Find the smallest index l such that a[k] < a[l]. Next Permutation Algorithm in Java 1 minute read In this post, I will tell you how to write the next permutation algorithm in Java. Any arrangement of any r â¤ n of these objects in a given order is called an r-permutation or a permutation of n object taken r at a time. C++ Algorithm next_permutation () function is used to reorder the elements in the range [first, last) into the next lexicographically greater permutation. I think there is a simplier way to work with permutations in Java: > For example, it lasts 0,3s to generate all lucky numbers (containing only digits 4 and 7) with length 24 (there are 24!/12!/12! Message Delivery Models in Distributed Systems. Java program to get the all permutation of a string : In this tutorial, we will learn how to print all the permutation of a string . Lately, I came accross with the CAP Theorem a few times so I want to read and learn about it. But this method is tricky because it involves recursion, stack storage, and skipping over duplicate values. I like Java the most. These two terms are always confused and I also was not aware of all the details. If such arrangement is not possible, it must be rearranged as the lowest possible order ie, sorted in an ascending order. I like Java the most. * Permutations 26/10/2015 PERMUTE CSECT USING PERMUTE,R15 set base register LA R9,TMP-A n=hbound(a) SR R10,R10 nn=0 So, an example code piece is like the following: Categories: Solving a permutation problem with recursion has been particularly difficult for me to wrap my head around. Java Stream to List. A permutation is each one of the N! Lecture. For exampl Permutation is denoted as nPr and combination is denoted as nCr. It changes the given permutation in-place. If such arrangement is not possible, it must rearrange it as the lowest possible order (ie, sorted in ascending order). such numbers). Loading... Unsubscribe from Aaron Writes Code? Permutation and Combination are a part of Combinatorics. kjkrol / Permutation.java. edit: corrected the "definition" of lucky number. Find the largest index l greater than k such that a[k] < a[l]. Your code generates permutation correctly if all elements are different, if there are same elements it generates same sequences. Iâve encountered this problem in one of the hackerrank challenge..Java is missing built-in nextPermutation() method, whereas C++ has one. α(m, n) time complexity of Union-Find. The replacement must be in-place, do not allocate extra memory. whereas C++ has one. Get code examples like "java next_permutation" instantly right from your google search results with the Grepper Chrome Extension. It is used to rearrange the elements in the range [first, last) into the next lexicographically greater permutation. Java Next Permutation of a String Algorithm Aaron Writes Code. But there is at least one thing missing in Java for sure â permutations. Implement next permutation, which rearranges numbers into the lexicographically next greater permutation of numbers. For example, it lasts 0,3s to generate all lucky numbers (containing only digits 4 and 7, where number of 4s and 7s is the same) with length 24 (there are 24!/12!/12! â¦ It has following lexicographic permutations with repetition of characters - AAA, AAB, AAC, ABA, ABB, ABC, â¦ ... Our next problem description is the following: Check Permutation: Given two strings, write a method to decide if one is a permutation of the other. in his blog.The logic behind this is: -Sort the sequence in increasing order There is a wikipedia link I suggest you to read to better understand the topic. nPr means permutation of â¦ Second, we'll look at some constraints. UVa_465_Overflow.java 10115 - Automatic Editing Constructing All Subsets Constructing All Permutations InterviewStreet: Flowers InterviewStreet: Pairs SRM268 SRM302 SRM342 SRM232 SRM356 If such an arrangement is not possible, it must rearrange it as the lowest possible order (i.e., sorted in ascending order). In this post, I will tell you how to write the next permutation algorithm in Java. A permutation is specified as each of several possible ways in which a set or number of things can be ordered or arranged. Each one of you have some preference. If no such index exists, the permutation is the last permutation. "23" in the first iteration. Infact I found the explanation under that link really useful. The function is next_permutation(a.begin(), a.end()). Table of Contents1 Using Collectors.toList()2 Using Collectors.toCollection()3 Using foreach4 Filter Stream and convert to List5 Convert infinite Stream to List In this post, we will see how to convert Stream to List in java. Also if there is need to generate only permutations from some permutation, for example: "generate all permutations of 11 elements, lexicographically greater than [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]", but your code was not meant to do it I know, I will rename the blog entry. Rearranges the elements in the range [first,last) into the