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  • Acwing272 最长公共上升子序列

    题目大意:给定两个大小为n的数组,让你找出最长公共上升子序列的长度。

    分析:这是一个比较好的dp题,LIS和LCS两大经典线性dp问题相结合,简称LCIS。

    代码(O(n*n*n)写法):

    #include<bits/stdc++.h>
    using namespace std;
    const int maxn = 3e3+7;
    int a[maxn],b[maxn];
    int dp[maxn][maxn];
    int main() {
        int n;
        cin >> n;
        for (int i = 1; i <= n; i++)
            cin >> a[i];
        for (int i = 1; i <= n; i++)
            cin >> b[i];
        a[0] = b[0] = -0x3f3f3f3f;
        for (int i = 1; i <= n; i++) {
            for (int j = 1; j <= n; j++) {
                if (a[i] == b[j]) {
                    for (int k = 0; k < j; k++) {
                        if (b[k] < a[i])
                            dp[i][j] = max(dp[i][j], dp[i - 1][k] + 1);
                    }
                } else dp[i][j] = dp[i - 1][j];
            }
        }
        int ans = 0;
        for (int i = 1; i <= n; i++) {
            for (int j = 1; j <= n; j++) {
                ans = max(ans, dp[i][j]);
            }
        }
        cout << ans << endl;
        return 0;
    }

    代码(O(n*n)写法):

    #include<bits/stdc++.h>
    using namespace std;
    const int maxn = 3e3+7;
    int a[maxn],b[maxn];
    int dp[maxn][maxn];
    int main() {
        int n;
        cin >> n;
        for (int i = 1; i <= n; i++)
            cin >> a[i];
        for (int i = 1; i <= n; i++)
            cin >> b[i];
        a[0] = b[0] = -0x3f3f3f3f;
        for (int i = 1; i <= n; i++) {
            int val = 0;
            if (b[0] < a[i]) val = dp[i - 1][0];
            for (int j = 1; j <= n; j++) {
                if (a[i] == b[j])
                    dp[i][j] = val + 1;
                else
                    dp[i][j] = dp[i - 1][j];
                if (b[j] < a[i])
                    val = max(val, dp[i - 1][j]);
            }
        }
        int ans = 0;
        for (int i = 1; i <= n; i++) {
            for (int j = 1; j <= n; j++)
                ans = max(ans, dp[i][j]);
        }
        cout << ans << endl;
        return 0;
    }
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  • 原文地址:https://www.cnblogs.com/SwiftAC/p/12198552.html
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