Javascript program to swap two numbers without using temporary variable

To swap two numbers without using a temporary variable, we have multiple approaches. In this article, we are going to learn how to swap two numbers without using a temporary variable.

Below are the approaches used to swap two numbers without using a temporary variable:

Method 1: Using Arithmetic Operators

Example 1: The idea is to get a sum in one of the two given numbers. The numbers can then be swapped using the sum and subtraction from the sum.

    // Javascript program to swap two
    // numbers without using temporary
    // variable

    let x = 10, y = 5;
    console.log("Before Swapping: x = " + 
        x + ", y = " + y);

    // Code to swap 'x' and 'y'

    // x now becomes 15
    x = x + y;

    // y becomes 10
    y = x - y;

    // x becomes 5
    x = x - y;

    console.log("After Swapping: x = " + 
        x + ", y = " + y);

Before Swapping: x = 10, y = 5
After Swapping: x = 5, y = 10

Time Complexity: O(1)
Auxiliary Space: O(1)

Example 2: Multiplication and division can also be used for swapping.

    // Javascript program to swap two numbers
    // without using a temporary variable
    let x = 10;
    let y = 5;

    console.log("Before swapping:" + " x = " + 
        x + ", y = " + y);

    // Code to swap 'x' and 'y'
    x = x * y; // x now becomes 50
    y = x / y; // y becomes 10
    x = x / y; // x becomes 5

    console.log("After swapping:" + " x = " + 
        x + ", y = " + y);

Before swapping: x = 10, y = 5
After swapping: x = 5, y = 10

Time Complexity: O(1)
Auxiliary Space: O(1)

Method 2: Using Bitwise XOR

The bitwise XOR operator can be used to swap two variables. The XOR of two numbers x and y returns a number that has all the bits as 1 wherever bits of x and y differ. For example, XOR of 10 (In Binary 1010) and 5 (In Binary 0101) is 1111, and XOR of 7 (0111) and 5 (0101) is (0010). 

Example: Below is the example that will illustrate the swap two numbers using Bitwise XOR Method:

// Javascript code to swap using XOR

    let x = 10, y = 5;
    console.log("Before Swapping: x =" +
        x + ", y=" + y);

    // Code to swap 'x' (1010) and 'y' (0101)
    x = x ^ y; // x now becomes 15 (1111)
    y = x ^ y; // y becomes 10 (1010)
    x = x ^ y; // x becomes 5 (0101)

    console.log("After Swapping: x =" +
        x + ", y=" + y);

Before Swapping: x =10, y=5
After Swapping: x =5, y=10

Time Complexity: O(1).
Auxiliary Space: O(1).

Problems with the above methods:

1: The multiplication and division-based approach doesn't work if one of the numbers is 0 as the product becomes 0 irrespective of the other number.
2: Both Arithmetic solutions may cause an arithmetic overflow. If x and y are too large, addition and multiplication may go out of the integer range.
3: When we use pointers to variable and make a function swap, all the above methods fail when both pointers point to the same variable. Let's take a look at what will happen in this case if both are pointing to the same variable.

// Bitwise XOR based method
x = x ^ x; // x becomes 0
x = x ^ x; // x remains 0
x = x ^ x; // x remains 0
// Arithmetic based method
x = x + x; // x becomes 2x
x = x - x; // x becomes 0
x = x - x; // x remains 0

Example 1: Let us see the following program:

function swap(xp, yp) {
        xp[0] = xp[0] ^ yp[0];
        yp[0] = xp[0] ^ yp[0];
        xp[0] = xp[0] ^ yp[0];
    }

    // Driver code

    let x = [10];
    console.log("Before swap(&x, &x): x = "
        + x[0]);

    // Calling Swap Function
    swap(x, x);
    console.log("After swap(&x, &x): x = "
        + x[0]);

Before swap(&x, &x): x = 10
After swap(&x, &x): x = 0

Time Complexity: O(1).
Auxiliary Space: O(1).

Example 2: Swapping a variable with itself may be needed in many standard algorithms. For example, see this implementation of QuickSort where we may swap a variable with itself. The above problem can be avoided by putting a condition before swapping.

function swap(xp, yp) {

        // Check if the two addresses are the same
        if (xp == yp)
            return;
        xp[0] = xp[0] + yp[0];
        yp[0] = xp[0] - yp[0];
        xp[0] = xp[0] - yp[0];
    }

    // Driver Code
    x = 10;
    console.log("Before swap(&x , &x) : x = " + x);

    // Calling swap function
    swap(x, x);
    console.log("After swap(&x , &x) : x = " + x);

Before swap(&x , &x) : x = 10
After swap(&x , &x) : x = 10

Time Complexity: O(1)
Auxiliary Space: O(1)

Method 3: A mixture of bitwise operators and arithmetic operators

The idea is the same as discussed in Method 1 but uses Bitwise addition and subtraction for swapping.

Example: Below is the implementation of the above approach. 

function swap(a, b) {
        // same as a = a + b
        a = (a & b) + (a | b);

        // same as b = a - b
        b = a + (~b) + 1;

        // same as a = a - b
        a = a + (~b) + 1;

        console.log("After swapping: a = " + 
            a + ", b = " + b);
    }

    let a = 5, b = 10;

    console.log("Before swapping: a = " + 
        a + ", b = " + b);

    // Function Call
    swap(a, b);

Before swapping: a = 5, b = 10
After swapping: a = 10, b = 5

Time Complexity: O(1).
Auxiliary Space: O(1), since no extra space has been taken.

Method 4: One Line Expression

We can write only one line to swap two numbers.

• x = x ^ y ^ (y = x);
• x = x + y – (y = x);
• x = (x * y) / (y = x);
• x , y = y, x (In Python)

Example: Below is the implementation of the above approach. 

// Javascript program to swap two
    // numbers without using temporary
    // variable
    
    let x = 10, y = 5;

    console.log("Before Swapping: x = " + x + ", y = " + y);

    // Code to swap 'x' and 'y'
    x = (x * y)/(y = x);
    
    console.log("After Swapping: x = " + x + ", y = " + y);

Before Swapping: x = 10, y = 5
After Swapping: x = 5, y = 10

Time Complexity: O(1)
Auxiliary Space: O(1)