Taking 1st two fibonacci numbers as 0 and 1. WriteLine fib n ;. Fibonacci numbers. Function for nth fibonacci number - Space Optimisation. Note that this function is designed only for fib and won't work as general. Helper function that multiplies. Fibonacci Series using. Write fib n ;. Python3 Program to find n'th fibonacci Number in. Returns n'th fibonacci number using table f[]. Base cases. If fib n is already computed. This code is contributed by Nikita Tiwari. Array MAX ];.
Python3 program to find n'th. It should be obvious to anyone who is told that they have misread something that they should read it again, and read it more carefully. Explicitly telling them seems patronizing, even if it's not intended to be. Add a comment. Active Oldest Votes.
Improve this answer. John L. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. The first few terms are 0, 0, 1, 1, 2, 4, 7, 13, 24, 44, Write a program to compute tribonacci numbers. What is the ratio successive terms? Sum of first n Fibonacci numbers. Combinational Gray code. Print out all combination of k of n items in such a way that consecutive combinations differ in exactly one element, e.
Hint : use the Gray code, but only print out those integers with exactly k 1's in their binary representation. Maze generation. Create a maze using divide-and-conquer: Begin with a rectangular region with no walls. Choose a random gridpoint in the rectangle and construct two perpendicular walls, dividing the square into 4 subregions.
Choose 3 of the four regions at random and open a one cell hole at a random point in each of the 3. Recur until each subregion has width or height 1. Program PlasmaCloud. Here's an by example. Here's a reference , including a simple 1D version. Note: some visual artifacts are noticeable parallel to the x and y axes. Doesn't have all of the statistical properties of 2D fractional Brownian motion. Fern fractal. Write a recursive program to draw a fern or tree, as in this fern fractal demo.
Integer set partition. Use memoization to develop a program that solves the set partition problem for positive integer values. You may use an array whose size is the sum of the input values. Voting power. John F. Banzhaf III proposed a ranking system for each coalition in a block voting system. Suppose party i control w[i] votes. A strict majority of the votes is needed to accept or reject a proposal.
The voting power of party i is the number of minority coalitions it can join and turn it into a winning majority coalition. Write a program VotingPower. Hint : use Schedule. Scheduling on two parallel machines.
Program Schedule. Compute f 3. Use dynamic programming. This sequence has many fascinating properties and connects with Pascal's triangle, the Gaussian distribution, Fibonacci numbers, and Catalan numbers. Running time recurrences. Use dynamic programming to compute a table of values T N , where T N is the solution to the following divide-and-conquer recurrence.
Gas station optimization. You are driving from Princeton to San Francisco in a car that gets 25 miles per gallon and has a gas tank capacity of 15 gallons.
Along the way, there are N gas stations where you can stop for gas. Gas station i is d[i] miles into the trip and sells gas for p[i] dollars per gallon. If you stop at station i for gas, you must completely fill up your tank. Assume that you start with a full tank and that the d[i] are integers. Use dynamic programming to find a minimum cost sequence of stops. Unix diff. The Unix diff program compares two files line-by-line and prints out places where they differ. Write a program Diff.
Longest common subsequence of 3 strings. Given 3 strings, find the longest common subsequence using dynamic programming. What is the running time and memory usage of your algorithm? Making change. Given A hundred dollar bills, B fifty dollar bills, C twenty dollar bills, D ten dollar bills, E five dollar bills, F one dollar bills, G half-dollars, H quarters, I dimes, J nickels, and K pennies, determine whether it is possible to make change for N cents. Hint: knapsack problem.
Greedy also works. Suppose that you are a cashier in a strange country where the currency denominations are: 1, 3, 8, 16, 22, 57, , and cents or more generally d 0 , d 1 , Describe a dynamic programming algorithm to make change for c cents using the fewest number of coins. Longest increasing sequence.
Given an array of N bit integers, find the longest subsequence that is strictly increasing. Compute the longest common subsequence between the original array and a sorted version of the array where duplicate copies of an integer are removed. Longest common increasing sequence. Computational biology. Given two sequences of N bit integers, find the longest increasing subsequence that is common to both sequences.
Activity selection with profits. Find best subset of jobs to schedule. Write a program that reads in two files and prints out their diff. Treat each line as a symbol and compute an LCS. Print out those lines in each file that aren't in the LCS.
Knapsack problem. The above recursion is called a linear recursion since it makes one recursive call at a time. The loop equivalent:. Let's take a close look at the mechanism with which a recursive program is actually implemented by the compiler. In the previous example, we have seen how a recursion executes its forward and backing-out phases. The order in which the recursive process backs out is the reverse of the order in which it goes forward.
Thus some action may be performed that involves recalling something that has been stored in the forward process. The compiler uses a stack to implement recursion. Exercise Exponentiation. Calculate x n using both iteration and recursion.
We can solve this problem using the linear recursion, by observing that the reversal of an array can be achieved by swapping the first and last elements and then recursively reversing the remaining elements in the array.
This is a standard problem where the recursive implementation is trivial but the non-recursive implementation is almost impossible. In the Towers of Hanoi puzzle, we are given a platform with three pegs, a , b , and c , sticking out of it.
On peg a is a stack of n disks, each larger than the next, so that the smallest is on the top and the largest is on the bottom. The puzzle is to move all the disks from peg a to c , moving one disk at a time, so that we never place a larger disk on top of a smaller one. Let's look at an example of moving 4 disks.
At the top level, we want to move 4 disks from peg a to c , with a spare peg b. We can break the problem of moving 4 disks into three steps:.
The pseudocode looks like the following. We call this function to move 4 disks by MoveDisk 4, a, c, b. Let's trace our solution.
To visualize the recursive calling process, we generate a call tree. This is a call tree for moving 3 disks from peg a to c. Notice that, each MoveDisk call will branch into two functions calls unless it's the base case.
If we want to move n disks, how many movements do we need with this recursive function? Assume M i represents the number of movement for the disks, let's calculate how long does it take to move n disks. A disk version of the puzzle lies in a Hanoi monastery, where monks continuously toward solving the puzzle. When they complete the puzzle, the world will come to an end. Now, you know the answer.
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