If it works for the array of size 2, it should work for an array of any size. We remove 2, since this is our first element now and get just. Then we add the missing 1 back to the nums array, we get nums =. In order to complete the permutations array, we should add the missing 1 to the permutations returned by the base case, which will get us ]. If we remove the first element, we get just, this is our base case. Is there a way to reduce this input to our base case? This process is repeated for each element, resulting in all possible permutations. Starting from the first element, we swap it with each element that comes after it, generating new permutations recursively. Then we need to handle the results returned by the base case in the recursive case and return the new result.įor example, let us take the array of size 2: nums =. To generate all permutations of an input array, we can use the backtracking algorithm. If we do that, the recursive case should work it's way to the base case. How do we reduce our initial problem to the base case? We could simply go through each element of the array, removing the first element of the array. Why? Permutations of the array is just ], we know that for certain, there is no need to do any extra operations here. The problem Permutations Leetcode Solution provides a simple sequence of integers and asks us to return a complete vector or array of all the permutations. Now, the base case is definitely an array of size 1. This is where the backtracking part fits in. In this problem all we have is a nums array, so probably we need to shrink the array size, until we hit the base case, and then work our way up, while keeping in mind the fact that we shrunk the array size, we do not want to lose any data. In order for the algorithm to work, we need our recursive case to get to the base case eventually by decreasing the problem size. For recursion-based solution, we have to figure out what is the base case for recursive calls and what is the recursive case. For example, 1,2,3 have the following permutations: 1. You can return the answer in any order.Īccording to LeetCode itself, the problem is suggested to be solved with recursion/backtracking. Problem: Given a collection of numbers, return all possible permutations. Given an array nums of distinct integers, return all the possible permutations. Also we will beat 94% of JS solutions on the site □ (at the time of writing). In this post, you will find the solution for the Permutations in C++, Java & Python-LeetCode problem. Let's dive into one of the LeetCode problems which is a great example to learn recursive/backtracking approach to solving algorithmic problems.
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