n-1 (0 is not useful for row count)
for i in range(n):        # i = 0, 1, 2, ..., n-1

# CORRECT — prints 1..n
for i in range(1, n + 1): # i = 1, 2, 3, ..., n

❌ Mistake 2: Not using `end=""`

python example

# WRONG — each star on new line!
for j in range(i):
    print("*")      # Newline after every star

# CORRECT — all stars on same line
for j in range(i):
    print("*", end=" ")
print()             # Move to next line after row

❌ Mistake 3: Forgetting to print newline

python example

n = 5
for i in range(1, n + 1):
    for j in range(i):
        print("*", end=" ")
    # Missing print() here!
    # All rows print on same line!

# CORRECT
for i in range(1, n + 1):
    for j in range(i):
        print("*", end=" ")
    print()   # ← Don't forget this!

❌ Mistake 4: Wrong space calculation

python example

n = 5

# WRONG — spaces don't decrease properly
for i in range(1, n+1):
    print(" " * n, end="")   # Always n spaces!
    print("* " * i)

# CORRECT — spaces = n - i
for i in range(1, n+1):
    print(" " * (n - i), end="")
    print("* " * i)

Practice Exercises (अभ्यास प्रश्न)

Exercise 1 — Easy

Print this pattern (n=5):

Example

* * * * * * * * * * * * * * *

Exercise 2 — Easy

Print this number pattern:

Example

1 2 3 4 5 1 2 3 4 1 2 3 1 2 1

Exercise 3 — Medium

Print zigzag pattern:

Example

* * * * * * * * * * * * *

Exercise 4 — Medium

Print this hollow triangle:

Example

* * * * * * * * * * * *

Exercise 5 — Hard

Print the following (hourglass):

Example

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

Exercise 6 — Hard

Print numbers in a spiral pattern for n=4:

Example

1 2 3 4 12 13 14 5 11 16 15 6 10 9 8 7

Solutions (हल)

Solution 1 — Inverted Right Triangle

python example

n = 5
for i in range(n, 0, -1):
    print("* " * i)

Solution 2 — Inverted Number Triangle

python example

n = 5
for i in range(n, 0, -1):
    for j in range(1, i + 1):
        print(j, end=" ")
    print()

Solution 4 — Hollow Triangle

python example

n = 5
for i in range(1, n + 1):
    for j in range(1, i + 1):
        if j == 1 or j == i or i == n:
            print("*", end=" ")
        else:
            print(" ", end=" ")
    print()

Solution 5 — Hourglass

python example

n = 4  # half height
# Upper half (inverted pyramid)
for i in range(n, 0, -1):
    print(" " * (n - i) + "* " * (2 * i - 1))
# Lower half (pyramid, skip middle)
for i in range(2, n + 1):
    print(" " * (n - i) + "* " * (2 * i - 1))

Interview Tips (Interview की तैयारी)

text example

Pattern Interview Checklist:
□ Start with the easy right triangle
□ Always analyze rows vs columns first
□ Draw the table: i, spaces, stars
□ Use end="" to print on same line
□ Use print() at end of each row
□ Test with n=3 or n=4 first
□ Common questions: pyramid, diamond, Floyd's
□ Know how chr(65) = 'A' works for alphabets
□ Practice without seeing the solution

Final Summary (अंतिम सारांश)

Pattern programs आपकी loop thinking test करते हैं:

Right Triangle — Basic nested loop
Pyramid — Add spaces before stars
Diamond — Pyramid + Inverted
Floyd's Triangle — Running counter
Pascal's Triangle — Math + loops
Alphabet patterns — chr() function
Hollow patterns — Border condition
Number patterns — Inner loop value

Practice करो: एक pattern बनाओ, समझो, फिर बिना देखे लिखो। यही interview में काम आएगा।

Previous Topic (पिछला विषय)

⬅️ Break, Continue & Pass

Next Section (अगला खंड)

➡️ Functions — Code को reusable बनाओ

📤 Output Examples (Pattern Outputs with Code)