next lexicographically greater permutation. In this post, we will see how to find all lexicographic permutations of a string where repetition of characters is allowed. Why so many downvotes for this comment ? If such arrangement is not possible, it must rearrange it as the lowest possible order (ie, sorted in ascending order). Suppose we have a finite sequence of numbers like (0, 3, 3, 5, 8), and want to generate all its permutations. Problem statement: Now this algorithm is not as complex as it seems. The function is next_permutation(a.begin(), a.end()). possible arrangements the elements can take (where N is the number of elements in the range). Star 0 Fork 1 Star Permutation Check in Java. Lets say you have String as ABC. Java program to find Permutation and Combination ( nPr and nCr ) of two numbers : In this example, we will learn how to find permutation and combination of two numbers. Reverse the sequence from a[k + 1] up to and including the final element a[n]. We are going to use recursive approach to print all the permutations. possible arrangements the elements can take (where N is the number of elements in the range). input 4 5 8 7 1 output 4 7 1 5 8 1> Find the largest index k such that a[k] < a[k + 1]. The class has several methods to walk or jump through the list of possible permutations. The only programming contests Web 2.0 platform, Educational Codeforces Round 102 (Rated for Div. The following algorithm generates the next permutation lexicographically after a given permutation. Permutation is the different arrangements that a set of elements can make if the elements are â¦ There are 2^24 lucky numbers of length 24; you said about lucky numbers which have equal numbers of '4' and '7'. Thanks for correction, of course lucky numbers in problem statements are the numbers that have only 4 and 7 digits and count of 4s and 7s is the same O:-). LeetCode â Next Permutation (Java) Implement next permutation, which rearranges numbers into the lexicographically next greater permutation of numbers. Subscribe Subscribed Unsubscribe 1.16K. The above code is inspired by wikipedia. The naive way would be to take a top-down, recursive approach. Probably most of you know, that number of permutations is n!, so checking all permutations is ok when n <= 10. Next Permutation in Java Codechef: CodeWars 2012 UVa_00156_Ananagrams.java UVa_10474_Where_is_the_Marble.java InterviewStreet: Equation. Permutation(int[] map) Construct the permutation where point i+1 goes to map[i]. First, thanks for correction for definition of lucky number. Coders always argue which programming language is better. Implement the next permutation, which rearranges numbers into the numerically next greater permutation of numbers. Bertram 36 For Sale, If You Care Parchment Paper Max Temp, Frog Monkey Bubble, Kensington Hotel Great Yarmouth, 2020 Wr250f Top Speed, Defiance College Student Population, " /> Find the smallest index l such that a[k] < a[l]. Next Permutation Algorithm in Java 1 minute read In this post, I will tell you how to write the next permutation algorithm in Java. Any arrangement of any r â¤ n of these objects in a given order is called an r-permutation or a permutation of n object taken r at a time. C++ Algorithm next_permutation () function is used to reorder the elements in the range [first, last) into the next lexicographically greater permutation. I think there is a simplier way to work with permutations in Java: > For example, it lasts 0,3s to generate all lucky numbers (containing only digits 4 and 7) with length 24 (there are 24!/12!/12! Message Delivery Models in Distributed Systems. Java program to get the all permutation of a string : In this tutorial, we will learn how to print all the permutation of a string . Lately, I came accross with the CAP Theorem a few times so I want to read and learn about it. But this method is tricky because it involves recursion, stack storage, and skipping over duplicate values. I like Java the most. These two terms are always confused and I also was not aware of all the details. If such arrangement is not possible, it must be rearranged as the lowest possible order ie, sorted in an ascending order. I like Java the most. * Permutations 26/10/2015 PERMUTE CSECT USING PERMUTE,R15 set base register LA R9,TMP-A n=hbound(a) SR R10,R10 nn=0 So, an example code piece is like the following: Categories: Solving a permutation problem with recursion has been particularly difficult for me to wrap my head around. Java Stream to List. A permutation is each one of the N! Lecture. For exampl Permutation is denoted as nPr and combination is denoted as nCr. It changes the given permutation in-place. If such arrangement is not possible, it must rearrange it as the lowest possible order (ie, sorted in ascending order). such numbers). Loading... Unsubscribe from Aaron Writes Code? Permutation and Combination are a part of Combinatorics. kjkrol / Permutation.java. edit: corrected the "definition" of lucky number. Find the largest index l greater