Bzoj 1592 Usaco Making the Grade pavement trimming DP

The main idea: to give an untidy road surface, you can increase or decrease a road surface, all need the cost of |x-x ' |, the road to the correction to a monotonous or monotonous non-rising minimum cost is how much.

Idea: The height span of the road is a little big ah, first discretization. After F[i][j], the road surface is guaranteed to be monotonically non-descending and the maximum height for the minimum cost of J is how much, using a prefix and optimization. Monotonous does not rise also the same, simple DP water over.

CODE:

#include <map> #include <cstdio> #include <cstring> #include <iostream> #include <algorithm > #define MAX 2010#define INF 0x3f3f3f3fusing namespace std; int Cnt,src[max];p air<int,int *> xx[max];map<int,int> G;    int f[max][max],_f[max][max];//monotone not descending int g[max][max],_g[max][max];//monotone not ascending int main () {CIN >> cnt;        for (int i = 1; I <= cnt; ++i) {scanf ("%d", &xx[i].first);    Xx[i].second = &src[i];    } sort (xx + 1,xx + cnt + 1);    int t = 0;        for (int i = 1; I <= cnt; ++i) {if (i = = 1 | | Xx[i].first! = xx[i-1].first) ++t;        *xx[i].second = t;    G[t] = Xx[i].first;    } memset (F,0x3f,sizeof (f));    memset (G,0x3f,sizeof (g));    for (int i = 1; I <= t; ++i) f[1][i] = G[1][i] = ABS (G[src[1]]-g[i]);    for (int i = 1; I <= cnt; ++i) _f[i][0] = _g[i][t + 1] = INF;    for (int i = 1; I <= t; ++i) _f[1][i] = min (_f[1][i-1],f[1][i]);       for (int i = t; i; i.) _g[1][i] = min (_g[1][i + 1],g[1][i]); for (int i = 2; I <= cnt, ++i) {for (int j = 1; j <= cnt; ++j) {f[i][j] = _f[i-1][j] + ABS (G[J]            -G[src[i]]);        G[I][J] = _g[i-1][j] + ABS (G[J]-g[src[i]);        } for (int j = 1; j <= T; ++j) _f[i][j] = min (_f[i][j-1],f[i][j]);    for (int j = t; j;--j) _g[i][j] = min (_g[i][j + 1],g[i][j]);    } int ans = INF;    for (int i = 1; I <= t; ++i) ans = min (ans,min (f[cnt][i],g[cnt][i]));    cout << ans << endl; return 0;}

Bzoj 1592 Usaco Making the Grade pavement trimming DP