Posted on by Kalkicode
Code Backtracking

# Split a number into smaller numbers

In this article, we will explore a problem where we need to split a given number into smaller numbers. We'll provide an explanation of the problem, a suitable example, the algorithm and pseudocode to solve it, and an explanation of the resulting output. Let's dive in!

## Problem Statement

The problem is to divide a positive number into a combination of smaller numbers that sum up to the original number. For example, if the input is 5, we need to find all possible combinations of smaller numbers that add up to 5.

## Example

Let's consider the number 5. We want to find all possible combinations of smaller numbers that add up to 5. The expected output should be:

```Split number 5
[1 1 1 1 1]
[1 1 1 2]
[1 1 3]
[1 2 2]
[1 4]
[2 3]
```

Similarly, if we consider the number 6, the expected output should be:

```Split number 6
[1 1 1 1 1 1]
[1 1 1 1 2]
[1 1 1 3]
[1 1 2 2]
[1 1 4]
[1 2 3]
[1 5]
[2 2 2]
[2 4]
[3 3]
```

## Algorithm

To solve this problem, we can use a recursive approach. Here is the algorithm:

1. Create a stack data structure to store the numbers.
2. Create a function to split the number.
3. If the number is 0 and the stack size is greater than 1, display the numbers in the stack as a valid split.
4. Iterate from the current location to the given number.
5. Push the current number onto the stack.
6. Recursively call the split function with the updated number and location.
7. Pop the top element from the stack.
8. Repeat steps 4-7 until all possible combinations are found.

The time complexity of this algorithm depends on the number of valid splits. In the worst case, when the number is n, the time complexity is O(2^n) because there can be 2^n possible splits.

## Pseudocode

Here is the pseudocode for the splitNumber function:

```function splitNumber(num):
if num <= 0:
return

stack = newStack()
print "Split number " + num

split(stack, 1, num)

function split(stack, location, num):
if num == 0 and size(stack) > 1:
print "[" + show(stack.top) + "]"

for i from location to num:
push(stack, i)
split(stack, i, num - i)
pop(stack)
```

## Code Solution

Here given code implementation process.

``````// C program
// Split a number into smaller numbers
#include <stdio.h>

#include <stdlib.h>
// Define stack node
struct StackNode
{
int element;
struct StackNode *next;
};
// Define a custom stack
struct MyStack
{
struct StackNode *top;
int size;
};
struct MyStack *newStack()
{
//Make a stack
struct MyStack *stack = (struct MyStack *) malloc(sizeof(struct MyStack));
if (stack != NULL)
{
//Set node values
stack->top = NULL;
stack->size = 0;
}
else
{
printf("\n Memory overflow when create new stack\n");
}
}
//Create a new node of stack
struct StackNode *newNode(int element, struct StackNode *next)
{
//Make a new node
struct StackNode *node = (struct StackNode *) malloc(sizeof(struct StackNode));
if (node == NULL)
{
printf("\n Memory overflow when create new stack Node \n");
}
else
{
node->element = element;
node->next = next;
}
return node;
}
// Returns the status of empty or non empty stacks
int isEmpty(struct MyStack *stack)
{
if (stack->size > 0 && stack->top != NULL)
{
return 0;
}
else
{
return 1;
}
}
// Add node at the top of stack
void push(struct MyStack *stack, int element)
{
stack->top = newNode(element, stack->top);
stack->size++;
}
int peek(struct MyStack *stack)
{
return stack->top->element;
}
// Remove top element of stack
void pop(struct MyStack *stack)
{
if (isEmpty(stack) == 0)
{
struct StackNode *temp = stack->top;
// Change top element of stack
stack->top = temp->next;
// remove previous top
free(temp);
temp = NULL;
stack->size--;
}
}
int size(struct MyStack *stack)
{
return stack->size;
}
// Display stack elements in reverse order
void show(struct StackNode *top)
{
if (top == NULL)
{
return;
}
// Get top element
int element = top->element;
// next top
show(top->next);
// Display element
printf("  %d", element);
}
// Divide a positive number into a smaller number that is equal to the original number
void split(struct MyStack *stack, int location, int num)
{
if (num == 0 && size(stack) > 1)
{
// Display split
printf(" [");
show(stack->top);
printf("  ]\n");
}
for (int i = location; i <= num; i++)
{
push(stack, i);
split(stack, i, num - i);
// Remove top element of stack
pop(stack);
}
}
// Handles the request to find subset of given number
void splitNumber(int num)
{
if (num <= 0)
{
return;
}
// Define a stack
struct MyStack *stack = newStack();
printf("\n Split number %d \n", num);
split(stack, 1, num);
}
int main()
{
// Test case
splitNumber(5);
splitNumber(6);
return 0;
}``````

#### Output

