最长上升子序列

一、思路

二、代码

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#include <bits/stdc++.h>
using namespace std;
constexpr int maxn = 1010;
int a[maxn], f[maxn];
int n;

int main() {
    scanf("%d", &n);
    for (int i = 1; i <= n; i ++ ) scanf("%d", &a[i]);

    int res = 0;
    for (int i = 1; i <= n; i ++ ) {
        f[i] = 1; 
        for (int j = 1; j < i; j ++ )
            if (a[j] < a[i])
                f[i] = max(f[i], f[j] + 1);
        res = max(res, f[i]);
    }
    printf("%d\n", res);

    return 0;
}

三、输出路径

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#include <bits/stdc++.h>
using namespace std;
constexpr int maxn = 1010;
int a[maxn], f[maxn];
int n;
int g[maxn];

int main() {
    scanf("%d", &n);
    for (int i = 1; i <= n; i ++ ) scanf("%d", &a[i]);

    for (int i = 1; i <= n; i ++ ) {
        f[i] = 1; 
        g[i] = 0;
        for (int j = 1; j < i; j ++ )
            if (a[j] < a[i])
                if (f[i] < f[j] + 1) {
                    g[i] = j;
                    f[i] = f[j] + 1;
                }
    }
    
    int k = 1;
    for (int i = 1; i <= n; i++)
        if (f[k] < f[i])
            k = i;
    printf("%d\n", f[k]);
    
    for (int i = 0, len = f[k]; i < len; i++) {
        cout << a[k] << " ";
        k = g[k];
    }

    return 0;
}

// 此路径为倒序

四、优化(贪心)

五、优化代码

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#include <bits/stdc++.h>
using namespace std;
constexpr int maxn = 101000;
int a[maxn], q[maxn];

int main() {
    int n;
    cin >> n;
    for (int i = 1; i <= n; i++) cin >> a[i];
    int len = 0;
    q[0] = -2e9;
    for (int i = 1; i <= n; i++) {
        int l = 0, r = len;
        while (l < r) {
            int mid = l + r + 1 >> 1;
            if (a[i] > q[mid]) l = mid;
            else r = mid - 1;
        }
        len = max(r + 1, len);
        q[r + 1] = a[i];
    }
    cout << len << endl;
}