Given a starting position ‘k’ and two jump sizes ‘d1’ and ‘d2’, our task is to find the minimum number of jumps needed to reach ‘x’ if it is possible.
At any position P, we are allowed to jump to positions :
- P + d1 and P – d1
- P + d2 and P – d2
Input : k = 10, d1 = 4, d2 = 6 and x = 8 Output : 2 1st step 10 + d1 = 14 2nd step 14 - d2 = 8 Input : k = 10, d1 = 4, d2 = 6 and x = 9 Output : -1 -1 indicates it is not possible to reach x.
In the previous article we discussed a strategy to check whether a list of numbers is reachable by K by making jump of two given lengths.
Here, instead of a list of numbers, we are given a single integer x and if it is reachable from k then the task is to find the minimum number of steps or jumps needed.
We will solve this using Breadth first Search:
- Check if ‘x’ is reachable from k. The number x is reachable from k if it satisfies (x – k) % gcd(d1, d2) = 0.
- If x is reachable :
- Maintain a hash table to store the already visited positions.
- Apply bfs algorithm starting from the position k.
- If you reach position P in ‘stp’ steps, you can reach p+d1 position in ‘stp+1’ steps.
- If position P is the required position ‘x’ then steps taken to reach P is the answer
The image below depicts how the algorithm finds out number of steps needed to reach x = 8 with k = 10, d1 = 4 and d2 = 6.
Below is the implementation of the above approach:
- Reach the numbers by making jumps of two given lengths
- Minimum number of jumps to reach end
- Minimum length of jumps to avoid given array of obstacles
- Check if it is possible to move from (a, 0) to (b, 0) with given jumps
- Word Ladder (Length of shortest chain to reach a target word)
- Find if two people ever meet after same number of jumps
- Number of jumps for a thief to cross walls
- Check if a graphs has a cycle of odd length
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- Check if it is possible to reach vector B by rotating vector A and adding vector C to it
- Maximize the number of segments of length p, q and r
- Convert a number of length N such that it contains any one digit at least 'K' times
- Number of balanced bracket subsequence of length 2 and 4
- Find the number of valid parentheses expressions of given length
- Number of decimal numbers of length k, that are strict monotone