55. Jump Game

Description of 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

Solution

Explantion

The core concept is to record the current maximum reachable distance. For each node, if the node is currently reachable, then update the current maximum reachable distance. Otherwise, the final node is unreachable.

Code (Java)

class Solution {
    public boolean canJump(int[] nums) {
        int reachable = 0;
        int n = nums.length;
        for(int i = 0; i < n; i++){
            if (reachable < i){
                return false;
            }
            reachable = Math.max(reachable, i + nums[i]);
            if (reachable >= n-1){
                return true;
            }
        }
        return true;
    }
}

Complexity

Time complexity:

• \(T(n)=O(n)\)

Auxiliary Space:

• \(S(n)=O(1)\)