LCIS-最长公共上升子序列

Posted 2021-02-16 dongdong25800

 

 

LCS最长公共子序列
for(int i=1; i<=n; i++)
    for(int j=1; j<=m; j++)
    {
        if(a[i]==b[j])
            f[i][j]=f[i-1][j-1]+1;
        else
            f[i][j]=max(f[i-1][j],f[i][j-1]);
    }

LIS最长上升子序列
for(int i=2; i<=n; i++)
    for(int j=1; j<i; j++)
    {
        if(a[i]>a[j])
            f[i]=max(f[i],f[j]+1);
        ans=max(ans,f[i]);
    }


// 例题：LCIS，O(N^3)
for (int i = 1; i <= n; i++)
    for (int j = 1; j <= m; j++)
        if (a[i] == b[j])
        {
            for (int k = 0; k < j; k++)
                if (b[k] < a[i])
                    f[i][j] = max(f[i][j], f[i - 1][k] + 1);
        }
        else f[i][j] = f[i - 1][j];


// 例题：LCIS，O(N^2)
for (int i = 1; i <= n; i++)
{
    // val是决策集合S(i,j)中f[i-1][k]的最大值
    int val = 0;
    // j=1时，0可以作为k的取值
    if (b[0] < a[i]) val = f[i - 1][0];
    for (int j = 1; j <= m; j++)
    {
        if (a[i] == b[j]) f[i][j] = val + 1;
        else f[i][j] = f[i - 1][j];
        // j即将增大为j+1，检查j能否进入新的决策集合
        if (b[j] < a[i]) val = max(val, f[i - 1][j]);
    }
}