【LOJ2292】【BZOJ4897】【THUSC2016】成绩单（DP）

Description

click me

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Solution

感觉自己还是太菜了，根本想不到啊

设$f_{i,j,l,r}$表示将区间$[i,j]$删去一些元素使得区间内只剩下数值在$[l,r]$中的数的最小代价。(注意，可以删去其中一些$[l,r]$中的数)
$g_{i,j}$表示将区间$[i,j]$内的元素删完的最小代价。
那么有以下转移：
f(i, j, l, r) = min{g(i, k) + f(k + 1, j, l, r), f(i, k, l, r) + f(k + 1, j, l, r)}
g(i, j) = min{f(i, j, l, r) + (r - l)^2 * b + a}

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Code

/************************************************
 * Au: Hany01
 * Date: May 28th, 2018
 * Prob: [BZOJ4897][LOJ2292] 成绩单
 * Email: [email protected]
************************************************/

#include<bits/stdc++.h>

using namespace std;

typedef long long LL;
typedef pair<int, int> PII;
#define File(a) freopen(a".in", "r", stdin), freopen(a".out", "w", stdout)
#define rep(i, j) for (register int i = 0, i##_end_ = (j); i < i##_end_; ++ i)
#define For(i, j, k) for (register int i = (j), i##_end_ = (k); i <= i##_end_; ++ i)
#define Fordown(i, j, k) for (register int i = (j), i##_end_ = (k); i >= i##_end_; -- i)
#define Set(a, b) memset(a, b, sizeof(a))
#define Cpy(a, b) memcpy(a, b, sizeof(a))
#define x first
#define y second
#define pb(a) push_back(a)
#define mp(a, b) make_pair(a, b)
#define ALL(a) (a).begin(), (a).end()
#define SZ(a) ((int)(a).size())
#define INF (0x3f3f3f3f)
#define INF1 (2139062143)
#define Mod (1000000007)
#define debuG(...) fprintF(stderr, __VA_ARGS__)
#define sqr(x) ((x) * (x))
#define y1 wozenmezhemecaia

template <typename T> inline bool chkmax(T &a, T b) { return a < b ? a = b, 1 : 0; }
template <typename T> inline bool chkmin(T &a, T b) { return b < a ? a = b, 1 : 0; }

inline int read()
{
    register int _, __; register char c_;
    for (_ = 0, __ = 1, c_ = getchar(); c_ < '0' || c_ > '9'; c_ = getchar()) if (c_ == '-') __ = -1;
    for ( ; c_ >= '0' && c_ <= '9'; c_ = getchar()) _ = (_ << 1) + (_ << 3) + (c_ ^ 48);
    return _ * __;
}

const int maxn = 53;

int n, w[maxn], f[maxn][maxn][maxn][maxn], g[maxn][maxn], ls[maxn], tot, a, b;

inline bool all(int i, int j, int l, int r) {
    For(k, i, j) if (w[k] < l || w[k] > r) return 0;
    return 1;
}

inline bool inc(int i, int j, int l, int r) {
    For(k, i, j) if (w[k] >= l && w[k] <= r) return 1;
    return 0;
}

int F(int, int, int, int);
int G(int, int);

int F(int i, int j, int l, int r)
{
    //F(i, j, l, r) = min{G(i, k) + F(k + 1, j, l, r), F(i, k, l, r) + F(k + 1, j, l, r)}
    if (f[i][j][l][r] != -1) return f[i][j][l][r];
    if (all(i, j, l, r)) return f[i][j][l][r] = 0;
    if (!inc(i, j, l, r)) return f[i][j][l][r] = G(i, j);
    f[i][j][l][r] = INF;
    For(k, i, j - 1)
        chkmin(f[i][j][l][r], F(i, k, l, r) + F(k + 1, j, l, r)), chkmin(f[i][j][l][r], G(i, k) + F(k + 1, j, l, r));
    return f[i][j][l][r];
}

int G(int i, int j)
{
    //G(i, j) = min{F(i, j, l, r) + (r - l)^2 * b + a}
    if (g[i][j] != -1) return g[i][j];
    g[i][j] = INF;
    For(l, 1, tot) For(r, l, tot)
        if (inc(i, j, l, r)) chkmin(g[i][j], F(i, j, l, r) + sqr(ls[r] - ls[l]) * b + a);
    return g[i][j];
}

int main()
{
#ifdef hany01
    File("bzoj4897");
#endif

    n = read(), a = read(), b = read();
    For(i, 1, n) ls[i] = w[i] = read();
    sort(ls + 1, ls + 1 + n), tot = unique(ls + 1, ls + 1 + n) - ls - 1;
    For(i, 1, n) w[i] = lower_bound(ls + 1, ls + 1 + tot, w[i]) - ls;

    Set(g, -1), Set(f, -1);
    printf("%d\n", G(1, n));

    return 0;
}
//斑竹枝，斑竹枝，泪痕点点寄相思。
//    -- 刘禹锡《潇湘神·斑竹枝》