45. Jump Game II

1. Description

You are given a 0-indexed array of integers nums of length n. You are initially positioned at index 0.
Each element nums[i] represents the maximum length of a forward jump from index i. In other words, if you are at index i, you can jump to any index (i + j) where:

• 0 <= j <= nums[i] and
• i + j < n

Return the minimum number of jumps to reach index n - 1. The test cases are generated such that you can reach index n - 1.

2. Example

Example 1

Input: nums = [2,3,1,1,4]
Output: 2
Explanation: The minimum number of jumps to reach the last index is 2. Jump 1 step from index 0 to 1, then 3 steps to the last index.

Example 2

Input: nums = [2,3,0,1,4]
Output: 2

3. Constraints

• 1 <= nums.length <= 10$^{4}$
• 0 <= nums[i] <= 1000
• It’s guaranteed that you can reach nums[n - 1].

4. Solutions

Greedy

n = nums.size()
Time complexity: O(n)
Space complexity: O(1)

class Solution {
public:
    int jump(vector<int> &nums) {
        const int n = nums.size();

        int count = 0, limit = 0, reach = 0;
        for (int i = 0; i < n - 1; ++i) {
            reach = max(reach, i + nums[i]);

            if (i == limit) {
                ++count;
                limit = reach;

                if (limit >= n - 1) {
                    break;
                }
            }
        }

        return count;
    }
};