`````` Split number 5
[  1  1  1  1  1  ]
[  1  1  1  2  ]
[  1  1  3  ]
[  1  2  2  ]
[  1  4  ]
[  2  3  ]

Split number 6
[  1  1  1  1  1  1  ]
[  1  1  1  1  2  ]
[  1  1  1  3  ]
[  1  1  2  2  ]
[  1  1  4  ]
[  1  2  3  ]
[  1  5  ]
[  2  2  2  ]
[  2  4  ]
[  3  3  ]``````
``````/*
Java Program for
Split a number into smaller numbers
*/
// Define stack node
class StackNode
{
public int element;
public StackNode next;
public StackNode(int element, StackNode next)
{
this.element = element;
this.next = next;
}
}
// Define a custom stack
class MyStack
{
public StackNode top;
public int size;
public MyStack()
{
//Set node values
this.top = null;
this.size = 0;
}
// Add node at the top of stack
public void push(int element)
{
this.top = new StackNode(element, this.top);
this.size++;
}
public boolean isEmpty()
{
if (this.size > 0 && this.top != null)
{
return false;
}
else
{
return true;
}
}
// Remove top element of stack
public void pop()
{
if (this.size > 0 && this.top != null)
{
StackNode temp = this.top;
// Change top element of stack
this.top = temp.next;
// remove previous top
temp = null;
this.size--;
}
}
public int peek()
{
return this.top.element;
}
public int size()
{
return this.size;
}
}
public class Partition
{
public MyStack stack;
public Partition()
{
this.stack = new MyStack();
}
// Display stack elements in reverse order
public void show(StackNode node)
{
if (node == null)
{
return;
}
// Get top element
int element = node.element;
// next top
show(node.next);
// Display element
System.out.print("  " + element);
}
public void split(int location, int num)
{
if (num == 0 && this.stack.size() > 1)
{
// Display split
System.out.print(" [");
show(this.stack.top);
System.out.print(" ]\n");
}
for (int i = location; i <= num; i++)
{
this.stack.push(i);
split(i, num - i);
// Remove top element of stack
this.stack.pop();
}
}
// Handles the request to find split Sum
public void splitNumber(int num)
{
if (num <= 0)
{
return;
}
System.out.print("\n Split number " + num + " \n");
split(1, num);
}
public static void main(String[] args)
{
// Test case
}
}``````

#### Output

`````` Split number 5
[  1  1  1  1  1 ]
[  1  1  1  2 ]
[  1  1  3 ]
[  1  2  2 ]
[  1  4 ]
[  2  3 ]

Split number 6
[  1  1  1  1  1  1 ]
[  1  1  1  1  2 ]
[  1  1  1  3 ]
[  1  1  2  2 ]
[  1  1  4 ]
[  1  2  3 ]
[  1  5 ]
[  2  2  2 ]
[  2  4 ]
[  3  3 ]``````
``````// Include header file
#include <iostream>
using namespace std;

/*
C++ Program for
Split a number into smaller numbers
*/
// Define stack node
class StackNode
{
public:
int element;
StackNode *next;
StackNode(int element, StackNode *next)
{
this->element = element;
this->next = next;
}
};
// Define a custom stack
class MyStack
{
public: StackNode *top;
int size;
MyStack()
{
//Set node values
this->top = NULL;
this->size = 0;
}
// Add node at the top of stack
void push(int element)
{
this->top = new StackNode(element, this->top);
this->size++;
}
bool isEmpty()
{
if (this->size > 0 && this->top != NULL)
{
return false;
}
else
{
return true;
}
}
// Remove top element of stack
void pop()
{
if (this->size > 0 && this->top != NULL)
{
StackNode *temp = this->top;
// Change top element of stack
this->top = temp->next;
// remove previous top
temp = NULL;
this->size--;
}
}
int peek()
{
return this->top->element;
}
int getSize()
{
return this->size;
}
};
class Partition
{
public: MyStack *stack;
Partition()
{
this->stack = new MyStack();
}
// Display stack elements in reverse order
void show(StackNode *node)
{
if (node == NULL)
{
return;
}
// Get top element
int element = node->element;
// next top
this->show(node->next);
// Display element
cout << "  " << element;
}
void split(int location, int num)
{
if (num == 0 && this->stack->getSize() > 1)
{
// Display split
cout << " [";
this->show(this->stack->top);
cout << " ]\n";
}
for (int i = location; i <= num; i++)
{
this->stack->push(i);
this->split(i, num - i);
// Remove top element of stack
this->stack->pop();
}
}
// Handles the request to find split Sum
void splitNumber(int num)
{
if (num <= 0)
{
return;
}
cout << "\n Split number " << num << " \n";
this->split(1, num);
}
};
int main()
{
// Test case
return 0;
}``````

#### Output

