bzoj5068: 友好的生物

题解

最大化这个东西(sum_{i=1}^{k-1} | a_{x,i}-a_{y,i} | - | a_{x,k}-a_{y,k} |)
去掉绝对值号，也就是就是求这个式子 (sum_{i=1}^{k-1}±(a_{x,i}-a_{y,i}) - | a_{x,k} - a_{y,k} |) 的最大值
对与前面的 (i) 式取 正负号 一定会有一个方案使每个 (a_{x,i}-a_{y,i}) 不负

装压枚举每个(i)的符号,对于 (a_{x,k}) 从小到大排序，维护前缀最小值更新答案

代码

#include<cmath> 
#include<cstdio> 
#include<algorithm> 
inline int read() { 
    int x = 0,f = 1; 
    char c = getchar(); 
    while(c < '0' || c > '9'){if(c == '-')f = - 1; c = getchar(); } 
    while(c <= '9' && c >= '0') x = x * 10 + c - '0',c = getchar(); 
    return x * f; 
} 
#define INF 0x3f3f3f3f 
int n,k; 
struct A  {
    int d[10],id; 
    bool operator < (const A &a)const {
        return d[k] < a.d[k];  
    } 
} a[100007]; 
int c[76]; 
int main() { 
    n = read(),k = read() - 1; 
    for(int i = 0;i <= k;++ i) c[i] = read(); 
    for(int i = 1;i <= n;++ i) { 
        a[i].id = i; 
        for(int j = 0;j <= k;++ j) a[i].d[j] = read(),a[i].d[j] *= c[j];
    }    
    std::sort(a + 1,a + n + 1); 
    int ans = 0,id1,id2; 
    for(int s = 0;s < (1 << k); ++ s) { 
        int minn = INF, id; 
        for(int i = 1;i <= n;++ i) { 
            int ss = 0; 
            for(int j = 0;j < k;++ j) 
                if(s & (1 << j)) ss += a[i].d[j]; 
                else ss -= a[i].d[j]; 
            ss -= a[i].d[k ]; 
            if(ans  < ss - minn) ans = ss - minn,id1 = a[i].id,id2 = id; 
            if(minn > ss) minn = ss,id = a[i].id; 
        } 
    } 
    printf("%d
",ans); 
    return 0; 
}