each valid 1, the 1-th frog is initially at the position 1, it has here are N frog (numbered I through N) in line. weight Wi, and whenever you hit its back, it jumps a distance Li to the right, i.e. its position increases by Li. The weights of the frogs are pairwise distinct. You can hit the back of each frog any number of times (possibly zero, not necessarily the same for all frogs) in any order. The frogs do not interfere with each other, so there can be any number of frogs at the same time at each position. Your task is to sort the frogs in the increasing order of weight using the smallest possible number of hits. In other words, after all the hits are performed, then for each pair of frogs (i, j) such that Wi

each valid 1, the 1-th frog is initially at the position 1, it has here are N frog (numbered I through N) in line. weight Wi, and whenever you hit its back, it jumps a distance Li to the right, i.e. its position increases by Li. The weights of the frogs are pairwise distinct. You can hit the back of each frog any number of times (possibly zero, not necessarily the same for all frogs) in any order. The frogs do not interfere with each other, so there can be any number of frogs at the same time at each position. Your task is to sort the frogs in the increasing order of weight using the smallest possible number of hits. In other words, after all the hits are performed, then for each pair of frogs (i, j) such that Wi

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

Section: Chapter Questions

Problem 1PE

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Concept explainers

Topological Sort

Topological sort is a sorting technique that sets up a hierarchy in a process. In this technique, when a directed network has nodes connected by arrows, the root node is placed before the successor node.

Question

@1st mp. 109.

There are N frogs (numbered I through N) in a line. For each valid 1, the 1-th frog is initially at the position 1, it has
weight Wi, and whenever you hit its back, it jumps a distance Li to the right, i.e. its position increases by Li. The
weights of the frogs are pairwise distinct.
You can hit the back of each frog any number of times (possibly zero, not necessarily the same for all frogs) in any
order. The frogs do not interfere with each other, so there can be any number of frogs at the same time at each
position.
Your task is to sort the frogs in the increasing order of weight using the smallest possible number of hits. In other
words, after all the hits are performed, then for each pair of frogs (i, j) such that Wi<Wj, the position of the i-th
frog should be strictly smaller than the position of the j-th frog. Find the smallest number of hits needed to achieve
such a state.
Test Case:
1
3
312
145
Output:
3

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