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55. Jump Game

Problem

You are given an integer array nums. You are initially positioned at the array’s first index, and each element in the array represents your maximum jump length at that position.

Return true if you can reach the last index, or false otherwise.

Example 1:

Input: nums = [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: nums = [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.

Constraints:

  • 1 <= nums.length <= 10**4
  • 0 <= nums[i] <= 10**5

Solve

Dynamic programming from top down

O(n)

It seem go backward is easier, as you have more information calculated than jump forward blindly

  • If you go backward, and found out you can’t find a good standing point to jump to the position you standing at, it mean we could just stop and return False
  • We can skip some standing point if there is a better one that can jump our current end point.
from random import randint
from typing import List

class Solution:
    def canJump(self, nums: List[int]) -> bool:
        checkCanJump = True

        lastIndex = len(nums) - 1
        startingPoint = 0
        canBeSkip = [False]* len(nums)

        for jumpEndPoint in range(lastIndex, -1, -1):
            if jumpEndPoint == startingPoint:
                break

            if canBeSkip[jumpEndPoint]:
                continue

            neededJumpLength = 1

            standingPoint = jumpEndPoint

            for standingPoint in range(jumpEndPoint-1, -1, -1):
                if nums[standingPoint] >= neededJumpLength:
                    break
                neededJumpLength += 1
                canBeSkip[jumpEndPoint] = True

            if nums[standingPoint] < neededJumpLength:
                checkCanJump = False
                break

        return checkCanJump

This is some test for the problem

def test():
    a = Solution()
    # Example 1
    nums = [2,3,1,1,4]
    Output = True
    result = a.canJump(nums)
    print("Test 1 is", Output == result)
    # Example 2
    nums = [3,2,1,0,4]
    Output = False
    result = a.canJump(nums)
    print("Test 2 is", Output == result)
    # Example 3
    nums = [3]
    Output = True
    result = a.canJump(nums)
    print("Test 3 is", Output == result)
    # Example 4
    nums = [0]
    Output = True
    result = a.canJump(nums)
    print("Test 4 is", Output == result)
    # Example 5
    nums = [2,0]
    Output = True
    result = a.canJump(nums)
    print("Test 5 is", Output == result)
    # Constraints
    # 1 <= nums.length <= 10**4
    # 0 <= nums[i] <= 10**5
    nums = [randint(0,10**5) for i in range(10**4)]
    Output = True               # Pretty much
    result = a.canJump(nums)
    print("Test time limit is OK")

if __name__ == "__main__":
    test()

Time complexity: O(n)

  • Two loop run independently (even if it nested loop)
Last update : September 17, 2023
Created : August 16, 2023