Memory is an optimization technology to improve function performance. Before we start with the memorization technique, let's use the following example to understand why we need it.
Example (Easy way to find Fibonacci numbers)
In the example below, we implement a simple method to find the nth Fibonacci number. We use a recursive method to find the nth Fibonacci number.
<html>
<body>
<h3>Finding the nth Fibonacci using recursive approach number in JavaScript</h3>
<p>Enter the number to find the nth Fibonacci number.</p>
<input type = "number" id = "fib"> <br>
<div id = "content"> </div> <br>
<button onclick = "executeFunc()"> Submit </button>
<script>
let content = document.getElementById('content');
// function to write the fibonacci series
function findFib(n) {
if (n <= 1) return n;
return findFib(n - 1) + findFib(n - 2);
}
function executeFunc() {
let n = document.getElementById('fib').value;
content.innerHTML = "The " + n + "th fibonacci number is " + findFib(n);
}
</script>
</body>
</html>
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The above example works well for small input values less than 1000, but when we enter input values in the range 104, it takes more time than usual, and for the range 10 The input of 6 caused the browser to crash due to memory out of bounds.
We can optimize the above code using memory technology, which allows us to store the results of previous calculations. For example, to find the 4th Fibonacci number, we need to find the 3rd and 2nd Fibonacci numbers. Likewise, to find the third Fibonacci number, we must find the second and first Fibonacci numbers. So here we calculate the second Fibonacci number twice.
Now, assuming you want to find the nth largest value of the Fibonacci sequence, you can think about how many times it needs to be repeated. So for optimization purposes we can calculate the second Fibonacci number for the first time and store it in a temporary variable. Later, when we need to calculate the second Fibonacci number again, we can access it from the array, making the code more efficient.
Additionally, storing previously calculated results in an array for later use is also memoization.
grammar
Users can follow the following syntax to memorize the nth Fibonacci number.
if (temp[n]) return temp[n];
if (n <= 1) return n;
return temp[n] = findFib(n - 1, temp) + findFib(n - 2, temp);
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In the above syntax, we first check whether the nth Fibonacci number already exists in the 'temp' object, and then return the value; otherwise, we calculate its value and add the ore to the temporary object.
method
Step 1 – Use an if statement to check whether the result of n exists in the temporary object. If so, the previously calculated value is returned.
Step 2 – If n is less than or equal to 1, return 1 as the base case for the recursive function.
Step 3 – Calculate n-1 and n-2 Fibonacci numbers, add them and store them in a temporary object for later use.
Step 4 – Store the nth Fibonacci number and return it to the temporary object.
Example (using memory to find the nth Fibonacci number)
Using memoization techniques, we optimized the code for the first example in the examples below. We use the temp object to store the results of previous calculations. In the output, the user can observe that the code below is more efficient than the code in the first example.
<html>
<body>
<h3>Finding the nth Fibonacci number using memoization using extra space in JavaScript</h3>
<p>Enter the number to find the nth Fibonacci number.</p>
<input type = "number" id = "fib"> <br>
<div id = "content"> </div> <br>
<button onclick = "start()"> Submit </button>
<script>
let content = document.getElementById('content');
function findFib(n, temp) {
if (temp[n]) return temp[n];
if (n <= 1) return n;
return temp[n] = findFib(n - 1, temp) + findFib(n - 2, temp);
}
function start() {
let n = document.getElementById('fib').value;
content.innerHTML = "The " + n + "th fibonacci number using memoization is " + findFib(n, {}) + "<br>";
}
</script>
</body>
</html>
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Method: Use memory without using extra space
Step 1 – Initialize a to 0 and b to 1.
Step 2 – Use a for loop for n iterations to find the nth Fibonacci number.
Step 3 – Here, c is a temporary variable that stores the (i-1)th Fibonacci number.
Step 4 – Store the value of b variable in a.
Step 5 – Store the value of variable c in variable b.
Example
The following example is also an optimized variant of the first example. In the second example, we used a temp object to store the results of the previous calculation, but in the code below, we use a single temporary variable named c.
The code below is the most efficient way to find the Fibonacci sequence because its time complexity is O(n) and space complexity is O(1).
<html>
<body>
<h3>Finding the nth Fibonacci number using memoization in JavaScript</h3>
<p>Enter the number to find the nth Fibonacci number:</p>
<input type = "number" id = "fib"> <br>
<div id = "content"> </div> <br>
<button onclick = "findFib()"> Submit </button>
<script>
let content = document.getElementById('content');
// function to write the fibonacci series
function findFib() {
let n = document.getElementById('fib').value;
let a = 0, b = 1, c;
if (n == 0) {
return a;
}
for (let i = 2; i <= n; i++) {
c = a + b;
a = b;
b = c;
}
content.innerHTML += "The " + n + "th Fibonacci number using memoization is " + b;
}
</script>
</body>
</html>
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In this tutorial, we learned about memory techniques for optimizing code to make it more time- and space-saving. You can see how we optimized the code of the first example using different algorithms in the second and third examples.
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