POJ

问题描述
Farmer John wants to repair a small length of the fence around the pasture. He measures the fence and finds that he needs N (1 ≤ N ≤ 20,000) planks of wood, each having some integer length Li (1 ≤ Li ≤ 50,000) units. He then purchases a single long board just long enough to saw into the N planks (i.e., whose length is the sum of the lengths Li). FJ is ignoring the “kerf”, the extra length lost to sawdust when a sawcut is made; you should ignore it, too.

FJ sadly realizes that he doesn’t own a saw with which to cut the wood, so he mosies over to Farmer Don’s Farm with this long board and politely asks if he may borrow a saw.

Farmer Don, a closet capitalist, doesn’t lend FJ a saw but instead offers to charge Farmer John for each of the N-1 cuts in the plank. The charge to cut a piece of wood is exactly equal to its length. Cutting a plank of length 21 costs 21 cents.

Farmer Don then lets Farmer John decide the order and locations to cut the plank. Help Farmer John determine the minimum amount of money he can spend to create the N planks. FJ knows that he can cut the board in various different orders which will result in different charges since the resulting intermediate planks are of different lengths.

Input
Line 1: One integer N, the number of planks
Lines 2.. N+1: Each line contains a single integer describing the length of a needed plank

Output
Line 1: One integer: the minimum amount of money he must spend to make N-1 cuts

Sample Input

3858

Sample Output

34

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分析：

对，实质上就是构造最优二叉树
附上弱渣我的一个TLE代码

#include<cstdio>#include<algorithm>using namespace std;const int maxn = 20000+10;int a[maxn];int main(){    int n;    scanf("%d",&n);    for(int i=0; i<n; i++)    {        scanf("%d",&a[i]);    }    int sum = 0;    for(int i=0; i<n-1; i++)    {        sort(a+i, a+n);        a[i+1] = a[i]+a[i+1];         sum += a[i+1];    }     printf("%d\n",sum);    return 0;}

天真如我啊，一个sort，O(nlogn)，再一个循环，一共O(n^2logn)，肯定爆炸，所以参考《挑程》里的代码。

#include<cstdio>#include<algorithm>using namespace std;const int maxn = 20000+10;int a[maxn];int main(){    int n;    scanf("%d",&n);    for(int i=0; i<n; i++)    {        scanf("%d",&a[i]);    }    int sum = 0;    for(int i=0; i<n-1; i++)    {        sort(a+i, a+n);        a[i+1] = a[i]+a[i+1];         sum += a[i+1];    }     printf("%d\n",sum);    return 0;}