than k such that a[k] < a[l]. Your code generates permutation correctly if all elements are different, if there are same elements it generates same sequences. Iâve encountered this problem in one of the hackerrank challenge..Java is missing built-in nextPermutation() method, whereas C++ has one. α(m, n) time complexity of Union-Find. The replacement must be in-place, do not allocate extra memory. whereas C++ has one. Get code examples like "java next_permutation" instantly right from your google search results with the Grepper Chrome Extension. It is used to rearrange the elements in the range [first, last) into the next lexicographically greater permutation. Java Next Permutation of a String Algorithm Aaron Writes Code. But there is at least one thing missing in Java for sure â permutations. Implement next permutation, which rearranges numbers into the lexicographically next greater permutation of numbers. For example, it lasts 0,3s to generate all lucky numbers (containing only digits 4 and 7, where number of 4s and 7s is the same) with length 24 (there are 24!/12!/12! â¦ It has following lexicographic permutations with repetition of characters - AAA, AAB, AAC, ABA, ABB, ABC, â¦ ... Our next problem description is the following: Check Permutation: Given two strings, write a method to decide if one is a permutation of the other. in his blog.The logic behind this is: -Sort the sequence in increasing order There is a wikipedia link I suggest you to read to better understand the topic. nPr means permutation of â¦ Second, we'll look at some constraints. UVa_465_Overflow.java 10115 - Automatic Editing Constructing All Subsets Constructing All Permutations InterviewStreet: Flowers InterviewStreet: Pairs SRM268 SRM302 SRM342 SRM232 SRM356 If such an arrangement is not possible, it must rearrange it as the lowest possible order (i.e., sorted in ascending order). In this post, I will tell you how to write the next permutation algorithm in Java. A permutation is specified as each of several possible ways in which a set or number of things can be ordered or arranged. Each one of you have some preference. If no such index exists, the permutation is the last permutation. "23" in the first iteration. Infact I found the explanation under that link really useful. The function is next_permutation(a.begin(), a.end()). Table of Contents1 Using Collectors.toList()2 Using Collectors.toCollection()3 Using foreach4 Filter Stream and convert to List5 Convert infinite Stream to List In this post, we will see how to convert Stream to List in java. Also if there is need to generate only permutations from some permutation, for example: "generate all permutations of 11 elements, lexicographically greater than [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]", but your code was not meant to do it I know, I will rename the blog entry. Rearranges the elements in the range [first,last) into the next lexicographically greater permutation. In this post, we will see how to find all lexicographic permutations of a string where repetition of characters is allowed. Why so many downvotes for this comment ? If such arrangement is not possible, it must rearrange it as the lowest possible order (ie, sorted in ascending order). Suppose we have a finite sequence of numbers like (0, 3, 3, 5, 8), and want to generate all its permutations. Problem statement: Now this algorithm is not as complex as it seems. The function is next_permutation(a.begin(), a.end()). possible arrangements the elements can take (where N is the number of elements in the range). Star 0 Fork 1 Star Permutation Check in Java. Lets say you have String as ABC. Java program to find Permutation and Combination ( nPr and nCr ) of two numbers : In this example, we will learn how to find permutation and combination of two numbers. Reverse the sequence from a[k + 1] up to and including the final element a[n]. We are going to use recursive approach to print all the permutations. possible arrangements the elements can take (where N is the number of elements in the range). input 4 5 8 7 1 output 4 7 1 5 8 1> Find the largest index k such that a[k] < a[k + 1]. The class has several methods to walk or jump through the list of possible permutations. The only programming contests Web 2.0 platform, Educational Codeforces Round 102 (Rated for Div. The following algorithm generates the next permutation lexicographically after a given permutation. Permutation is the different arrangements that a set of elements can make if the elements are â¦ There are 2^24 lucky numbers of length 24; you said about lucky numbers which have equal numbers of '4' and '7'. Thanks for correction, of course lucky numbers in problem statements are the numbers that have only 4 and 7 digits and count of 4s and 7s is the same O:-). LeetCode â Next Permutation (Java) Implement next permutation, which rearranges numbers into the lexicographically next greater permutation of numbers. Subscribe Subscribed Unsubscribe 1.16K. The above code is inspired by