最长增长子序列 DP

#include<iostream>
using namespace std;
#define INF 0x7fffffff
#define N 10000

// O(n^2)
int len[N];
int dp(int *a, int n){
    int mx = 0, mxlen = 1;
    for (int i = 0; i < n; ++i)
        len[i] = 1;
    for (int i = 1; i < n; ++i){
        mx = 0;
        for (int j = 0; j < i; ++j)        // 寻找len[0...i-1]最大值
            if (a[j]<a[i] && len[j]>mx)
                mx = len[j];
        len[i] = mx + 1;
        if (mxlen < len[i]) mxlen = len[i];    // 更新最大长度
    }
    return mxlen;
}

// O(nlogn)
int mv[N];    //mv[i]存放序列长度为 i+1 的最小元素
int binarySearch(int r, int val)
{
    int left = 0, right = r, mid;
    while (left < right){
        mid = (left + right) / 2;
        if (mv[mid] < val) left = mid + 1;
        else right = mid;
    }
    return left;
}
int binaryLIS(int *a, int n)
{
    int len = 0;
    mv[0] = a[0];
    for (int i = 1; i < n; ++i){
        if (a[i]>mv[len]) mv[++len] = a[i];
        else mv[binarySearch(len, a[i])] = a[i];
        for (int i = 0; i < len; ++i)
            cout << mv[i] << ' ';
        cout << mv[len] << endl;
    }
    return len + 1;
}

int main()
{
    int a[] = { 1, 7, 3, 5, 9, 4, 8 };
    cout << dp(a, 7) << endl;
    cout << binaryLIS(a, 7) << endl;
}