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(const vector<int> &nums) {
        const int n = nums.size();
        int jump_count = 0, current_right_border = 0, next_right_border = nums[0];
        for (int i = 0; i < n - 1; ++i) {
            if (current_right_border >= n - 1) {
                break;
            }

            next_right_border = max(i + nums[i], next_right_border);
            if (i == current_right_border) {
                current_right_border = next_right_border;
                ++jump_count;
            }
        }

        return jump_count;
    }
};