algorithm Dynamic Programming Fibonacci Number
Example
Bottom up approach for printing the nth Fibonacci number using Dynamic Programming.
Recursive Tree
fib(5)
/ \
fib(4) fib(3)
/ \ / \
fib(3) fib(2) fib(2) fib(1)
/ \ / \ / \
fib(2) fib(1) fib(1) fib(0) fib(1) fib(0)
/ \
fib(1) fib(0)
Overlapping Sub-problems
Here fib(0),fib(1) and fib(3) are the overlapping sub-problems.fib(0) is getting repeated 3 times, fib(1) is getting repeated 5 times and fib(3) is getting repeated 2 times.
Implementation
public int fib(int n){
int f[] = new int[n+1];
f[0]=0;f[1]=1;
for(int i=2;i<=n;i++){
f[i]=f[i-1]+f[i-2];
}
return f[n];
}
Time Complexity
O(n)
