Lab 6 – Active Control Structures: Nested Loops

PSUC Lab 6 — Multidimensional Iterations

Active Logic: Nested Loops (Outer & Inner)

Master 2D loop mechanics for pattern generation (Floyd's triangle, pyramids), multiplication table matrices, bounded Fibonacci ranges, and N-th Prime/Armstrong search.

Nested Loop Rules

Concept	Outer Loop (i)	Inner Loop (j)
Role	Controls Rows / Steps	Controls Columns / Print per Row
Execution Count	Runs `N` times	Runs `N * M` total times!
Reset Behavior	Increments once per row	Re-initializes completely every outer iteration!

🎯 Learning Philosophy: Active Logic Building

Test your nested loop logic across 3 Interactive Learning Modes:

🧠 Tab 1 (Logic & Hints): Row-column mapping & loop invariants.
🧩 Tab 2 (Logic Puzzle): Fill in missing outer/inner loop bounds & live pattern previewers!
💻 Tab 3 (C Solution): Reference verified C code solutions.

Complete pattern puzzles before peeking at C source code!

Exercise 1 of 5

Pattern Printing (Floyd's Triangle & Pyramids)

Pattern 1: Floyd's Triangle (1 to 15 sequence) | Pattern 2: Number Repeat Pyramid.

Pattern Bounds

Outer loop i = 1 to 5: controls row number
Inner loop j = 1 to i: controls number of items printed in row i
Floyd's Triangle uses persistent counter num++

Interactive Logic Hints

💡 Hint 1: Why does inner loop run j <= i? ▼

Because row 1 needs 1 item, row 2 needs 2 items, row 3 needs 3 items... so inner loop limit is j <= i!

🧩 Complete Nested Pattern Loops

int num = 1;
for (i = 1; i <= 5; i++) {
  for (j = 1; j ; j++) {
    printf("%d ", num++);
  }
  printf("\n");
}

Select inner loop bound above and click Check!

🎨 Live Pattern Generator

Pattern Type:

Rows (1-8):

Pattern output...

pattern_floyd.cReference C Code

#include <stdio.h>

int main() {
    int i, j, num = 1;
    for (i = 1; i <= 5; i++) {
        for (j = 1; j <= i; j++) {
            printf("%d ", num++);
        }
        printf("\n");
    }
    return 0;
}

Exercise 2 of 5

Multiplication Tables Matrix (N Numbers up to K Terms)

Generates multiplication tables for numbers 1 to N up to K terms using nested loops.

Matrix Table Logic

Outer loop i = 1 to N: table number
Inner loop j = 1 to K: multiplier term
Cell value: i * j

Interactive Logic Hints

💡 Hint 1: How does matrix formatting work? ▼

Use printf("%4d", i * j) to format numbers cleanly into aligned columns!

🧩 Complete Multiplication Table Loops

for (i = 1; i <= n; i++) {
  for (j = 1; j <= k; j++) {
    printf("%d\t", i j);
  }
  printf("\n");
}

Select operator above and click Check!

✖️ Multiplication Matrix Generator

Tables N (1-5):

Terms K (1-10):

Matrix output...

mult_table.cReference C Code

#include <stdio.h>

int main() {
    int n = 3, k = 5, i, j;
    for (i = 1; i <= n; i++) {
        printf("Table of %d: ", i);
        for (j = 1; j <= k; j++) {
            printf("%d ", i * j);
        }
        printf("\n");
    }
    return 0;
}

Exercise 3 of 5

Fibonacci Numbers in Range [Min, Max]

Generates Fibonacci series numbers F_n = F_n-1 + F_n-2 and prints only those falling within [Min, Max].

Fibonacci Update Rule

Initial: a = 0, b = 1, c = a + b
Shift: a = b; b = c; c = a + b;
Filter: Print c only if c >= min && c <= max

Interactive Logic Hints

💡 Hint 1: When should loop stop? ▼

Stop loop when next Fibonacci term c > max!