यहाँ कुछ key patterns के outputs verify करें:

Right Triangle Output

python example

n = 5
for i in range(1, n + 1):
    print("* " * i)

Output

*
* *
* * *
* * * *
* * * * *

Full Pyramid Output

python example

n = 5
for i in range(1, n + 1):
    print(" " * (n - i) + "* " * (2 * i - 1))

Output

        *
      * * *
    * * * * *
  * * * * * * *
* * * * * * * * *

Diamond Output

python example

n = 5
for i in range(1, n + 1):
    print(" " * (n - i) + "* " * (2 * i - 1))
for i in range(n - 1, 0, -1):
    print(" " * (n - i) + "* " * (2 * i - 1))

Output

        *
      * * *
    * * * * *
  * * * * * * *
* * * * * * * * *
  * * * * * * *
    * * * * *
      * * *
        *

Number Triangle Output

python example

n = 5
for i in range(1, n + 1):
    for j in range(1, i + 1):
        print(j, end=" ")
    print()

Output

Floyd's Triangle Output

python example

n = 5
num = 1
for i in range(1, n + 1):
    for j in range(i):
        print(num, end="\t")
        num += 1
    print()

Output

1
2	3
4	5	6
7	8	9	10
11	12	13	14	15

Alphabet Triangle Output

python example

n = 5
for i in range(n):
    for j in range(i + 1):
        print(chr(65 + j), end=" ")
    print()

Output

A
A B
A B C
A B C D
A B C D E

✅ Key Takeaways

🔁 Nested loops = Pattern programs — Outer loop rows handle करता है, inner loop columns print करता है
📐 Spaces matter — Pyramid और diamond patterns में " " * (n - i) spaces center alignment देते हैं
🖨️ end="" is essential — Same line पर print करने के लिए end=" " या end="" ज़रूरी है
🔢 Formula find करो — हर pattern में row number (i) से spaces और symbols का count derive होता है
💎 Diamond = Pyramid + Inverted Pyramid — Complex patterns को simple patterns combine करके बनाओ
📊 Table बनाओ — Row, spaces, और stars का table बनाकर formula discover करो
🔤 chr(65) = 'A' — Alphabet patterns के लिए ASCII values use करो (chr(65 + j))
🧱 Hollow patterns — Border condition check करो: first/last row OR first/last column
🧮 Pascal's Triangle — Math formula C(n, r) use करता है — loops + math combination
🎯 Practice without looking — Interview में pattern देखकर 2 min में code लिखने की ability चाहिए

❓ FAQ

Q1: Pattern programs क्यों important हैं? 🤔

Q2: Outer loop और Inner loop में क्या difference है? 🔄

Q3: `end=""` और `end=" "` में क्या अंतर है? 🖨️

Q4: Pyramid pattern में spaces कैसे calculate करें? 📐

Answer: Formula simple है: Spaces = n - i (जहाँ n = total rows, i = current row number 1 से शुरू)।

Row 1: n-1 spaces (4 spaces for n=5)
Row 2: n-2 spaces (3 spaces)
Row n: 0 spaces

Stars formula: 2*i - 1 (odd numbers: 1, 3, 5, 7, 9)

Q5: Floyd's Triangle और Pascal's Triangle में क्या difference है? 🔢

Q6: Diamond pattern कैसे बनाएं easily? 💎

Answer: Diamond = Upper pyramid + Lower inverted pyramid (without repeating middle row)।

python example

# Upper: range(1, n+1) — rows 1 to n
# Lower: range(n-1, 0, -1) — rows n-1 to 1

इसे divide and conquer approach कहते हैं — complex pattern को 2 simple patterns में तोड़ो।

Q7: Pattern programs को solve करने का best approach क्या है? 🎯

Answer: 5-step approach follow करो:

Observe — Pattern को ध्यान से देखो
Table बनाओ — Row number, spaces count, symbols count लिखो
Formula find करो — i के terms में express करो
Code लिखो — Outer loop (rows), inner loops (spaces + symbols)
Test करो — Small n (3 or 4) से verify करो

Q8: Hollow patterns कैसे बनाते हैं? 🧱

Answer: Hollow patterns में border condition check करो — star सिर्फ तभी print करो जब:

First row (i == 1) या Last row (i == n)
First column (j == 1) या Last column (j == n)

Baaki सब positions पर space print करो। यही logic hollow square, hollow triangle, hollow diamond सबमें apply होता है।

🎯 Interview Questions

Q1: Write a program to print a right-angled triangle with numbers instead of stars.

