<四边形不等式优化>[NOI1995]石子合并

留个坑

挺套路的

明天来写个总结

#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;
}
const int maxn = 2007;
int dp[maxn][maxn],s[maxn][maxn],cnt[maxn];
int sum[maxn];
int dpm[maxn][maxn];
int main () {
    int n = read();
    for(int i = 1;i <= n;++ i) cnt[n + i] = cnt[i] = read(),sum[i] = sum[i - 1] + cnt[i];
    for(int i = n + 1;i <= n * 2;++ i) sum[i] = sum[i - 1] + cnt[i];
    for(int i = 1;i <= 2 * n;++ i) s[i][i] = i;
    for(int i = n * 2 - 1;i >= 1;-- i) {
        for(int j = i + 1;j <= n * 2;++ j) {
            int tmp = 0x7fffffff,loc = 0;
            dpm[i][j] = std::max(dpm[i][j - 1],dpm[i + 1][j]) + sum[j] - sum[i - 1];
            for(int k = s[i][j - 1];k <= s[i + 1][j];++ k) {
                if(tmp >dp[i][k] + dp[k + 1][j] + sum[j] - sum[i - 1]) {
                    tmp = dp[i][k] + dp[k + 1][j] + sum[j] - sum[i - 1];
                    loc = k;
                }
            }
            dp[i][j] = tmp;
            s[i][j] = loc;
        }
    }
    int ansm = 0x7fffffff,ansx = 0;
    for(int i = 1;i <= n;++ i) {
        ansm = std::min(dp[i][i + n - 1],ansm) ;
        ansx = std::max(dpm[i][i + n - 1],ansx) ;
    }
    printf("%d\n%d",ansm,ansx);
    return 0;
}