Break the problem into smaller and simpler problems.
Solve the smaller and simpler problems obtained in the step above.
As we solve these smaller and simpler problems, we store the solutions obtained in the memory so that we can reuse them later while solving bigger and more complex problems.
Solve the bigger and more complex problems using the previously obtained solution from the memory.
Let’s see this approach in action using the example of the Fibonacci series.
Given an integer n
, print the first n
integers of the Fibonacci series.
Before looking into my solution below, please try to solve this by yourself.
Here we solve the problem for smaller numbers first and store them in an array. Later, we will use these values to calculate larger values from the Fibonacci series.
Below is the code:
import java.util.*; class Main { // array to store fibonacci series. static int[] fib; public static void fibonacci(int n) { fib = new int[n+1]; fib[0] = 1; fib[1] = 1; for(int i = 2; i <= n; i++) { // fib[i-2] and fib[i-1] were calculated // in previous iterations. fib[i] = fib[i-1] + fib[i-2]; } // printing the fibonacci series System.out.println(Arrays.toString(fib)); } public static void main(String[] args) { fibonacci(5); } }
In the code above, we have a single for loop with (n - 1)
iterations O(n - 1)
and a call to Arrays.toString(fib)
method that will have complexity of O(n)
. The overall time complexity of the program above is:
O(n - 1) + O(n) = O( 2 * n) = O(n)
Since we need a single array with n+1
elements to store the results, the total space complexity of the program is:
O(n + 1) = O (n)
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