Minimum Jumps

Posted: 3 Jan, 2021
Difficulty: Moderate

PROBLEM STATEMENT

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Bob lives with his wife in a city named Berland. Bob is a good husband, so he goes out with his wife every Friday to ‘Arcade’ mall.

‘Arcade’ is a very famous mall in Berland. It has a very unique transportation method between shops. Since the shops in the mall are laying in a straight line, you can jump on a very advanced trampoline from the shop i, and land in any shop between (i) to (i + Arr[i]), where Arr[i] is a constant given for each shop.

There are N shops in the mall, numbered from 0 to N-1. Bob's wife starts her shopping journey from shop 0 and ends it in shop N-1. As the mall is very crowded on Fridays, unfortunately, Bob gets lost from his wife. So he wants to know, what is the minimum number of trampoline jumps from shop 0 he has to make in order to reach shop N-1 and see his wife again. If it is impossible to reach the last shop, return -1.

Input format :
The first line of input contains a single integer T, representing the number of test cases or queries to be run. 

Then the T test cases follow.

The first line of each test case contains a positive integer N, which represents the number of shops.

The next line contains 'N' single space-separated positive integers representing a constant given for each shop.
Output Format :
For each test case, print the minimum number of jumps or -1, if it is impossible to reach the last shop.
Note:
You do not need to print anything, it has already been taken care of. Just implement the given function.
Constraints :
1 <= T <= 10
1 <= N <= 5 * 10^4
0 <= Arr[i] <= N
Where T is the number of test cases, N is the size of the array and Arr[i] is the ith element in the array.
Approach 1

We will recursively find the minimum number of jumps.

 

Algorithm:

 

Let’s say we have a recursive function ‘minimumJumpsHelper’ which will return the minimum number of jumps to reach the last shop.

 

  • Call the function: minimumJumpsHelper(i).
  • If i is equal to N-1, return 0.
  • Make a variable ‘ans’ that stores the minimum number of jumps needed to reach the last shop from the current shop.
    • Initialize ‘ans’ with a maximum value (INT_MAX).
  • Iterate on the shops from (i + 1) to (i + Arr[i]) and update the answer, i.e., ans = min( ans, 1 + minimumJumpsHelper(j) ) (where j denotes the shop, where we jumped).
  • Return the ‘ans’.
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