wikipedia. The naive way would be to take a top-down, recursive approach. Probably most of you know, that number of permutations is n!, so checking all permutations is ok when n <= 10. Next Permutation in Java Codechef: CodeWars 2012 UVa_00156_Ananagrams.java UVa_10474_Where_is_the_Marble.java InterviewStreet: Equation. Permutation(int[] map) Construct the permutation where point i+1 goes to map[i]. First, thanks for correction for definition of lucky number. Coders always argue which programming language is better. Implement the next permutation, which rearranges numbers into the numerically next greater permutation of numbers. Bertram 36 For Sale, If You Care Parchment Paper Max Temp, Frog Monkey Bubble, Kensington Hotel Great Yarmouth, 2020 Wr250f Top Speed, Defiance College Student Population, " /> Tipareste

# next permutation in java

Cancel Unsubscribe. We could pick the first element, then recurse and pick the second element from the remaining ones, and so on. Swap the value of a[k] with that of a[l]. It just doesnât seem as natural as iteration. Next Permutation. http://www.uwe-alex.de/Permutation/Permutation.html, https://www.quora.com/How-would-you-explain-an-algorithm-that-generates-permutations-using-lexicographic-ordering. Permutation and Combinations: Permutation: Any arrangement of a set of n objects in a given order is called Permutation of Object. Every digit can be either 4 or 7, no other restrictions, so it should be 2^24, shouldn't it? Moreover, this guy also explained very well C has a function (next_permutation ()), that modifies permutation (parameter) to next permutation (lexicographically greater), if such permutation exists is function return value is true, false otherwise. -Repeat the following algorithm until it returns false: In this post, we will see how to find all permutations of String in java. This is a really good explanation of the derivation of the algorithm: https://www.quora.com/How-would-you-explain-an-algorithm-that-generates-permutations-using-lexicographic-ordering. The Method next() creates the next Permutation, the method next(int n) creates the first Permutation wich is greater than this and has a change in index n Example: Permutation: 0 1 2 3 4 5 6 next(3) Permutation: 0 1 2 4 3 5 6. Implement next permutation, which rearranges numbers into the lexicographically next greater permutation of numbers. Take out first character of String and insert into different places of permutations of remaining String recursively. Permutation(javamath.util.math.OMApplication app) Construct the permutation from an OpenMath application. 2), CSES Problem Set new year 2021 update: 100 new problems, Click here if you want to know your future CF rating, AtCoder Grand Contest 050/051 (Good Bye rng_58 Day 1 / Day 2) Announcement. Recursive call ends when it reaches to base case i.e. Moreover, if we insist on manipulating the sequence in place (without producing tempâ¦ Skip to content. Find the largest index k such that a[k] < a[k + 1]. In this article, we are going to how find next permutation (Lexicographically) from a given one?This problem has been featured in interview coding round of Amazon, OYO room, MakeMyTrip, Microsoft. If such an arrangement is not possible, it must rearrange it as the lowest possible order (i.e., sorted in ascending order). A permutation is each one of the N! What is the best way to do so? It is denoted as N! And third, we'll look at three ways to calculate them: recursively, iteratively, and randomly.We'll focus on the implementation in Java and therefore won't go into a lot of mathematical detail. In this article, we'll look at how to create permutations of an array.First, we'll define what a permutation is. So, we need to build our own method. Update: generating these numbers using bitmasks also takes 0.3 seconds, but is easier to code: 1238640, or with Integer.bitCount() instead of bitcounts array: 1238647. Here is an UVa problem if you want to try your algorithms for obtaining the next permutation: http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=24&page=show_problem&problem=82. C has a function (next_permutation()), that modifies permutation (parameter) to next permutation (lexicographically greater), if such permutation exists is function return value is true, false otherwise. If no such index exists, the permutation is the last permutation. Not Able to solve any question in the contest. Thanks for the link. The replacement â¦ If it's "any number that contains only digits 4 and 7", then I don't understand how you get the quantity of such numbers of length 24. C has a function (next_permutation()), that modifies permutation (parameter) to next permutation (lexicographically greater), if such permutation exists is function return value is true, false otherwise. Permutation algorithm for array of integers in Java - Permutation.java. But there is at least one thing missing in Java for sure — permutations. Find largest index i such that str [i-1] is less than str [i]. We will use a very simple