Greedy Algorithms Questions
The Maximum Number of Steps problem is a problem where we are given an array of non-negative integers representing the maximum number of steps that can be jumped from each position in the array. The goal is to determine the minimum number of steps needed to reach the last position of the array.
This problem can be solved using a greedy algorithm by iteratively choosing the maximum reachable position from the current position. We start from the first position and keep track of the maximum reachable position. At each step, we update the maximum reachable position by comparing the current position plus the maximum number of steps that can be jumped from that position. We continue this process until we reach the last position or cannot move forward anymore.
The greedy approach works because at each step, we choose the locally optimal choice by jumping to the position that can reach the farthest. By doing so, we ensure that we are always making progress towards the last position.