old_contents: """Leetcode 55. Jump Game
  Medium
  
  URL: https://leetcode.com/problems/jump-game/
  
  Given an array of non-negative integers, you are initially positioned at the 
  first index of the array.
  
  Each element in the array represents your maximum jump length at that position.
  
  Determine if you are able to reach the last index.
  
  Example 1:
  Input: [2,3,1,1,4]
  Output: true
  Explanation: Jump 1 step from index 0 to 1, then 3 steps to the last index.
  
  Example 2:
  Input: [3,2,1,0,4]
  Output: false
  Explanation: You will always arrive at index 3 no matter what. Its maximum
  jump length is 0, which makes it impossible to reach the last index.
  """
  
  class SolutionGreedy(object):
      def canJump(self, nums):
          """
          :type nums: List[int]
          :rtype: bool
  
          Time complexity: O(n).
          Space complexity: O(1).
          """
          # Create max reachable index.
          reach = 0
  
          for i in range(len(nums)):
              # Check if index i is not reachable.
              if reach < i:
                  return False
  
              # Update reach by taking max of itself and i+nums[i].
              reach = max(reach, i + nums[i])
  
          return True
  
  
  def main():
      # Ans: True
      nums = [2,3,1,1,4]
      print SolutionGreedy().canJump(nums)
  
      # Ans: False
      nums = [3,2,1,0,4]
      print SolutionGreedy().canJump(nums)
  
  
  if __name__ == '__main__':
      main()
  
new_contents: """Leetcode 55. Jump Game
  Medium
  
  URL: https://leetcode.com/problems/jump-game/
  
  Given an array of non-negative integers, you are initially positioned at the 
  first index of the array.
  
  Each element in the array represents your maximum jump length at that position.
  
  Determine if you are able to reach the last index.
  
  Example 1:
  Input: [2,3,1,1,4]
  Output: true
  Explanation: Jump 1 step from index 0 to 1, then 3 steps to the last index.
  
  Example 2:
  Input: [3,2,1,0,4]
  Output: false
  Explanation: You will always arrive at index 3 no matter what. Its maximum
  jump length is 0, which makes it impossible to reach the last index.
  """
  
  
  class SolutionDP(object):
      def canJump(self, nums):
          """
          :type nums: List[int]
          :rtype: bool
  
          Time complexity: O(n).
          Space complexity: O(n).
          """
          # Apply bottom-up DP with memo table T, where T[i] = True means reachable.
          n = len(nums)
          T = [False] * n
          T[0] = True
  
          # Check if i is reachable from some reachable j.
          for i in range(1, n):
              for j in range(i, -1, -1):
                  if i - j <= nums[j] and T[j]:
                      T[i] = True
                      break
          return T[-1]
  
  
  class SolutionGreedy(object):
      def canJump(self, nums):
          """
          :type nums: List[int]
          :rtype: bool
  
          Time complexity: O(n).
          Space complexity: O(1).
          """
          # Apply greedy approach with early stopping.
          # Create max reachable index.
          reach = 0
  
          for i in range(len(nums)):
              # Check if ifndex i is not reachable.
              if reach < i:
                  return False
  
              # Update reach by taking max of itself and i+nums[i].
              reach = max(reach, i + nums[i])
  
          return True
  
  
  def main():
      import time
  
      # Ans: True
      nums = [2,3,1,1,4]
  
      start_time = time.time()
      print 'DP:', SolutionDP().canJump(nums)
      print 'Time:', time.time() - start_time
  
      start_time = time.time()
      print 'DP:', SolutionGreedy().canJump(nums)
      print 'Time:', time.time() - start_time
  
      # Ans: False
      nums = [3,2,1,0,4]
  
      start_time = time.time()
      print 'DP:', SolutionDP().canJump(nums)
      print 'Time:', time.time() - start_time
  
      start_time = time.time()
      print 'DP:', SolutionGreedy().canJump(nums)
      print 'Time:', time.time() - start_time
  
  
  if __name__ == '__main__':
      main()
  
subject: Complete DP sol