给定n个大小不等的圆c , c , , cn 1 2  ，现要将这n个圆排进一个矩形框中，且要求各圆与矩形框的底边相切。圆排列问题要求从n个圆的所有排列中找出有最小长度的圆排列。例如，当n=3，且所给的3 个圆的半径分别为1，1，2时，这3个圆的最小长度的圆排列如图所示。其最小长度为2 + 4 2 。-Given n circles of varying sizes c, c,, cn 1 2  , now to the n rows into a round rectangle, and require each circle and tangent to the bottom edge of the rectangle. Circular permutation problem requires from all permutations of n circles to find a minimum length, arranged in a circle. For example, when n = 3, and the three given radius of the circle, respectively 1,1,2, this minimum length of three round circle arrangement shown in Fig. The minimum length is 2+ 4 2.