A loop can be nested inside of another loop. C++ allows at least 256 levels of nesting. When a loop is created inside another loop, forming multiple levels of loops then it is said to be a nested loop. Where the inner loop executes completely for each iteration of the outer loop. These are mainly useful for multi-dimensional data structures like matrices or grids, or to solve problems requiring repeated nested iterations.
Nested for LoopsWhen a for loop is nested inside another for loop is known to be a nested for loop. This is the most common form used for nesting.
SyntaxThe syntax for a nested for loop statement in C++ is as follows −
for ( init; condition; increment ) {
for ( init; condition; increment ) {
statement(s);
}
statement(s); // you can put more statements.
}
Example
#include <iostream>
using namespace std;
int main() {
for (int i = 1; i <= 3; i++) { // Outer loop
for (int j = 1; j <= 2; j++) { // Inner loop
cout << "Outer: " << i << ", Inner: " << j << endl;
}
}
return 0;
}
This would produce the following result −
Outer: 1, Inner: 1 Outer: 1, Inner: 2 Outer: 2, Inner: 1 Outer: 2, Inner: 2 Outer: 3, Inner: 1 Outer: 3, Inner: 2Nested while Loops
When a while loop is nested inside another while loop then its said to be nested while loop. This is mainly used when needed to determine the number of iterations dynamically.
SyntaxThe syntax for a nested while loop statement in C++ is as follows −
while(condition) {
while(condition) {
statement(s);
}
statement(s); // you can put more statements.
}
Example
#include <iostream>
using namespace std;
int main() {
int i = 1;
while (i <= 3) {
int j = 1;
while (j <= 2) {
cout << "Outer: " << i << ", Inner: " << j << endl;
j++;
}
i++;
}
return 0;
}
This would produce the following result −
Outer: 1, Inner: 1 Outer: 1, Inner: 2 Outer: 2, Inner: 1 Outer: 2, Inner: 2 Outer: 3, Inner: 1 Outer: 3, Inner: 2Nested do-while Loops
When a do-while loop is nested inside another do-while loop then its said to be a nested do-while loop. This ensures the loop is executed at least once before checking the condition.
SyntaxThe syntax for a nested do...while loop statement in C++ is as follows −
do {
statement(s); // you can put more statements.
do {
statement(s);
} while( condition );
} while( condition );
Example
#include <iostream>
using namespace std;
int main() {
int i = 1;
do {
int j = 1;
do {
cout << "Outer: " << i << ", Inner: " << j << endl;
j++;
} while (j <= 2);
i++;
} while (i <= 3);
return 0;
}
This would produce the following result −
Outer: 1, Inner: 1 Outer: 1, Inner: 2 Outer: 2, Inner: 1 Outer: 2, Inner: 2 Outer: 3, Inner: 1 Outer: 3, Inner: 2Nested Loops Example
The following program uses a nested for loop to find the prime numbers from 2 to 100 −
#include <iostream>
using namespace std;
int main () {
int i, j;
for(i = 2; i<100; i++) {
for(j = 2; j <= (i/j); j++)
if(!(i%j)) break; // if factor found, not prime
if(j > (i/j)) cout << i << " is prime\n";
}
return 0;
}
This would produce the following result −
2 is prime 3 is prime 5 is prime 7 is prime 11 is prime 13 is prime 17 is prime 19 is prime 23 is prime 29 is prime 31 is prime 37 is prime 41 is prime 43 is prime 47 is prime 53 is prime 59 is prime 61 is prime 67 is prime 71 is prime 73 is prime 79 is prime 83 is prime 89 is prime 97 is primeHow Nested Loops Affect Computational Complexity
Nested loops directly impact the computational complexity of a program because they increase the number of operations performed as the nesting depth increases.
If the Outer loop executes n times and the inner loop executes m times for each iteration of the outer loop, then the total iterations equals n*m, So time complexity equals O(mn), and if both loops have a similar range nm, then the complexity is approximately O(n^k), where k is the depth of nesting.
Example (O(n^2)) multi-dimensional arrays like matrix and pairs, (O(n^3)) triplets, (O(n^4)) etc.
As the nested loop is an important concept while dealing with a few problems, optimizing it will further improve the performance of your algorithms, especially when dealing with large data sets.
Nested loops often lead to exponential time complexities(e.g., O(n), O(n)), so optimizing it will make differences in execution time. Below are a few techniques to optimize it.
The more loops you have, the slower the program becomes. So try to avoid any unnecessary nesting, sometimes rearranging the loops or changing its order can reduce the need for nested loops.
2. Use efficient data structuresDepending on the problem, you can use heaps, queues, and stacks to optimize access patterns. use hash sets or hash maps, which allows for constant time complexity for insertions and deletions. This is often used for a large array or list to avoid complex iteration over it.
3. Break Early (Exit Conditions)You can break out the loop early if needed or can continue to reduce unnecessary work.
4. Use Divide and Conquer or Dynamic ProgrammingDivide and conquer algorithms help in reducing nesting by breaking the problem into smaller subproblems, which are further solved independently and combined later. By dynamic programming, you can transform an exponential time complexity problem into a polynomial one.
5. ParallelizationYou can use multithreading or multiprocessing if your nested loops are independent and can be computed parallel, this can speed up your program.
6. Applying Mathematical Optimizations and Built-in Functions or LibrariesMathematical optimizations can help in reducing the need for nested loops for some problems.
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