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
- Find the minimum of maximum length of a jump required to reach the last island in exactly k jumps
- Minimum number of jumps to reach end
- Find the number of jumps to reach X in the number line from zero
- Count minimum factor jumps required to reach the end of an Array
- Minimum steps to reach the Nth stair in jumps of perfect power of 2
- Count ways to reach end from start stone with at most K jumps at each step
- 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
- Check if the length of all connected components is a Fibonacci number
- Find if two people ever meet after same number of jumps
- Number of jumps for a thief to cross walls
- Check if it is possible to reach (x, y) from origin in exactly Z steps using only plus movements
- Word Ladder (Length of shortest chain to reach a target word)
- Number of ways to cut a stick of length N into in even length at most K units long pieces
- Minimize number of cuts required to break N length stick into N unit length sticks
- Number of ways to reach the end of matrix with non-zero AND value
- Find the minimum number of steps to reach M from N
- Number of steps required to reach point (x,y) from (0,0) using zig-zag way
- Minimum number of moves to reach N starting from (1, 1)
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