🧩 Complete Fibonacci Range Loop

int a = 0, b = 1, c = a + b;
while (c max) {
  if (c >= min) printf("%d ", c);
  a = b;
  b = ;
  c = a b;
}

Select statements above and click Check!

🌀 Fibonacci Range Generator

Min Limit:

Max Limit:

Fibonacci range...

fibo_range.cReference C Code

#include <stdio.h>

int main() {
    int min = 10, max = 100;
    int a = 0, b = 1, c = a + b;
    printf("Fibonacci in [%d, %d]: ", min, max);
    while (c <= max) {
        if (c >= min) printf("%d ", c);
        a = b; b = c; c = a + b;
    }
    printf("\n");
    return 0;
}

Exercise 4 of 5

Find the N-th Prime Number

Uses nested loops to search numbers starting from 2, testing each for primality until the N-th prime is discovered.

Search Loop Logic

Outer loop: test candidates num = 2, 3, 4...
Inner loop: test prime divisors i = 2 to num/2
If prime, count++. When count == N, stop!

Interactive Logic Hints

💡 Hint 1: What is the 10th Prime Number? ▼

The 10th prime number is 29! (2, 3, 5, 7, 11, 13, 17, 19, 23, 29).

🧩 Complete N-th Prime Search Loop

int count = 0, num = 2;
while (count N) {
  bool isPrime = true;
  for (i = 2; i <= num / 2; i++) {
    if (num % i == 0) { isPrime = false; break; }
  }
  if (isPrime) ;
  if (count < N) num++;
}

Select statements above and click Check!

🔢 N-th Prime Discovery Generator

Find N-th Prime (N = 1 to 50):

Prime output...

nth_prime.cReference C Code

#include <stdio.h>
#include <stdbool.h>

int main() {
    int targetN = 10, count = 0, num = 2, i;
    while (count < targetN) {
        bool isPrime = true;
        for (i = 2; i <= num / 2; i++) {
            if (num % i == 0) { isPrime = false; break; }
        }
        if (isPrime) count++;
        if (count < targetN) num++;
    }
    printf("The %d-th Prime Number is %d\n", targetN, num);
    return 0;
}

Exercise 5 of 5

Find the N-th Armstrong Number

Uses nested loops to search numbers starting from 1, checking power sums for each until the N-th Armstrong number is found.

Armstrong Sequence

Single digits (1-9) are Armstrong numbers (d¹ = d).
10th Armstrong number = 153 (1³ + 5³ + 3³ = 153).
11th Armstrong number = 370 (3³ + 7³ + 0³ = 370).

Interactive Logic Hints

💡 Hint 1: How many Armstrong numbers exist? ▼

There are only 88 Armstrong numbers in base 10! The largest has 39 digits!

🧩 Complete N-th Armstrong Search Loop

while (count < targetN) {
  int d = countDigits(num);
  if (sumPowerDigits(num, d) num) {
    count++;
  }
  if (count < targetN) num++;
}

Select comparison operator above and click Check!

✨ N-th Armstrong Discovery Generator

Find N-th Armstrong (N = 1 to 15):

Armstrong output...

nth_armstrong.cReference C Code

#include <stdio.h>
#include <math.h>

int main() {
    int targetN = 10, count = 0, num = 1, temp, d, sum, rem;
    while (count < targetN) {
        d = 0; temp = num;
        while (temp > 0) { d++; temp /= 10; }
        
        sum = 0; temp = num;
        while (temp > 0) {
            rem = temp % 10;
            sum += pow(rem, d);
            temp /= 10;
        }
        if (sum == num) count++;
        if (count < targetN) num++;
    }
    printf("The %d-th Armstrong Number is %d\n", targetN, num);
    return 0;
}

Knowledge Check

Test Your Nested Loops Mastery

Question 1 of 5

Loading question...