P1108 低价购买

 和LIS反着

本题直接做就行，

注意计算方案数，不是说找到最大的方案，然后再找比他小的就可以了，还要注意去重，所以再建立一个数组c;记录方案数目

#include <bits/stdc++.h>
using namespace std;
#define int long long
const int maxn = 5e3 + 10;
int n,a[maxn],dp[maxn];
int maxx,c[maxn],ans;
signed main(){
    //freopen("in","r",stdin);
    ios::sync_with_stdio(0);
    cin >> n;
    for(int i = 1; i <= n; i++)
        cin >> a[i];
    for(int i = 1; i <= n; i++){
        dp[i] = 1;
        for(int j = 1; j < i; j++){
            if(a[j] > a[i]){
                dp[i] = max(dp[i],dp[j] + 1);
            }
        }
        maxx = max(dp[i],maxx);
    }
    for (int i = 1; i <= n; i++) {
        if (dp[i] == 1) c[i] = 1;
        for (int j = 1; j < i; j++) {
            //去重
            if (dp[i] == dp[j] && a[i] == a[j])
                c[i] -= c[j];
            if (dp[j] + 1 == dp[i] && a[j] > a[i])
                c[i] += c[j];
        }
    }
    for(int i = 1; i <= n; i++){
        if(dp[i] == maxx)
            ans += c[i];
    }
    cout << maxx << " " << ans << endl;
    return 0;
}