Gargari got bored to play with the bishops and now, after solving the problem about them, he is trying to do math homework. In a math book he have foundk permutations. Each of them consists of numbers1, 2, ..., n in some order. Now he should find the length of the longest common subsequence of these permutations. Can you help Gargari?
You can read about longest common subsequence there: https://en.wikipedia.org/wiki/Longest_common_subsequence_problem
The first line contains two integers n andk (1 ≤ n ≤ 1000; 2 ≤ k ≤ 5). Each of the nextk lines contains integers 1, 2, ..., n in some order — description of the current permutation.
Print the length of the longest common subsequence.
4 3 1 4 2 3 4 1 2 3 1 2 4 3
3
The answer for the first test sample is subsequence [1, 2, 3].
题意:求k个长度为n的最长公共子序列
思路1:保存每一个数在各自串的位置,由于结果是第1个串中的某个可能,所以我们枚举第1个串的可能,然后检查假设一个以a[j]为结束的最长公共子序列成立的情况是,对于每一个串的a[i]都在a[j]的前面,那么就有dp[j] = max(dp[j], dp[i]+1)
#include <iostream> #include <cstring> #include <cstdio> #include <algorithm> using namespace std; const int maxn = 1010; int n, k; int a[maxn][maxn], b[maxn][maxn], dp[maxn]; int check(int x, int y) { for (int i = 2; i <= k; i++) if (b[i][x] > b[i][y]) return 0; return 1; } int main() { scanf("%d%d", &n, &k); for (int i = 1; i <= k; i++) for (int j = 1; j <= n; j++) { scanf("%d", &a[i][j]); b[i][a[i][j]] = j; } for (int i = 1; i <= n; i++) dp[i] = 1; int ans = 0; for (int i = 1; i <= n; i++) { for (int j = i+1; j <= n; j++) { if (check(a[1][i], a[1][j])) dp[j] = max(dp[i]+1, dp[j]); } } for (int i = 1; i <= n; i++) ans = max(ans, dp[i]); printf("%d ", ans); return 0; }
思路2:假设一个数字i在每一个串的位置都在j前面,那么i到j就有一条有向边,那么题目就转换为DAG求最长
#include <iostream> #include <cstdio> #include <cstring> #include <algorithm> #include <vector> using namespace std; const int maxn = 1010; int num[10][maxn], vis[maxn]; int n, k; vector<int> g[maxn]; int check(int x, int y) { for (int i = 0; i < k; i++) if (num[i][x] >= num[i][y]) return 0; return 1; } int dfs(int x) { int ans = 0; if (vis[x]) return vis[x]; int size = g[x].size(); for (int i = 0; i < size; i++) ans = max(ans, dfs(g[x][i])); return vis[x] = ans + 1; } int main() { scanf("%d%d", &n, &k); memset(vis, 0, sizeof(vis)); for (int i = 0; i <= n; i++) g[i].clear(); int a; for (int i = 0; i < k; i++) for (int j = 1; j <= n; j++) { scanf("%d", &a); num[i][a] = j; } for (int i = 1; i <= n; i++) for (int j = 1; j <= n; j++) if (check(i, j)) g[i].push_back(j); int ans = 0; for (int i = 1; i <= n; i++) if (!vis[i]) ans = max(ans, dfs(i)); printf("%d ", ans); return 0; }