![]() So, recursion seems to be the most generic way to solve the problem. Thus, we are recurring to make permutations here. It can be easily noticed that for the number 1234, we are first making permutations of 234 first and for 234, permutations of 34 and so on. So, you have understood the logic of making the permutations. Similarly, after having the permutation of last three digits, we will replace the first digit and will again get all the permutations of the last three digits. Now, we made the permutation of these digits and got 13. For example, After making all the permutations of 34 (34 and 43) and getting the numbers 12, we replaced 2 with 3 (2 was the last fixed digit in the number). After having all the permutations of the smaller number, we are just replacing one of the digits of this new number with the last digit which was fixed and again making permutations of the newer number. You can see that we are breaking the problem into smaller problems and then making the permutations of these smaller ones. Similarly, we will keep all other digits at the first position and get the corresponding permutations. Now, we have all the numbers which can be made by keeping 1 at the first position. Thus the numbers obtained are:Īgain, keeping 4 fixed out of 2, 3 and 4. So, we will make the permutations of 2, 3 and 4 by keeping 2 fixed. And we have to make all the permutations of the digits 2, 3 and 4. Thus, we are left with the digits 2, 3 and 4. We will start by keeping 1 at the first position. So, let's use this logic to make the permutations of the digits 1, 2, 3 and 4. And of course, making permutations of only 3 digits is quite easy. So, now we have all our permutations which can be made by the digits 1, 2 and 3. Similarly, keeping 3 at the first position, the numbers are: So, let's keep 2 at the first position this time and make the permutations. Thus the numbers obtained by keeping 1 fixed are: 1, fixed, and will make the permutations of the other numbers. One way I am going to make the permutation is: I will start by keeping the first number, i.e. So before going into the coding part, let's first understand the logic of making the permutations in reality and then we will code that logic. Writing the code for a problem is not a big deal if you know how to solve the problem practically or understand the logic of solving the problem in reality. This is also a very common question of computer programming. In: Proceedings of International Conference on DSP, pp.This post is about printing all the permutations of an array with the use of recursion. Sanei, S., Phan, A.H., Lo, J.L., Abolghasemi, V., Cichocki, A.: Compressive sensing approach for progressive transmission of images. In: Proceedings of International Conference on Digital Signal Processing, pp. Gan, L.: Block compressed sensing of natural images. ![]() ![]() In: Proceedings of International Conference on Multimedia and Expo (ICME), pp. Theory 53(12), 4655–4666 (2007)ĭeng, C., Lin, W., Lee, B.S., Lau, C.T.: Robust image compression based on compressive sensing. Tropp, J.A., Gilbert, A.C.: Signal recovery from random measurements via orthogonal matching pursuit. Gao, Z., Xiong, C., Ding, L., Zhou, C.: Image representation using block compressive sensing for compression applications. In: Proceedings of International Conference on Multimedia and Signal Processing, pp. Gao, Z., Xiong, C., Zhou, C., Wang, H.: Compressive sampling with coefficients random permutations for image compression. Candes, E.J., Wakin, M.B.: An introduction to compressive sampling.
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