Min_Jump_to reach_end_array

#Recursive Approach

def minJumps(arr, start, end):
    if (start == end):
        return 0
    if (arr[start] == 0):
        return float('inf')


    min = float('inf')
    for i in range(start + 1, end + 1):
        if i <= start + arr[start]:
            jumps = minJumps(arr, i, end)
            if (jumps + 1 < min):
                min = jumps + 1
    return min
    
    
  #Dynamic Approach
  
  def minJumpsDP(arr):
    if arr[0] == 0:
        return float('inf')

    end = len(arr)

    dp = [0 for i in range(end)]

    for i in range(1, end):
        dp[i] = float('inf')
        for j in range(0, i):
                if i <= j + arr[j]:
                    dp[i] = min(dp[i], dp[j] + 1)
    return dp[-1]