What is the Minimum Number of Jumps problem and how can it be solved using a greedy algorithm?

The Minimum Number of Jumps problem is a problem where we are given an array of non-negative integers, representing the maximum jump length from each position in the array. The goal is to find the minimum number of jumps needed to reach the last position starting from the first position.

This problem can be solved using a greedy algorithm. The idea is to always choose the jump that can reach the furthest position.

To solve this problem using a greedy algorithm, we can follow these steps:
1. Initialize three variables: "maxReach" to store the maximum index that can be reached, "steps" to store the number of steps taken so far, and "lastJump" to store the index of the last jump.
2. Iterate through the array from the first position to the second-to-last position.
3. Update "maxReach" by taking the maximum of its current value and the sum of the current index and the maximum jump length from that index.
4. If the current index is equal to "lastJump", it means we have reached the end of the current jump. In this case, update "lastJump" to "maxReach" and increment "steps" by 1.
5. If "maxReach" is greater than or equal to the last index, it means we can reach the end of the array. In this case, return "steps".
6. If "maxReach" is still less than the current index, it means we cannot reach the end of the array. In this case, it is not possible to solve the problem, so return -1.

By following this greedy approach, we can find the minimum number of jumps needed to reach the last position efficiently.