`````` Split number 5
[  1  1  1  1  1 ]
[  1  1  1  2 ]
[  1  1  3 ]
[  1  2  2 ]
[  1  4 ]
[  2  3 ]

Split number 6
[  1  1  1  1  1  1 ]
[  1  1  1  1  2 ]
[  1  1  1  3 ]
[  1  1  2  2 ]
[  1  1  4 ]
[  1  2  3 ]
[  1  5 ]
[  2  2  2 ]
[  2  4 ]
[  3  3 ]``````
``````// Include namespace system
using System;
/*
C# Program for
Split a number into smaller numbers
*/
// Define stack node
public class StackNode
{
public int element;
public StackNode next;
public StackNode(int element, StackNode next)
{
this.element = element;
this.next = next;
}
}
// Define a custom stack
public class MyStack
{
public StackNode top;
public int size;
public MyStack()
{
//Set node values
this.top = null;
this.size = 0;
}
// Add node at the top of stack
public void push(int element)
{
this.top = new StackNode(element, this.top);
this.size++;
}
public Boolean isEmpty()
{
if (this.size > 0 && this.top != null)
{
return false;
}
else
{
return true;
}
}
// Remove top element of stack
public void pop()
{
if (this.size > 0 && this.top != null)
{
StackNode temp = this.top;
// Change top element of stack
this.top = temp.next;
// remove previous top
temp = null;
this.size--;
}
}
public int peek()
{
return this.top.element;
}
public int getSize()
{
return this.size;
}
}
public class Partition
{
public MyStack stack;
public Partition()
{
this.stack = new MyStack();
}
// Display stack elements in reverse order
public void show(StackNode node)
{
if (node == null)
{
return;
}
// Get top element
int element = node.element;
// next top
show(node.next);
// Display element
Console.Write("  " + element);
}
public void split(int location, int num)
{
if (num == 0 && this.stack.getSize() > 1)
{
// Display split
Console.Write(" [");
show(this.stack.top);
Console.Write(" ]\n");
}
for (int i = location; i <= num; i++)
{
this.stack.push(i);
split(i, num - i);
// Remove top element of stack
this.stack.pop();
}
}
// Handles the request to find split Sum
public void splitNumber(int num)
{
if (num <= 0)
{
return;
}
Console.Write("\n Split number " + num + " \n");
split(1, num);
}
public static void Main(String[] args)
{
// Test case
}
}``````

#### Output

`````` Split number 5
[  1  1  1  1  1 ]
[  1  1  1  2 ]
[  1  1  3 ]
[  1  2  2 ]
[  1  4 ]
[  2  3 ]

