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 = 2010;
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 0;
    if (l == r) return 1;
    int pos = -1, mx = -1;
    for (int i=l; i<=r; ++i) if (y[i] > mx) pos = i, mx = y[i];
    int ans1 = solve(l, pos - 1) + solve(pos + 1, r); // select max_height_node
    
    int ans2 = 0; // don't select this node
    for (int i=pos-1,j; i>=l; i=j) {
        for (j=i-1; j>=l; --j) {  // i can see pos
            if (Judge(j, i, pos)) { // j can't see pos
                if (j == l) ans2 += solve(l, i - 1); 
                continue;
            }
            if (j + 1 <= i - 1) ans2 += solve(j + 1, i - 1); // this Section can't see pos
            break;
        }
    }
    for (int i=pos+1,j; i<=r; i=j) {
        for (j=i+1; j<=r; ++j) {
            if (Judge(pos, i, j)) {
                if (j == r) ans2 += solve(i + 1, r);
                continue;
            }
            if (i + 1 <= j - 1) ans2 += solve(i + 1, j - 1);
            break;
        }
    } 
    return f[l][r] = max(ans1, ans2 + 1);
}
 
int maximum_deevs(vector<int> A) {
    int n = A.size();
    for (int i=1; i<=n; ++i) y[i] = A[i - 1];
    return solve(1, n);
}