Given N number of stairs. Also given the number of steps that one can cover at most in one leap (K). The task is to find the number of possible ways one (only consider combinations) can climb to the top of the building in K leaps or less from the ground floor.
Input: N = 5, K = 3
To reach stair no-5 we can choose following combination of leaps:
1 1 1 1 1
1 1 1 2
1 2 2
1 1 3
Therefore the answer is 5.
Input: N = 29, K = 5
Let combo[i] be the number of ways to reach the i-th floor. Hence the number of ways to reach combo[i] from combo[j] by taking a leap of i-j will be combo[i] += combo[j]. So iterate for all possible leaps, and for each possible leaps keep adding the possible combinations to the combo array. The final answer will be stored in combo[N].
Below is the implementation of the above approach.
Time Complexity: O(N*K)
Auxiliary Space: O(N)
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.
- Sum of all numbers formed having 4 atmost X times, 5 atmost Y times and 6 atmost Z times
- Count ways to reach Nth Stairs by taking 1 and 2 steps with exactly one 3 step
- Value of continuous floor function : F(x) = F(floor(x/2)) + x
- Number of ways to arrange K different objects taking N objects at a time
- Count ways to reach the Nth stair using multiple 1 or 2 steps and a single step 3
- Count ways to reach the nth stair using step 1, 2 or 3
- Minimum cost to reach the top of the floor by climbing stairs
- Count the number of ways to tile the floor of size n x m using 1 x m size tiles
- Count number of ways to reach a given score in a game
- Count number of ways to reach destination in a Maze
- Count number of ways to jump to reach end
- Number of ways to reach the end of matrix with non-zero AND value
- Count number of ways to reach a given score in a Matrix
- Find the number of ways to reach Kth step in stair case
- Number of ways to reach (M, N) in a matrix starting from the origin without visiting (X, Y)
- Number of ways to reach (X, Y) in a matrix starting from the origin
- Maximise array sum after taking non-overlapping sub-arrays of length K
- Check if it is possible to get given sum by taking one element from each row
- Count ways to reach the n'th stair
- Count ways to reach a score using 1 and 2 with no consecutive 2s
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.