Problem#
There are $N$ piles of stones arranged around a circular playground, and we need to merge the stones into one pile in an orderly manner. It is stipulated that only two adjacent piles can be merged into a new pile at a time, and the number of stones in the new pile is recorded as the score for that merge.
Design an algorithm to calculate the minimum and maximum scores for merging $N$ piles of stones into one pile.
$1\leq N\leq 100$, $0\leq a_i\leq 20$.
Solution#
There is not much to say; the circular problem can be transformed into a linear problem of double the length.
Code#
#include<bits/stdc++.h>
using namespace std;
const int N = 110;
int a[2 * N];
int read()
{
int f = 1, x = 0;
char ch = getchar();
while(ch < '0' || ch > '9')
{
if(ch == '-') f = -1;
ch = getchar();
}
while(ch >= '0' && ch <= '9')
{
x = x * 10 + ch - '0';
ch = getchar();
}
return f * x;
}
int n;
int f_min[2 * N][2 * N], f_max[2 * N][2 * N], sum[2 * N];
int main()
{
n = read();
memset(f_min, 0x3f, sizeof f_min);
memset(f_max, -0x3f, sizeof f_max);
for(int i = 1;i <= n;i++)
{
a[n + i] = a[i] = read();
}
for(int i = 1;i <= 2 * n;i++)
{
sum[i] = sum[i - 1] + a[i];
f_min[i][i] = f_max[i][i] = 0;
}
for(int L = 1;L <= 2 * n;L++)
{
for(int i = 1;i + L - 1 <= 2 * n;i++)
{
int j = i + L - 1;
for(int k = i;k <= j;k++)
{
f_min[i][j] = min(f_min[i][j], f_min[i][k] + f_min[k + 1][j] + sum[j] - sum[i - 1]);
f_max[i][j] = max(f_max[i][j], f_max[i][k] + f_max[k + 1][j] + sum[j] - sum[i - 1]);
}
}
}
int min_ans = 0x3f3f3f3f, max_ans = -0x3f3f3f3f;
for(int i = 1;i + n - 1 <= 2 * n;i++)
{
min_ans = min(min_ans, f_min[i][i + n - 1]);
max_ans = max(max_ans, f_max[i][i + n - 1]);
}
cout << min_ans << endl << max_ans;
return 0;
}