Answer:

python example

n = 5
for i in range(1, n + 1):
    for j in range(1, i + 1):
        print(j, end=" ")
    print()

Output

Q2: How would you print a hollow pyramid? Explain the logic.

Answer:

python example

n = 5
for i in range(1, n + 1):
    for j in range(n - i):
        print(" ", end="")
    for j in range(1, 2 * i):
        if j == 1 or j == 2 * i - 1 or i == n:
            print("*", end="")
        else:
            print(" ", end="")
    print()

Q3: What is the time complexity of printing a pattern of size n?

Q4: How do you print a diamond pattern using minimum lines of code?

Answer:

python example

n = 5
for i in range(1, n + 1):
    print(" " * (n - i) + "* " * (2 * i - 1))
for i in range(n - 1, 0, -1):
    print(" " * (n - i) + "* " * (2 * i - 1))

Q5: Explain the difference between `range(n)`, `range(1, n+1)`, and `range(n, 0, -1)`.

Answer:

range(n) → 0, 1, 2, ..., n-1 (n elements, 0 से start)
range(1, n+1) → 1, 2, 3, ..., n (n elements, 1 से start)
range(n, 0, -1) → n, n-1, n-2, ..., 1 (reverse order, 0 excluded)

Pattern programs में: ascending patterns (growing triangle) → range(1, n+1), descending patterns (inverted triangle) → range(n, 0, -1) use करो।

Q6: Write a program to print Pascal's Triangle. Explain the mathematical formula.

Answer:

python example

n = 5
for i in range(n):
    val = 1
    print(" " * (n - i - 1), end="")
    for j in range(i + 1):
        print(f"{val:3d}", end="")
        val = val * (i - j) // (j + 1)
    print()

Q7: How would you print a pattern using recursion instead of loops?

Answer:

python example

def print_triangle(n, current=1):
    if current > n:
        return
    print("* " * current)
    print_triangle(n, current + 1)

print_triangle(5)

Output

*
* *
* * *
* * * *
* * * * *

Q8: What is the approach to solve any unknown pattern in an interview?

Answer: 5-step systematic approach:

Pattern observe करो — Rows count करो, हर row में क्या है लिखो
Table बनाओ — | Row (i) | Spaces | Symbols | Formula |
Formula derive करो — Spaces और symbols को i के terms में express करो
Code structure — Outer loop = rows, Inner loop(s) = spaces + content
Edge cases handle करो — First/last row, hollow conditions

Pro tip: Always start with n=3 for verification — less computation, easy to trace mentally।

Q9: Print a sandglass (hourglass) pattern. What's the trick?

Answer:

python example

n = 4
# Upper inverted pyramid
for i in range(n, 0, -1):
    print(" " * (n - i) + "* " * (2 * i - 1))
# Lower pyramid (skip middle)
for i in range(2, n + 1):
    print(" " * (n - i) + "* " * (2 * i - 1))

Output

* * * * * * *
  * * * * *
    * * *
      *
    * * *
  * * * * *
* * * * * * *

Q10: How do you optimize pattern programs for large values of n?

Answer: Optimization techniques:

String multiplication — "* " * n is faster than loop-based printing
List comprehension + join — print("".join(["* " for _ in range(i)])) avoids multiple I/O calls
Buffer output — Store all rows in list, then print("\n".join(rows)) — single I/O operation
Avoid repeated calculations — Pre-calculate spaces/stars formulas

Example

# Optimized pyramid rows = [" " * (n - i) + "* " * (2 * i - 1) for i in range(1, n + 1)] print("\n".join(rows))

Key insight: For n > 1000, I/O bottleneck matters more than loop computation। Buffer everything, print once।

Exam Focus

Revise definitions, diagrams, examples, and short-answer points for Pattern Programs in Python.

