Jump Game II - Java Solution

1. Introduction

In this blog post, we delve into the "Jump Game II" problem, a classic in array manipulation and dynamic programming. The problem presents a scenario where you're given an array of integers, each representing the maximum length of a forward jump from its index. The challenge is to find the minimum number of jumps to reach the end of the array.

Problem

Given a 0-indexed array of integers nums of length n, with each element nums[i] representing the maximum length of a forward jump from index i, the task is to return the minimum number of jumps needed to reach the last element in the array. It is guaranteed that reaching the last element is possible.

2. Solution Steps

1. Use a greedy approach to solve the problem.

2. Initialize two variables, steps to count the number of jumps and maxReach to keep track of the farthest index that can be reached.

3. Also, maintain a nextMaxReach variable to store the farthest index that can be reached in the next step.

4. Iterate through the array, updating maxReach and nextMaxReach.

5. When the current index reaches maxReach, increment steps and update maxReach to nextMaxReach.

6. Continue this process until the end of the array is reached.

7. Return the value of steps.

3. Code Program

public class JumpGameII {
    public static void main(String[] args) {
        int[] nums = {2, 3, 1, 1, 4};
        System.out.println(jump(nums)); // Test the function
    }

    // Function to find the minimum number of jumps to reach the end
    public static int jump(int[] nums) {
        int steps = 0, maxReach = 0, nextMaxReach = 0;

        for (int i = 0; i < nums.length - 1; i++) {
            nextMaxReach = Math.max(nextMaxReach, i + nums[i]);
            if (i == maxReach) {
                steps++;
                maxReach = nextMaxReach;
            }
        }
        return steps;
    }
}

Output:

2

Explanation:

1. jump: This function calculates the minimum number of jumps required to reach the end of the array.

2. It uses a greedy approach to find the farthest index that can be reached in each jump.

3. maxReach keeps track of the farthest index that can be reached with the current number of jumps, and nextMaxReach stores the farthest index for the next jump.

4. On each iteration, if the current index i reaches the maxReach, the function increments steps and updates maxReach to nextMaxReach.

5. The process continues until the end of the array is reached.

6. The function returns the total number of steps taken, which represents the minimum jumps needed to reach the end.

7. This approach efficiently calculates the minimum jumps by always opting for the jump that reaches the farthest possible index in each step.