Given integers N, P and Q where N denotes the destination position. The task is to move from position 0 to position N with minimum cost possible and print the calculated cost. All valid movements are:
- From position X you can go to position X + 1 with a cost of P
- Or, you can go to the position 2 * X with a cost of Q
Input: N = 1, P = 3, Q = 4
Move from position 0 to 1st position with cost = 3.
Input: N = 9, P = 5, Q = 1
Move from position 0 to 1st position with cost = 5,
then 1st to 2nd with cost = 1,
then 2nd to 4th with cost = 1,
then 4th to 8th with cost = 1,
finally 8th to 9th with cost = 5.
Total cost = 5 + 1 + 1 + 1 + 5 = 13.
Approach: Instead of going from beginning to destination we can start moving from the destination to initial position and keep track of the cost of jumps.
- If N is odd then the only valid move that could lead us here is N-1 to N with a cost of P.
- If N is even then we calculate cost of going from N to N/2 position with both the moves and take the minimum of them.
- When N equals 0, we return our total calculated cost.
Below is the implementation of above approach:
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