Split number 6
[  1  1  1  1  1  1 ]
[  1  1  1  1  2 ]
[  1  1  1  3 ]
[  1  1  2  2 ]
[  1  1  4 ]
[  1  2  3 ]
[  1  5 ]
[  2  2  2 ]
[  2  4 ]
[  3  3 ]``````
``````<?php
/*
Php Program for
Split a number into smaller numbers
*/
// Define stack node
class StackNode
{
public \$element;
public \$next;

function __construct(\$element, \$next)
{
\$this->element = \$element;
\$this->next = \$next;
}
}
// Define a custom stack
class MyStack
{
public \$top;
public \$size;

function __construct()
{
//Set node values
\$this->top = null;
\$this->size = 0;
}
// Add node at the top of stack
public	function push(\$element)
{
\$this->top = new StackNode(\$element, \$this->top);
\$this->size++;
}
public	function isEmpty()
{
if (\$this->size > 0 && \$this->top != null)
{
return false;
}
else
{
return true;
}
}
// Remove top element of stack
public	function pop()
{
if (\$this->size > 0 && \$this->top != null)
{
\$temp = \$this->top;
// Change top element of stack
\$this->top = \$temp->next;
// remove previous top
\$temp = null;
\$this->size--;
}
}
public	function peek()
{
return \$this->top->element;
}
public	function getSize()
{
return \$this->size;
}
}
class Partition
{
public \$stack;

function __construct()
{
\$this->stack = new MyStack();
}
// Display stack elements in reverse order
public	function show(\$node)
{
if (\$node == null)
{
return;
}
// Get top element
\$element = \$node->element;
// next top
\$this->show(\$node->next);
// Display element
echo "  ". \$element;
}
public	function split(\$location, \$num)
{
if (\$num == 0 && \$this->stack->getSize() > 1)
{
// Display split
echo " [";
\$this->show(\$this->stack->top);
echo " ]\n";
}
for (\$i = \$location; \$i <= \$num; \$i++)
{
\$this->stack->push(\$i);
\$this->split(\$i, \$num - \$i);
// Remove top element of stack
\$this->stack->pop();
}
}
// Handles the request to find split Sum
public	function splitNumber(\$num)
{
if (\$num <= 0)
{
return;
}
echo "\n Split number ". \$num ." \n";
\$this->split(1, \$num);
}
}

function main()
{
// Test case
}
main();``````

#### Output

`````` Split number 5
[  1  1  1  1  1 ]
[  1  1  1  2 ]
[  1  1  3 ]
[  1  2  2 ]
[  1  4 ]
[  2  3 ]

Split number 6
[  1  1  1  1  1  1 ]
[  1  1  1  1  2 ]
[  1  1  1  3 ]
[  1  1  2  2 ]
[  1  1  4 ]
[  1  2  3 ]
[  1  5 ]
[  2  2  2 ]
[  2  4 ]
[  3  3 ]``````
``````/*
Node Js Program for
Split a number into smaller numbers
*/
// Define stack node
class StackNode
{
constructor(element, next)
{
this.element = element;
this.next = next;
}
}
// Define a custom stack
class MyStack
{
constructor()
{
//Set node values
this.top = null;
this.size = 0;
}
// Add node at the top of stack
push(element)
{
this.top = new StackNode(element, this.top);
this.size++;
}
isEmpty()
{
if (this.size > 0 && this.top != null)
{
return false;
}
else
{
return true;
}
}
// Remove top element of stack
pop()
{
if (this.size > 0 && this.top != null)
{
var temp = this.top;
// Change top element of stack
this.top = temp.next;
// remove previous top
temp = null;
this.size--;
}
}
peek()
{
return this.top.element;
}
getSize()
{
return this.size;
}
}
class Partition
{
constructor()
{
this.stack = new MyStack();
}
// Display stack elements in reverse order
show(node)
{
if (node == null)
{
return;
}
// Get top element
var element = node.element;
// next top
this.show(node.next);
// Display element
process.stdout.write("  " + element);
}
split(location, num)
{
if (num == 0 && this.stack.getSize() > 1)
{
// Display split
process.stdout.write(" [");
this.show(this.stack.top);
process.stdout.write(" ]\n");
}
for (var i = location; i <= num; i++)
{
this.stack.push(i);
this.split(i, num - i);
// Remove top element of stack
this.stack.pop();
}
}
// Handles the request to find split Sum
splitNumber(num)
{
if (num <= 0)
{
return;
}
process.stdout.write("\n Split number " + num + " \n");
this.split(1, num);
}
}

function main()
{
// Test case
}
main();``````

#### Output

`````` Split number 5
[  1  1  1  1  1 ]
[  1  1  1  2 ]
[  1  1  3 ]
[  1  2  2 ]
[  1  4 ]
[  2  3 ]

