# Algorithm Puzzles: Jump Game

Algorithm Puzzles ~~everyday~~ ~~every week~~ sometimes: Jump Game

## Puzzle

Puzzle from leetcode:

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.

## Solution

Looks like a typical DP puzzle, let `dp[i]`

as largest index we can jump from index i, we can have:

1 | dp[0] = nums[0] |

Base on this we have:

1 | class Solution { |

We may use size-initialed `vector`

to reduce runtime:

1 | class Solution { |

Now we have much better runtime result:

In worst case T.C. should be `O(n)`

and S.C. should be `O(2n)`

.