Code360 powered by Coding Ninjas X Code360 powered by Coding Ninjas X
Last Updated: 17 Dec, 2021

Frog Jump

Asked in companies
MicrosoftDunzoCIS - Cyber Infrastructure

Problem statement

There is a frog on the '1st' step of an 'N' stairs long staircase. The frog wants to reach the 'Nth' stair. 'HEIGHT[i]' is the height of the '(i+1)th' stair.If Frog jumps from 'ith' to 'jth' stair, the energy lost in the jump is given by absolute value of ( HEIGHT[i-1] - HEIGHT[j-1] ). If the Frog is on 'ith' staircase, he can jump either to '(i+1)th' stair or to '(i+2)th' stair. Your task is to find the minimum total energy used by the frog to reach from '1st' stair to 'Nth' stair.

For Example
If the given ‘HEIGHT’ array is [10,20,30,10], the answer 20 as the frog can jump from 1st stair to 2nd stair (|20-10| = 10 energy lost) and then a jump from 2nd stair to last stair (|10-20| = 10 energy lost). So, the total energy lost is 20.
Input Format:
The first line of the input contains an integer, 'T,’ denoting the number of test cases.

The first line of each test case contains a single integer,' N’, denoting the number of stairs in the staircase,

The next line contains ‘HEIGHT’ array.
Output Format:
For each test case, return an integer corresponding to the minimum energy lost to reach the last stair.
You do not need to print anything. It has already been taken care of. Just implement the given function.
1 <= T <= 10
1 <= N <= 100000.
1 <= HEIGHTS[i] <= 1000 .

Time limit: 1 sec


01 Approach

In this approach, we will define a recursive function REC(i,HEIGHT) that will return the minimum energy needed to reach the last stair from the ith stair.

The base case will be if i is greater than or equal to ‘N’ answer will be 0 as we already reached the final stair.

As we have two choices at each step,REC(i) will be the maximum of energy lost for jumping from ith to (i+1)th step + REC(i+1) and energy lost for jumping from i th to (i+2)th step + REC(i+2).


The final answer will be REC(1, HEIGHTS) corresponding to the minimum energy required to reach the last stair from the first stair.



  • Defining 'REC'(i,’ HEIGHTS’) function :
    • If i is equal to the length of ‘HEIGHTS’ - 1:
      • Return 0.
    • Set ‘ONE_JUMP’ as INF.
    • Set ‘TWO_JUMP’ as INF.
    • If i+1 < length of ‘HEIGHTS’:
      • Set ‘ONE_JUMP’ as abs(HEIGHTS[i]-HEIGHTS[i+1]) + REC(i+1,HEIGHTS).
    • If i+2 < length of ‘HEIGHTS’:
      • Set ‘TWO_JUMP’ as abs(HEIGHTS[i]-HEIGHTS[i+2]) + REC(i+2,HEIGHTS).
    • Set ‘ANS’ as minimum of ONE_JUMP and TWO_JUMP.
    • Return ‘ANS’.
  • Set ‘ANS’ as REC(1,HEIGHTS).
  • Return ‘ANS’.