Split number 6
[  1  1  1  1  1  1 ]
[  1  1  1  1  2 ]
[  1  1  1  3 ]
[  1  1  2  2 ]
[  1  1  4 ]
[  1  2  3 ]
[  1  5 ]
[  2  2  2 ]
[  2  4 ]
[  3  3 ]``````
``````#  Python 3 Program for
#  Split a number into smaller numbers

#  Define stack node
class StackNode :

def __init__(self, element, next) :
self.element = element
self.next = next

#  Define a custom stack
class MyStack :

def __init__(self) :
# Set node values
self.top = None
self.size = 0

#  Add node at the top of stack
def push(self, element) :
self.top = StackNode(element, self.top)
self.size += 1

def isEmpty(self) :
if (self.size > 0 and self.top != None) :
return False
else :
return True

#  Remove top element of stack
def pop(self) :
if (self.size > 0 and self.top != None) :
temp = self.top
#  Change top element of stack
self.top = temp.next
#  remove previous top
temp = None
self.size -= 1

def peek(self) :
return self.top.element

def getSize(self) :
return self.size

class Partition :

def __init__(self) :
self.stack = MyStack()

#  Display stack elements in reverse order
def show(self, node) :
if (node == None) :
return

#  Get top element
element = node.element
#  next top
self.show(node.next)
#  Display element
print(element, end = " ")

def split(self, location, num) :
if (num == 0 and self.stack.getSize() > 1) :
#  Display split
print(end = " [ ")
self.show(self.stack.top)
print("]")

i = location
while (i <= num) :
self.stack.push(i)
self.split(i, num - i)
#  Remove top element of stack
self.stack.pop()
i += 1

#  Handles the request to find split Sum
def splitNumber(self, num) :
if (num <= 0) :
return

print("\n Split number ", num ," ")
self.split(1, num)

def main() :
#  Test case

if __name__ == "__main__": main()``````

#### Output

`````` Split number  5
[ 1 1 1 1 1 ]
[ 1 1 1 2 ]
[ 1 1 3 ]
[ 1 2 2 ]
[ 1 4 ]
[ 2 3 ]

Split number  6
[ 1 1 1 1 1 1 ]
[ 1 1 1 1 2 ]
[ 1 1 1 3 ]
[ 1 1 2 2 ]
[ 1 1 4 ]
[ 1 2 3 ]
[ 1 5 ]
[ 2 2 2 ]
[ 2 4 ]
[ 3 3 ]``````
``````#  Ruby Program for
#  Split a number into smaller numbers

#  Define stack node
class StackNode
# Define the accessor and reader of class StackNode
attr_accessor :element, :next

def initialize(element, top)
self.element = element
self.next = top
end

end

#  Define a custom stack
class MyStack
# Define the accessor and reader of class MyStack
attr_accessor :top, :size

def initialize()
# Set node values
self.top = nil
self.size = 0
end

#  Add node at the top of stack
def push(element)
self.top = StackNode.new(element, self.top)
self.size += 1
end

def isEmpty()
if (self.size > 0 && self.top != nil)
return false
else
return true
end

end

#  Remove top element of stack
def pop()
if (self.size > 0 && self.top != nil)
temp = self.top
#  Change top element of stack
self.top = temp.next
#  remove previous top
temp = nil
self.size -= 1
end

end

def peek()
return self.top.element
end

def getSize()
return self.size
end

end

class Partition
# Define the accessor and reader of class Partition
attr_accessor :stack

def initialize()
self.stack = MyStack.new()
end

#  Display stack elements in reverse order
def show(node)
if (node == nil)
return
end

#  Get top element
element = node.element
#  next top
self.show(node.next)
#  Display element
print("  ", element)
end

def split(location, num)
if (num == 0 && self.stack.getSize() > 1)
#  Display split
print(" [")
self.show(self.stack.top)
print(" ]\n")
end

i = location
while (i <= num)
self.stack.push(i)
self.split(i, num - i)
#  Remove top element of stack
self.stack.pop()
i += 1
end

end

#  Handles the request to find split Sum
def splitNumber(num)
if (num <= 0)
return
end

print("\n Split number ", num ," \n")
self.split(1, num)
end

end

def main()
#  Test case
end

main()``````

#### Output

`````` Split number 5
[  1  1  1  1  1 ]
[  1  1  1  2 ]
[  1  1  3 ]
[  1  2  2 ]
[  1  4 ]
[  2  3 ]

