最长xx子序列

最长上升子序列

最长公共子序列

最长上升子序列

朴素算法 O(n*n)

dp[i]表示以a[i]为末尾的最长上升子序列的长度

#include <iostream>#include <algorithm>#include <cstdio>using namespace std;const int maxn = 100010;const int inf = 0x3f3f3f3f;int a[maxn],dp[maxn];int main(){    int n;    while(~scanf("%d",&n))    {        for(int i = 0;i<n;i++)        {            scanf("%d",&a[i]);            dp[i] = 1;        }        int ans = 0;        for(int i = 1;i<n;i++)        {            for(int j = 0;j<i;j++)                if(a[j] < a[i])                    dp[i] = max(dp[i],dp[j] + 1);            ans = max(ans,dp[i]);        }        printf("%d\n",ans);    }}

O(nlogn)

dp[i] = 长度为i+1的上升子序列中末尾元素的最小值，直接运用STL 中的lower_bound()很方便

#include <iostream>#include <algorithm>#include <cstdio>using namespace std;const int maxn = 100010;const int inf = 0x3f3f3f3f;int a[maxn],dp[maxn];int main(){    int n;    while(~scanf("%d",&n))    {        for(int i = 0;i<n;i++)        {            scanf("%d",&a[i]);            dp[i] = inf;        }        for(int i = 0;i<n;i++)        {            a[i] = *lower_bound(dp,dp+n,a[i]) = a[i];        }        printf("%d\n",lower_bound(dp,dp+n,inf) - dp);    }}

最长公共子序列

#include <iostream>#include <algorithm>#include <cstring>using namespace std;string s1,s2;int dp[1010][1010];int main(){    while(cin >> s1 >> s2)    {        int len1 = s1.length();        int len2 = s2.length();        memset(dp,0,sizeof dp);        for(int i = 1;i<=len1;i++)        {            for(int j = 1;j<=len2;j++)            {                if(s1[i-1] == s2[j-1])                {                    dp[i][j] = dp[i-1][j-1] + 1;                }                else                    dp[i][j] = max(dp[i-1][j],dp[i][j-1]);            }        }        cout<<dp[len1][len2]<<endl;    }}