approach to do it. Implement next permutation, which rearranges numbers into the next greater permutation of numbers. The replacement â¦ For example you can replace {"a", "ab", "ab"} with {0, 1, 1}, I did write a class for to handle permutations: http://www.uwe-alex.de/Permutation/Permutation.html. But I've never seen such problems :D. That is the same code as the one above, but I used Comparable intentionally — it can compare other type of objects too, for example Strings, characters (I know that you can do int n = 'a'), BigDecimals and so on without the change. Next, we take out that character and pass the remaining characters to permutation method again e.g. Each one of you have some preference. You can always replace your Comparable[] array with an integer permutation. So, we need to build our own method. What's your definition of a lucky number? This sounds awsome. [LeetCode] Next Permutation (Java) July 15, 2014 by decoet. It changes the given permutation in-place. Java â¦ when remaining word becomes empty, at that point "perm" parameter contains a valid permutation to be printed. such numbers). where N = number of elements in the range. The following algorithm generates the next permutation lexicographically after a given permutation. We can also implement our own next_permutation () function. But there is at least one thing missing in Java for sure â permutations. This method can be used to sort data lexicographically. Created Sep 3, 2015. All gists Back to GitHub Sign in Sign up Sign in Sign up {{ message }} Instantly share code, notes, and snippets. It returns âtrueâ if the function could rearrange the object as a lexicographically greater permutation. Permutation() Construct the identity permutation. Java, Implement next permutation, which rearranges numbers into the lexicographically next greater permutation of numbers. Could you please post it here, because the site is down? Permutation(java.lang.String perm) Construct a permutation from a string encoding cycle notation. Is there a way to fix this Appreciate your help. There are multiple ways to convert Stream to List in java. Otherwise, the function returns âfalseâ. I agree. If my input is of larger length and the pivot index( where c[k] Find the smallest index l such that a[k] < a[l]. Next Permutation Algorithm in Java 1 minute read In this post, I will tell you how to write the next permutation algorithm in Java. Any arrangement of any r â¤ n of these objects in a given order is called an r-permutation or a permutation of n object taken r at a time. C++ Algorithm next_permutation () function is used to reorder the elements in the range [first, last) into the next lexicographically greater permutation. I think there is a simplier way to work with permutations in Java: > For example, it lasts 0,3s to generate all lucky numbers (containing only digits 4 and 7) with length 24 (there are 24!/12!/12! Message Delivery Models in Distributed Systems. Java program to get the all permutation of a string : In this tutorial, we will learn how to print all the permutation of a string . Lately, I came accross with the CAP Theorem a few times so I want to read and learn about it. But this method is tricky because it involves recursion, stack storage, and skipping over duplicate values. I like Java the most. These two terms are always confused and I also was not aware of all the details. If such arrangement is not possible, it must be rearranged as the lowest possible order ie, sorted in an ascending order. I like Java the most. * Permutations 26/10/2015 PERMUTE CSECT USING PERMUTE,R15 set base register LA R9,TMP-A n=hbound(a) SR R10,R10 nn=0 So, an example code piece is like the following: Categories: Solving a permutation problem with recursion has been particularly difficult for me to wrap my head around. Java Stream to List. A permutation is each one of the N! Lecture. For exampl Permutation is denoted as nPr and combination is denoted as nCr. It changes the given permutation in-place. If such arrangement is not possible, it must rearrange it as the lowest possible order (ie, sorted in ascending order). such numbers). Loading... Unsubscribe from Aaron Writes Code? Permutation and Combination are a part of Combinatorics. kjkrol / Permutation.java. edit: corrected the "definition" of lucky number. Find the largest index l greater than k such that a[k] < a[l]. Your code generates permutation correctly if all elements are different, if there are same elements it generates same sequences. Iâve encountered this problem in one of the hackerrank challenge..Java is missing built-in nextPermutation() method, whereas C++ has one. α(m, n) time complexity of Union-Find. The replacement must be in-place, do not allocate extra memory. whereas C++ has one. Get code examples like "java next_permutation" instantly right from your google search results with the Grepper Chrome Extension. It is used to rearrange the elements in the range [first, last) into the next lexicographically greater permutation. Java Next Permutation of a String Algorithm Aaron Writes Code. But there is at least one thing missing in Java for sure â permutations. Implement next permutation, which rearranges numbers into the lexicographically next greater permutation of numbers. For example, it lasts 0,3s to generate all lucky numbers (containing only digits 4 and 7, where number of 4s and 7s is the same) with length 24 (there are 24!