IOI 2017 Practice Contest mountains
2018-09-07 10:33
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Mountains
题意:
选最多的点使得亮亮看不见。
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 ; int f ; 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); }
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