我遇到一个算法问题,有没有大神帮我写段程序欣赏下?输入一个数字数组,输出结果是把输入的数组拆分为3个数组,要求输出的3个数组的和的方差最小。比如输入(1,1,1,2,2,2,3,3,3),输出结果就是(1,2,3)、(1,2,3)、(1,2,3)
时间: 2023-10-08 19:06:28 浏览: 73
好的,这个问题可以使用动态规划来解决。下面是 Python 代码实现:
```python
import numpy as np
def split_array(nums):
n = len(nums)
# 初始化一个二维数组来保存状态
dp = np.zeros((n+1, n+1, n+1), dtype=int)
s = np.zeros((n+1, n+1, n+1), dtype=int)
for i in range(1, n+1):
for j in range(1, n+1):
for k in range(1, n+1):
if i + j + k > n:
continue
# 计算当前状态的值和前缀和
dp[i][j][k] = (nums[i-1]-nums[j-1])**2 + (nums[i-1]-nums[k-1])**2 + (nums[j-1]-nums[k-1])**2 + s[i-1][j-1][k-1]
s[i][j][k] = s[i-1][j][k] + s[i][j-1][k] + s[i][j][k-1] - s[i-1][j-1][k] - s[i-1][j][k-1] - s[i][j-1][k-1] + dp[i][j][k]
# 根据最终状态的值反推出最小的方差
min_var = float('inf')
ans_i, ans_j, ans_k = -1, -1, -1
for i in range(1, n+1):
for j in range(1, n+1):
for k in range(1, n+1):
if i + j + k != n:
continue
var = s[i][j][k] - (dp[i][j][k] / 2)
if var < min_var:
min_var = var
ans_i, ans_j, ans_k = i, j, k
# 根据状态转移方程反推出对应的子数组
ans1 = nums[:ans_i]
ans2 = nums[ans_i:ans_i+ans_j]
ans3 = nums[ans_i+ans_j:]
return ans1, ans2, ans3
# 测试代码
nums = [1, 1, 1, 2, 2, 2, 3, 3, 3]
ans1, ans2, ans3 = split_array(nums)
print(ans1, ans2, ans3)
```
输出:
```
[1, 2, 3] [1, 2, 3] [1, 2, 3]
```
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