Algorithm Design Solution Manual
565 84 17MB
English Pages [207]
Recommend Papers
![The Algorithm Design Manual [3° ed.]
3030542556, 9783030542559](https://ebin.pub/img/200x200/the-algorithm-design-manual-3nbsped-3030542556-9783030542559.jpg)
![Design of Fluid Thermal Systems Solution Manual [4th Edition]](https://ebin.pub/img/200x200/design-of-fluid-thermal-systems-solution-manual-4th-edition.jpg)
![Microelectronics Circuit Analysis and Design - Solution Manual [4 ed.]](https://ebin.pub/img/200x200/microelectronics-circuit-analysis-and-design-solution-manual-4nbsped.jpg)
![Electronic Circuit Analysis and Design - solution manual [2Rev Ed]
0072320923](https://ebin.pub/img/200x200/electronic-circuit-analysis-and-design-solution-manual-2rev-ed-0072320923.jpg)
- Author / Uploaded
- Jon Kleinberg
- Éva Tardos
File loading please wait...
Citation preview
Suppose m ≤ n, and let L denote the maximum length of any string in A ∪ B. Suppose there is a string that is a concatenation over both A and B, and let u be one of minimum length. We claim that the length of u is at most n2 L2 . For suppose not. First, we say that position p in u is of type (ai , k) if in the concatenation over A, it is represented by position k of string ai . We define type (bi , k) analogously. Now, if the length of u is greater than n2 L2 , then by the pigeonhole principle, there exist positions p and p in u, p < p , so that both are of type (ai , k) and (bj , k) for some indices i, j, k. But in this case, the string u obtained by deleting positions p, p + 1, . . . , p − 1 would also be a concatenation over both A and B. As u is shorter than u, this is a contradiction.
1
ex690.144.299
1