Split number 6
[  1  1  1  1  1  1 ]
[  1  1  1  1  2 ]
[  1  1  1  3 ]
[  1  1  2  2 ]
[  1  1  4 ]
[  1  2  3 ]
[  1  5 ]
[  2  2  2 ]
[  2  4 ]
[  3  3 ]
``````
``````/*
Scala Program for
Split a number into smaller numbers
*/
// Define stack node
class StackNode(var element: Int , var next: StackNode);
// Define a custom stack
class MyStack(var top: StackNode , var size: Int)
{
def this()
{
this(null, 0);
}
// Add node at the top of stack
def push(element: Int): Unit = {
this.top = new StackNode(element, this.top);
this.size += 1;
}
def isEmpty(): Boolean = {
if (this.size > 0 && this.top != null)
{
return false;
}
else
{
return true;
}
}
// Remove top element of stack
def pop(): Unit = {
if (this.size > 0 && this.top != null)
{
var temp: StackNode = this.top;
// Change top element of stack
this.top = temp.next;
// remove previous top
temp = null;
this.size -= 1;
}
}
def peek(): Int = {
return this.top.element;
}
def getSize(): Int = {
return this.size;
}
}
class Partition(var stack: MyStack)
{
def this()
{
this(new MyStack());
}
// Display stack elements in reverse order
def show(node: StackNode): Unit = {
if (node == null)
{
return;
}
// Get top element
var element: Int = node.element;
// next top
this.show(node.next);
// Display element
print("  " + element);
}
def split(location: Int, num: Int): Unit = {
if (num == 0 && this.stack.getSize() > 1)
{
// Display split
print(" [");
this.show(this.stack.top);
print(" ]\n");
}
var i: Int = location;
while (i <= num)
{
this.stack.push(i);
this.split(i, num - i);
// Remove top element of stack
this.stack.pop();
i += 1;
}
}
// Handles the request to find split Sum
def splitNumber(num: Int): Unit = {
if (num <= 0)
{
return;
}
print("\n Split number " + num + " \n");
this.split(1, num);
}
}
object Main
{
def main(args: Array[String]): Unit = {
var task: Partition = new Partition();
// Test case
}
}``````

#### Output

`````` Split number 5
[  1  1  1  1  1 ]
[  1  1  1  2 ]
[  1  1  3 ]
[  1  2  2 ]
[  1  4 ]
[  2  3 ]

Split number 6
[  1  1  1  1  1  1 ]
[  1  1  1  1  2 ]
[  1  1  1  3 ]
[  1  1  2  2 ]
[  1  1  4 ]
[  1  2  3 ]
[  1  5 ]
[  2  2  2 ]
[  2  4 ]
[  3  3 ]``````
``````/*
Swift 4 Program for
Split a number into smaller numbers
*/
// Define stack node
class StackNode
{
var element: Int;
var next: StackNode? ;
init(_ element: Int, _ next: StackNode? )
{
self.element = element;
self.next = next;
}
}
// Define a custom stack
class MyStack
{
var top: StackNode? ;
var size: Int;
init()
{
//Set node values
self.top = nil;
self.size = 0;
}
// Add node at the top of stack
func push(_ element: Int)
{
self.top = StackNode(element, self.top);
self.size += 1;
}
func isEmpty()->Bool
{
if (self.size > 0 && self.top  != nil)
{
return false;
}
else
{
return true;
}
}
// Remove top element of stack
func pop()
{
if (self.size > 0 && self.top  != nil)
{
var temp: StackNode? = self.top;
// Change top element of stack
self.top = temp!.next;
// remove previous top
temp = nil;
self.size -= 1;
}
}
func peek()->Int
{
return self.top!.element;
}
func getSize()->Int
{
return self.size;
}
}
class Partition
{
var stack: MyStack ;
init()
{
self.stack = MyStack();
}
// Display stack elements in reverse order
func show(_ node: StackNode? )
{
if (node == nil)
{
return;
}
// Get top element
let element: Int = node!.element;
// next top
self.show(node!.next);
// Display element
print("", element, terminator: " ");
}
func split(_ location: Int, _ num: Int)
{
if (num == 0 && self.stack.getSize() > 1)
{
// Display split
print(" [ ", terminator: "");
self.show(self.stack.top);
print(" ]");
}
var i: Int = location;
while (i <= num)
{
self.stack.push(i);
self.split(i, num - i);
// Remove top element of stack
self.stack.pop();
i += 1;
}
}
// Handles the request to find split Sum
func splitNumber(_ num: Int)
{
if (num <= 0)
{
return;
}
print("\n Split number ", num ," ");
self.split(1, num);
}
}
func main()
{
// Test case
}
main();``````

