Greedy Algorithms

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What is Greedy Algorithm?

Greedy is an algorithmic paradigm that builds up a solution piece by piece, always choosing the next piece that offers the most obvious and immediate benefit. So the problems where choosing locally optimal also leads to global solution are the best fit for Greedy.

For example consider the Fractional Knapsack Problem. The local optimal strategy is to choose the item that has maximum value vs weight ratio. This strategy also leads to a globally optimal solution because we are allowed to take fractions of an item.

Topics:

Introduction:

1. Introduction to Greedy Algorithm – Data Structures and Algorithm Tutorials
2. Greedy Algorithms (General Structure and Applications)
3. Difference between Greedy Algorithm and Divide and Conquer Algorithm
4. Greedy approach vs Dynamic programming
5. Comparison among Greedy, Divide and Conquer and Dynamic Programming algorithm

Standard Greedy Algorithms:

1. Activity Selection Problem
2. Job Sequencing Problem
3. Huffman Coding
4. Huffman Decoding
5. Water Connection Problem
6. Minimum Swaps for Bracket Balancing
7. Egyptian Fraction
8. Policemen catch thieves
9. Fitting Shelves Problem
10. Assign Mice to Holes

Greedy Problems on Array:

1. Minimum product subset of an array
2. Maximize array sum after K negations using Sorting
3. Minimum sum of product of two arrays
4. Minimum sum of absolute difference of pairs of two arrays
5. Minimum increment/decrement to make array non-Increasing
6. Sorting array with reverse around middle
7. Sum of Areas of Rectangles possible for an array
8. Largest lexicographic array with at-most K consecutive swaps
9. Partition into two subarrays of lengths k and (N – k) such that the difference of sums is maximum

Greedy Problems on Operating System:

1. First Fit algorithm in Memory Management
2. Best Fit algorithm in Memory Management
3. Worst Fit algorithm in Memory Management
4. Shortest Job First Scheduling
5. Job Scheduling with two jobs allowed at a time
6. Program for Optimal Page Replacement Algorithm

Greedy Problems on Graph:

1. Kruskal’s Minimum Spanning Tree
2. Prim’s Minimum Spanning Tree
3. Boruvka’s Minimum Spanning Tree
4. Dijkastra’s Shortest Path Algorithm
5. Dial’s Algorithm
6. Minimum cost to connect all cities
7. Max Flow Problem Introduction
8. Number of single cycle components in an undirected graph

Approximate Greedy Algorithm for NP Complete:

1. Set cover problem
2. Bin Packing Problem
3. Graph Coloring
4. K-centers problem
5. Shortest superstring problem
6. Approximate solution for Travelling Salesman Problem using MST

Greedy for Special cases of DP:

1. Fractional Knapsack Problem
2. Minimum number of coins required

Some practice problems on Greedy:

• Easy:
  1. Split n into maximum composite numbers
  2. Buy Maximum Stocks if i stocks can be bought on i-th day
  3. Find the minimum and maximum amount to buy all N candies
  4. Maximum sum possible equal to sum of three stacks
  5. Divide cuboid into cubes such that sum of volumes is maximum
  6. Maximum number of customers that can be satisfied with given quantity
  7. Minimum rotations to unlock a circular lock
  8. Minimum rooms for m events of n batches with given schedule
  9. Minimum cost to make array size 1 by removing larger of pairs
  10. Minimum cost for acquiring all coins with k extra coins allowed with every coin
  11. Minimum increment by k operations to make all elements equal
  12. Find minimum number of currency notes and values that sum to given amount
  13. Smallest subset with sum greater than all other elements
• Medium:
  1. Maximum trains for which stoppage can be provided
  2. Minimum Fibonacci terms with sum equal to K
  3. Divide 1 to n into two groups with minimum sum difference
  4. Paper cut into minimum number of squares
  5. Minimum difference between groups of size two
  6. Connect n ropes with minimum cost
  7. Minimum number of Platforms required for a railway/bus station
  8. Minimum initial vertices to traverse whole matrix with given conditions
  9. Largest palindromic number by permuting digits
  10. Find Smallest number with given number of digits and digits sum
  11. Lexicographically largest subsequence such that every character occurs at least k times
• Hard:
  1. Maximum elements that can be made equal with k updates
  2. Minimize cash flow among friends
  3. Minimum Cost to cut a board into squares
  4. Minimum cost to process m tasks where switching costs
  5. Minimum time to finish all jobs with given constraints
  6. Minimize the maximum difference between the heights of towers
  7. Minimum edges to reverse to make path from a source to a destination
  8. Find the Largest Cube formed by Deleting minimum Digits from a number
  9. Rearrange characters in a string such that no two adjacent are same
  10. Rearrange a string so that all same characters become d distance away

Quick Links :

1. Learn Data Structure and Algorithms | DSA Tutorial
2. Top 20 Greedy Algorithms Interview Questions
3. ‘Practice Problems’ on Greedy Algorithms
4. ‘Quiz’ on Greedy Algorithms

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