Given an array of integers where each element represents the max number of steps that can be made forward from that element. Write a function to return the minimum number of jumps to reach the end of the array (starting from the first element). If an element is 0, they cannot move through that element. If the end isn’t reachable, return -1.

Examples: 

Input: arr[] = {1, 3, 5, 8, 9, 2, 6, 7, 6, 8, 9}

Output: 3 (1-> 3 -> 9 -> 9)

Explanation: Jump from 1st element 

to 2nd element as there is only 1 step, 

now there are three options 5, 8 or 9. 

If 8 or 9 is chosen then the end node 9 

can be reached. So 3 jumps are made.

 

Input: arr[] = {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

Output: 10

Explanation: In every step a jump 

is needed so the count of jumps is 10.

The first element is 1, so can only go to 3. The second element is 3, so can make at most 3 steps eg to 5 or 8 or 9.

 

Method 1: Naive Recursive Approach. 

Approach: A naive approach is to start from the first element and recursively call for all the elements reachable from first element. The minimum number of jumps to reach end from first can be calculated using minimum number of jumps needed to reach end from the elements reachable from first. 

minJumps(start, end) = Min ( minJumps(k, end) ) for all k reachable from start 

 

# Python3 program to find Minimum
# number of jumps to reach end
 
# Returns minimum number of jumps
# to reach arr[h] from arr[l]
def minJumps(arr, l, h):
 
    # Base case: when source and
    # destination are same
    if (h == l):
        return 0
 
    # when nothing is reachable
    # from the given source
    if (arr[l] == 0):
        return float('inf')
 
    # Traverse through all the points
    # reachable from arr[l]. Recursively
    # get the minimum number of jumps
    # needed to reach arr[h] from
    # these reachable points.
    min = float('inf')
    for i in range(l + 1, h + 1):
        if (i < l + arr[l] + 1):
            jumps = minJumps(arr, i, h)
            if (jumps != float('inf') and
                       jumps + 1 < min):
                min = jumps + 1
 
    return min
 
# Driver program to test above function
arr = [1, 3, 6, 3, 2, 3, 6, 8, 9, 5]
n = len(arr)
print('Minimum number of jumps to reach',
     'end is', minJumps(arr, 0, n-1))
 
# This code is contributed by Soumen Ghosh