55. Jump Game
Description
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 <= 104
0 <= nums[i] <= 105
Solutions
Solution 1: Greedy
We use a variable $mx$ to maintain the farthest index that can currently be reached, initially $mx = 0$.
We traverse the array from left to right. For each position $i$ we traverse, if $mx < i$, it means that the current position cannot be reached, so we directly return false
. Otherwise, the farthest position that we can reach by jumping from position $i$ is $i+nums[i]$, we use $i+nums[i]$ to update the value of $mx$, that is, $mx = \max(mx, i + nums[i])$.
At the end of the traversal, we directly return true
.
The time complexity is $O(n)$, where $n$ is the length of the array. The space complexity is $O(1)$.
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