Xi, a developmental biologist is working on developmental distances of chromosomes. A chromosome, in the Xi‘s simplistic view, is a permutation from n genes numbered 1 to n. Xi is working on an evolutionary distance metric between two chromosomes. In Xi‘s theory of evolution any subset of genes lying together in both chromosomes is a positive witness for chromosomes to be similar.
A positive witness is a pair of sequence of the same length A and A‘, where A is a consecutive subsequence of the first chromosome, A‘ is a consecutive subsequence of the second chromosome, and A is a permutation ofA‘. The goal is to count the number of positive witnesses of two given chromosomes that have a length greater than one.
Input
There are several test case in the input. Each test case starts with a line containing the number of genes(2n3000). The next two lines contain the two chromosomes, each as a list of positive integers. The input terminates with a line containing ``0‘‘ which should not be processed as a test case.
Output
For each test case, output a single line containing the number of positive witness for two chromosomes to be similar.
Sample Input
4 3 2 1 4 1 2 4 3 5 3 2 1 5 4 3 2 1 5 4 0
Sample Output
3 10
题意:说白了就是求两个集合有几个相同的连续子集。
思路:记录下第二个集合每个数的位置。然后去枚举第一个集合。把子集内的数字位置的Max和Min记录下来,然后如果Max - Min + 1 == len说明集合长度相同。在记录过程中,利用了类似前缀和的思想,复杂度为O(n^2)。
代码:
#include <stdio.h> #include <string.h> #define max(a,b) ((a)>(b)?(a):(b)) #define min(a,b) ((a)<(b)?(a):(b)) const int N = 3005; int n, a[N], vis[N]; void init() { int num; for (int i = 0; i < n; i++) scanf("%d", &a[i]); for (int j = 0; j < n; j++) { scanf("%d", &num); vis[num] = j; } } int solve() { int ans = 0; for (int i = 0; i < n; i++) { int Max = vis[a[i]], Min = vis[a[i]], len = 1; for (int j = i + 1; j < n; j++) { Max = max(Max, vis[a[j]]); Min = min(Min, vis[a[j]]); len++; if (Max - Min + 1 == len) { ans++; } } } return ans; } int main() { while (~scanf("%d", &n) && n) { init(); printf("%d\n", solve()); } return 0; }