Interview Use

Prepare one clear explanation, one practical example, and one common mistake for this Python Master Course topic.

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Introduction (परिचय)

Pattern 1: Right Triangle (दाएँ त्रिभुज)

Code

Short Version

Logic Table

Pattern 2: Inverted Right Triangle (उल्टा दाएँ त्रिभुज)

Code

Logic

Pattern 3: Full Pyramid (पूर्ण पिरामिड)

Code

Cleaner Version

Logic Table

Pattern 4: Inverted Pyramid (उल्टा पिरामिड)

Code

Pattern 5: Diamond (हीरा / Diamond)

Code

Logic

Pattern 6: Hollow Square (खाली वर्ग)

Code

Pattern 7: Number Triangle (संख्या त्रिभुज)

Code

Pattern 8: Repeated Number Triangle

Code

Pattern 9: Floyd's Triangle (फ्लॉयड का त्रिभुज)

Code

Pattern 10: Pascal's Triangle (पास्कल का त्रिभुज)

Code

Logic (Pascal's Triangle Rule)

Pattern 11: Alphabet Triangle (वर्णमाला त्रिभुज)

Code

Same-Letter Triangle

Pattern 12: Butterfly Pattern (तितली)

Code

Pattern 13: Number Pyramid (संख्या पिरामिड)

Code

Pattern 14: Hollow Diamond (खोखला हीरा)

Code

Pattern 15: Cross / Plus Pattern (क्रॉस / प्लस)

X Pattern

Pattern 16: Spiral Number Pattern (संख्या सर्पिल — Simulated)

Code (Snail/Spiral Fill)

Pattern Summary Table (पैटर्न सारांश तालिका)

Quick Pattern Cheat Sheet (त्वरित संदर्भ)

Common Mistakes in Patterns (सामान्य गलतियाँ)

❌ Mistake 1: Off-by-one in range

❌ Mistake 2: Not using end=""

❌ Mistake 3: Forgetting to print newline

❌ Mistake 4: Wrong space calculation

Practice Exercises (अभ्यास प्रश्न)

Exercise 1 — Easy

Exercise 2 — Easy

Exercise 3 — Medium

Exercise 4 — Medium

Exercise 5 — Hard

Exercise 6 — Hard

Solutions (हल)

Solution 1 — Inverted Right Triangle

Solution 2 — Inverted Number Triangle

Solution 4 — Hollow Triangle

Solution 5 — Hourglass

Interview Tips (Interview की तैयारी)

Final Summary (अंतिम सारांश)

Previous Topic (पिछला विषय)

Next Section (अगला खंड)

📤 Output Examples (Pattern Outputs with Code)

Right Triangle Output

Full Pyramid Output

Diamond Output

Number Triangle Output

Floyd's Triangle Output

Alphabet Triangle Output

✅ Key Takeaways

❓ FAQ

Q1: Pattern programs क्यों important हैं? 🤔

Q2: Outer loop और Inner loop में क्या difference है? 🔄

Q3: end="" और end=" " में क्या अंतर है? 🖨️

Q4: Pyramid pattern में spaces कैसे calculate करें? 📐

Q5: Floyd's Triangle और Pascal's Triangle में क्या difference है? 🔢

Q6: Diamond pattern कैसे बनाएं easily? 💎

Q7: Pattern programs को solve करने का best approach क्या है? 🎯

❌ Mistake 2: Not using `end=""`

Q3: `end=""` और `end=" "` में क्या अंतर है? 🖨️

Q5: Explain the difference between `range(n)`, `range(1, n+1)`, and `range(n, 0, -1)`.

❌ Mistake 2: Not using `end=""`