Consider the array A[1 . . . n] consisting of n non-negative integers. There is a frog on the LAST index of the array, i.e. the nth index of the array. In each step, if the frog is positioned on the i th index, then it can make a jump of size at most A[i] towards the beginning of the array. In other words, it can hop to any of the indices i, . . . , i − A[i].

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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Consider the array A[1 . . . n] consisting of n non-negative integers. There is a frog on the LAST index of the array, i.e. the nth index of the array. In each step, if the frog is positioned on the i th index, then it can make a jump of size at most A[i] towards the beginning of the array. In other words, it can hop to any of the indices i, . . . , i − A[i].

(a) Develop a Greedy algorithm to determine whether the frog can reach the FIRST index of A.

(b) Show the correctness of your algorithm in part (a).

(c) Find and justify the time complexity of your algorithm.`

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