IOI 2017 Practice Contest mountains

Mountains

题面

题意：

　　　选最多的点使得两两看不见。

分析：

　　分治，solve(l,r)为区间[l,r]的答案。那么如果不选最高点，分治两边即可，选了最高点，那么在最高点看不见的区间里分治。

代码：

 #include"mountains.h"
 #include<bits/stdc++.h>
 using namespace std;

 const int N = ;
 int y[N];
 int f[N][N];

 bool Judge(int a,int b,int c) { // a see c ?
     // ((y[a] - y[b]) / (a - b)) > ((y[a] - y[c]) / (a - c));
     return 1ll * (y[a] - y[b]) * (a - c) > 1ll * (y[a] - y[c]) * (a - b);
 }

 int solve(int l,int r) {
     if (f[l][r]) return f[l][r];
     if (l > r) return ;
     if (l == r) return ;
     int pos = -, mx = -;
     for (int i=l; i<=r; ++i) if (y[i] > mx) pos = i, mx = y[i];
     int ans1 = solve(l, pos - ) + solve(pos + , r); // select max_height_node

     int ans2 = ; // don't select this node
     for (int i=pos-,j; i>=l; i=j) {
         for (j=i-; j>=l; --j) {  // i can see pos
             if (Judge(j, i, pos)) { // j can't see pos
                 if (j == l) ans2 += solve(l, i - );
                 continue;
             }
             if (j +  <= i - ) ans2 += solve(j + , i - ); // this Section can't see pos
             break;
         }
     }
     for (int i=pos+,j; i<=r; i=j) {
         for (j=i+; j<=r; ++j) {
             if (Judge(pos, i, j)) {
                 if (j == r) ans2 += solve(i + , r);
                 continue;
             }
             if (i +  <= j - ) ans2 += solve(i + , j - );
             break;
         }
     }
     return f[l][r] = max(ans1, ans2 + );
 }

 int maximum_deevs(vector<int> A) {
     int n = A.size();
     for (int i=; i<=n; ++i) y[i] = A[i - ];
     return solve(, n);
 }