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Algorithms Articles
Page 24 of 39
Rod Cutting
A rod is given of length n. Another table is also provided, which contains different size and price for each size. Determine the maximum price by cutting the rod and selling them in the market.To get the best price by making a cut at different positions and comparing the prices after cutting the rod.Let the f(n) will return the max possible price after cutting a row with length n. We can simply write the function f(n) like this.f(n) := maximum value from price[i]+f(n – i – 1), where i is in range 0 to (n – 1).Input and OutputInput:The price ...
Read MoreShortest Common Super Sequence
Shortest common super-sequence is a sequence where each element of both of the given sequences is present. In other words, we can say that the given two strings, both are sub-sequence of Shortest Common Super-Sequence.When there are no common characters in two strings, then we can simply concatenate them to get Super-sequence. But when they have some common characters, then firstly we have to find the longest string, then add extra characters of the other string.Input and OutputInput: Two strings. “ABCDEF” and “XYDEF” Output: The length of the shortest common super-sequence. Here the super-sequence is “ABCDEFXY”. So the length is ...
Read MoreUgly Numbers
Ugly numbers are those number whose prime factors are 2, 3 or 5. From 1 to 15, there are 11 ugly numbers 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15. The numbers 7, 11, 13 are not ugly because they are prime. The number 14 is not ugly because in its prime factor the 7 will come.In this program, we will try to find the nth ugly number.Input and OutputInput: Take the term number. Say it is 10 Output: The 10th ugly number is 12AlgorithmgetUglyNumbers(n)Input: The number of terms.Output: Find nth Ugly numbers.Begin define array named ...
Read MoreWord Wrap Problem
A sequence of words is given, there is a limit on the number of characters for each line. By putting line breaks, in such a way that lines are printed clearly.The lines must be balanced, when some lines have lots of extra spaces and some lines are containing a small number of extra spaces, it will balance them to separate lines. It tries to use the same number of extra spaces to make them balanced.This algorithm will produce how many words can be placed in one line, and how many lines are needed.Input and OutputInput: The length of words for ...
Read MoreWeighted Job Scheduling
A list of different jobs is given, with the starting time, the ending time and profit of that job are also provided for those jobs. Our task is to find a subset of jobs, where the profit is maximum and no jobs are overlapping each other.In this algorithm, we use a table to store the results of sub-problems and using the results of subproblems, the whole problem can be solved in a bottom-up manner.The time complexity of this algorithm is O(n^2), but we can change it to O(n Log n) by using a binary search method to search con-conflicting jobs.Input ...
Read MoreConvert Infix to Prefix Expression
To solve expressions by the computer, we can either convert it in postfix form or to the prefix form. Here we will see how infix expressions are converted to prefix form.At first infix expression is reversed. Note that for reversing the opening and closing parenthesis will also be reversed.for an example: The expression: A + B * (C - D)after reversing the expression will be: ) D – C ( * B + Aso we need to convert opening parenthesis to closing parenthesis and vice versa.After reversing, the expression is converted to postfix form by using infix to postfix algorithm. ...
Read MoreMinimum Number of Jumps Problem
In this problem, a list of positive integers is given. Each integer is denoting that how many maximum steps that can be made from the current element. Starting from the first element, we have to find the minimum number of jumps to reach the end item of the list.For the dynamic programming approach, a jumps array is defined to store the minimum number of jumps required. Like for a value of jumps[i], it indicates that how many minimum jumps are needed to reach the ith index of the array from the 0th index.Input and OutputInput: A list of integers. {1, ...
Read MoreMinimum number of squares whose sum equals to given number
Any numbers can be represented by the sum of some perfect square numbers. In this problem, we need to find that how many minimum numbers of perfect square terms are needed to represent the given value.let the value is 94, so 95 = 92 + 32 + 22 + 12. so the answer will be 4The idea is to start from 1, we move further to get perfect squared numbers. When the value is 1 to 3, they must be formed with only 1s.Input and OutputInput: An integer number. Say 63. Output: Number of squared terms. Here the answer is ...
Read MoreBreak Number Into 3 parts to find max sum
A number is given. Our task is to break the number three times by n/2, n/3, and n/4 and find maximum sum we can make by dividing the number into three parts.For an example, 50 can be divided into {25, 16, 12}, now break each of the set {25, 16, 12}, into three divisions again, and so on. After completing the division up to 3 times, we will calculate the sum to find the maximum of them.This program can be solved in a recursive way, but in the recursive approach, we need to find the same results for multiple times, ...
Read MoreMobile Numeric Keypad Problem
In this problem, a Numeric mobile keypad is given. We can only press top, bottom, right and left buttons of the current button, diagonal keys are not Allowed. We also cannot press the * and # buttons in the keypad.A digit is given, we have to find the number of possible numbers of given digits can be formed, using the keypad, maintaining given rules.Input and OutputInput: Digit count. Say 3 digit numbers. Output: Number of possible 3 digit numbers, that can be formed with the given conditions. Here the answer is 138.AlgorithmgetCount(n)Input: number of digits n.Output: Possible ways to type n ...
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