Greedy Algorithms

Minimum number of Fibonacci terms with sum equal to a given number N

Given a number N, we need to find the minimum number of fibonacci numbers required that sums up to a given number N. Note a fibonacci number can be repeated

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Find the largest number with given number of digits and sum of digits

In this problem, we need to find the largest number with a given number of digits N and given sum of digits say M. We will use a greedy algorithm to solve this is O(N) time complexity.

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Find the smallest number with given number of digits and sum of digits

We are given two positive integers M and N. The task is to find the smallest number that has length M (number of digits) and sum of digits as N. We will solve this using a greedy approach in O(M)

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Split N into maximum composite numbers

Given a number N, the problem is to count the maximum number of composite numbers that sum up to N. We solve this using a greedy algorithm in constant time

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Maximize the sum of array[i]*i

Given an array of N integer, we have to maximize the sum of arr[i] * i. Brute force approach will take O(N*N!) time while greedy algorithm will take O(N log N) time

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The smallest subset with sum greater than sum of all other elements

In this article, we explored a greedy algorithm to find the smallest subset with sum greater than sum of all other elements in O(N log N) time complexity

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Find Minimum sum of product of two arrays

In this article, we explored a greedy algorithm to find the minimum sum of product of two arrays in O(N log N) time whereas the brute force approach takes O(N!^2) time

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Find the Largest Cube formed by deleting minimum number of digits from a number

In this article, we find the Largest Cube formed by deleting minimum number of digits from a number using a greedy algorithm which takes O(N^(1/3)log(N)log(N)) time

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Find the Largest lexicographic array with at most K consecutive swaps

For a given array, find the largest lexicographic array which can be obtained from it after performing at most K consecutive swaps.

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Minimum Product Subset of an array

For a given array of elements, we have to find the non-empty subset having the minimum product. We will explore two techniques brute force O(2^N) and Greedy algorithm O(N)

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Maximum Product Subset of an array

For a given array of elements, we have to find the non-empty subset having the maximum product. We will explore two techniques brute force O(2^N) and Greedy algorithm O(N)

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Greedy approach to find a single maximal clique in O(V^2) time complexity

There can be more than one single maximal clique in a non-complete graph (since complete graph is a maximal clique itself). To find a single maximal clique in a graph we use a straightforward greedy algorithm in O(V^2) time complexity

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Divide numbers from 1 to n into two groups with minimum sum difference from O(2^N) to O(N)

For numbers from 1 to given n, we have to find the division of the elements into two groups having minimum absolute sum difference. We will explore two techniques Brute force which will take O(2^N) time complexity and Greedy algorithm which will take O(N) time complexity

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Activity Selection Problem using Greedy algorithm

For activity selection, Dynamic Programming Approach takes O(n^3) time while Greedy Approach takes O(N) time when unsorted and O(n log n) when sorted. It follows Greedy approach as at every step, we make a choice that looks best at the moment to get the optimal solution of the complete problem

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Graph Coloring Greedy Algorithm [O(V^2 + E) time complexity]

In this article, we have explored the greedy algorithm for graph colouring. graph coloring is a special case of graph labeling ; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints.

graph algorithm

Kruskal Minimum Spanning Tree Algorithm

Kruskal's algorithm is a minimum-spanning-tree algorithm which finds an edge of the least possible weight that connects any two trees in the forest. It is a greedy algorithm in graph theory as it finds a minimum spanning tree for a connected weighted graph adding increasing cost arcs at each step