/12!/12! â¦ It has following lexicographic permutations with repetition of characters - AAA, AAB, AAC, ABA, ABB, ABC, â¦ ... Our next problem description is the following: Check Permutation: Given two strings, write a method to decide if one is a permutation of the other. in his blog.The logic behind this is: -Sort the sequence in increasing order There is a wikipedia link I suggest you to read to better understand the topic. nPr means permutation of â¦ Second, we'll look at some constraints. UVa_465_Overflow.java 10115 - Automatic Editing Constructing All Subsets Constructing All Permutations InterviewStreet: Flowers InterviewStreet: Pairs SRM268 SRM302 SRM342 SRM232 SRM356 If such an arrangement is not possible, it must rearrange it as the lowest possible order (i.e., sorted in ascending order). In this post, I will tell you how to write the next permutation algorithm in Java. A permutation is specified as each of several possible ways in which a set or number of things can be ordered or arranged. Each one of you have some preference. If no such index exists, the permutation is the last permutation. "23" in the first iteration. Infact I found the explanation under that link really useful. The function is next_permutation(a.begin(), a.end()). Table of Contents1 Using Collectors.toList()2 Using Collectors.toCollection()3 Using foreach4 Filter Stream and convert to List5 Convert infinite Stream to List In this post, we will see how to convert Stream to List in java. Also if there is need to generate only permutations from some permutation, for example: "generate all permutations of 11 elements, lexicographically greater than [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]", but your code was not meant to do it I know, I will rename the blog entry. Rearranges the elements in the range [first,last) into the next lexicographically greater permutation. In this post, we will see how to find all lexicographic permutations of a string where repetition of characters is allowed. Why so many downvotes for this comment ? If such arrangement is not possible, it must rearrange it as the lowest possible order (ie, sorted in ascending order). Suppose we have a finite sequence of numbers like (0, 3, 3, 5, 8), and want to generate all its permutations. Problem statement: Now this algorithm is not as complex as it seems. The function is next_permutation(a.begin(), a.end()). possible arrangements the elements can take (where N is the number of elements in the range). Star 0 Fork 1 Star Permutation Check in Java. Lets say you have String as ABC. Java program to find Permutation and Combination ( nPr and nCr ) of two numbers : In this example, we will learn how to find permutation and combination of two numbers. Reverse the sequence from a[k + 1] up to and including the final element a[n]. We are going to use recursive approach to print all the permutations. possible arrangements the elements can take (where N is the number of elements in the range). input 4 5 8 7 1 output 4 7 1 5 8 1> Find the largest index k such that a[k] < a[k + 1]. The class has several methods to walk or jump through the list of possible permutations. The only programming contests Web 2.0 platform, Educational Codeforces Round 102 (Rated for Div. The following algorithm generates the next permutation lexicographically after a given permutation. Permutation is the different arrangements that a set of elements can make if the elements are â¦ There are 2^24 lucky numbers of length 24; you said about lucky numbers which have equal numbers of '4' and '7'. Thanks for correction, of course lucky numbers in problem statements are the numbers that have only 4 and 7 digits and count of 4s and 7s is the same O:-). LeetCode â Next Permutation (Java) Implement next permutation, which rearranges numbers into the lexicographically next greater permutation of numbers. Subscribe Subscribed Unsubscribe 1.16K. The above code is inspired by wikipedia. The naive way would be to take a top-down, recursive approach. Probably most of you know, that number of permutations is n!, so checking all permutations is ok when n <= 10. Next Permutation in Java Codechef: CodeWars 2012 UVa_00156_Ananagrams.java UVa_10474_Where_is_the_Marble.java InterviewStreet: Equation. Permutation(int[] map) Construct the permutation where point i+1 goes to map[i]. First, thanks for correction for definition of lucky number. Coders always argue which programming language is better. Implement the next permutation, which rearranges numbers into the numerically next greater permutation of numbers.

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