#### Output

`````` Split number  5
[  1  1  1  1  1  ]
[  1  1  1  2  ]
[  1  1  3  ]
[  1  2  2  ]
[  1  4  ]
[  2  3  ]

Split number  6
[  1  1  1  1  1  1  ]
[  1  1  1  1  2  ]
[  1  1  1  3  ]
[  1  1  2  2  ]
[  1  1  4  ]
[  1  2  3  ]
[  1  5  ]
[  2  2  2  ]
[  2  4  ]
[  3  3  ]``````
``````/*
Kotlin Program for
Split a number into smaller numbers
*/
// Define stack node
class StackNode
{
var element: Int;
var next: StackNode ? ;
constructor(element: Int, next: StackNode ? )
{
this.element = element;
this.next = next;
}
}
// Define a custom stack
class MyStack
{
var top: StackNode ? ;
var size: Int;
constructor()
{
//Set node values
this.top = null;
this.size = 0;
}
// Add node at the top of stack
fun push(element: Int): Unit
{
this.top = StackNode(element, this.top);
this.size += 1;
}
fun isEmpty(): Boolean
{
if (this.size > 0 && this.top != null)
{
return false;
}
else
{
return true;
}
}
// Remove top element of stack
fun pop(): Unit
{
if (this.size > 0 && this.top != null)
{
var temp: StackNode ? = this.top;
// Change top element of stack
this.top = temp?.next;
this.size -= 1;
}
}
fun peek(): Int
{
return this.top!!.element;
}
fun size(): Int
{
return this.size;
}
}
class Partition
{
var stack: MyStack;
constructor()
{
this.stack = MyStack();
}
// Display stack elements in reverse order
fun show(node: StackNode ? ): Unit
{
if (node == null)
{
return;
}
// Get top element
var element: Int = node.element;
// next top
this.show(node.next);
// Display element
print("  " + element);
}
fun split(location: Int, num: Int): Unit
{
if (num == 0 && this.stack.size() > 1)
{
// Display split
print(" [");
this.show(this.stack.top);
print(" ]\n");
}
var i: Int = location;
while (i <= num)
{
this.stack.push(i);
this.split(i, num - i);
// Remove top element of stack
this.stack.pop();
i += 1;
}
}
// Handles the request to find split Sum
fun splitNumber(num: Int): Unit
{
if (num <= 0)
{
return;
}
print("\n Split number " + num + " \n");
this.split(1, num);
}
}
fun main(args: Array < String > ): Unit
{
// Test case
}``````

#### Output

`````` Split number 5
[  1  1  1  1  1 ]
[  1  1  1  2 ]
[  1  1  3 ]
[  1  2  2 ]
[  1  4 ]
[  2  3 ]

Split number 6
[  1  1  1  1  1  1 ]
[  1  1  1  1  2 ]
[  1  1  1  3 ]
[  1  1  2  2 ]
[  1  1  4 ]
[  1  2  3 ]
[  1  5 ]
[  2  2  2 ]
[  2  4 ]
[  3  3 ]``````

## Resultant Output Explanation

The resultant output shows all the valid splits for the given numbers. Each line represents a valid split, where the numbers in brackets represent the combination of smaller numbers that add up to the original number.

For example, in the output for number 5, the line [1 1 1 1 1] means that the number 5 can be split into five 1s. Similarly, [1 4] represents a split where the number 5 is divided into 1 and 4.

The output for number 6 follows the same pattern, showing all possible combinations of smaller numbers that add up to 6.

## Finally

In this article, we explored the problem of splitting a number into smaller numbers. We provided a detailed explanation of the problem, a suitable example, the algorithm, and pseudocode to solve it. We also explained the resultant output and discussed the time complexity of the code.

By using the recursive approach and the stack data structure, we can find all possible combinations of smaller numbers that sum up to the given number. This problem can be useful in various scenarios, such as partitioning resources or solving optimization problems.

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