Dynamic Programming for Coding Interviews: A Bottom-Up approach to problem solving

Dynamic Programming for Coding Interviews: A Bottom-Up approach to problem solving

I wanted to compute 80th term of the Fibonacci series. I wrote the rampant recursive function, <BR><BR> int fib(int n){ <BR><BR> return (1==n || 2==n) ? 1 : fib(n-1) + fib(n-2); <BR><BR> } <BR><BR> and waited for the result. I wait… and wait… and wait… <BR><BR> With an 8GB RAM and an Intel i5 CPU, why is it taking so long? I terminated the process and tried computing the 40th term. It took about a second. I put a check and was shocked to find that the above recursive function was called 204,668,309 times while computing the 40th term. <BR><BR> More than 200 million times? Is it reporting function calls or scam of some government? <BR><BR> The Dynamic Programming solution computes 100th Fibonacci term in less than fraction of a second, with a single function call, taking linear time and constant extra memory. <BR><BR> A recursive solution, usually, neither pass all test cases in a coding competition, nor does it impress the interviewer in an interview of company like Google, Microsoft, etc. <BR><BR> The most difficult questions asked in competitions and interviews, are from dynamic programming. This book takes Dynamic Programming head-on. It first explain the concepts with simple examples and then deep dives into complex DP problems.