Permutations

Implement next permutation, which rearranges numbers into the lexicographically next greater permutation of numbers.

If such arrangement is not possible, it must rearrange it as the lowest possible order (ie, sorted in ascending order).

The replacement must be in-place, do not allocate extra memory.

Here are some examples. Inputs are in the left-hand column and its corresponding outputs are in the right-hand column.
1,2,3 → 1,3,2
3,2,1 → 1,2,3

1,1,5 → 1,5,1




class Solution:    # @param num, a list of integer    # @return a list of lists of integers    def permute(self, num):        ret=[num]        while True:            new_num = self.nextPermutation(ret[-1])            if new_num != num:                ret.append(new_num)            else:                break        return ret    # @param num, a list of integer    # @return a list of integer    def nextPermutation(self, num):        num_copy=num[:]        if len(num_copy)<=1:            return num_copy                   #right to left ,find partition index        partition_index = -1        for i in range(len(num_copy)-2,-1,-1):            if num_copy[i] < num_copy[i+1]:                partition_index=i                break        #could not find        if partition_index==-1:            num_copy.reverse()            return num_copy        #right to left ,find change index        change_index=-1        for i in range(len(num_copy)-1,-1,-1):            if num_copy[i] > num_copy[partition_index]:                change_index=i                break        #swap        num_copy[partition_index],num_copy[change_index]=num_copy[change_index],num_copy[partition_index]        num_copy[partition_index+1:] = reversed(num_copy[partition_index+1:])        return num_copy