This problem can be solved using dynamic programming. Here are the steps:

1. Initialize a 2D array dp of size n x 3, where dp[i][j] represents the minimum possible sum of costs when the array is divided into j+1 subarrays and the last subarray ends at index i. Fill this array with a large number (e.g., Integer.MAX_VALUE) as we want to find the minimum sum.

2. Iterate over the array from left to right. For each element, calculate the prefix sum from the start of the array to the current element. This prefix sum represents the cost of a subarray starting from the first element and ending at the current element.

3. For each element, update dp[i][j] for all j from 0 to 2. The new value of dp[i][j] is the minimum of its current value and dp[k][j-1] + prefix_sum[i] - prefix_sum[k], where k ranges from 0 to i-1. This represents the cost of dividing the array into j+1 subarrays, where the last subarray starts at index k+1 and ends at index i.

4. After filling the dp array, the minimum possible sum of costs is dp[n-1][2], which represents the cost of dividing the array into 3 subarrays.

5. Return dp[n-1][2] as the result.

Here is a Python code snippet that implements these steps:

```python
def minCost(nums):
n = len(nums)
prefix_sum = [0] * (n+1)
for i in range(n):
prefix_sum[i+1] = prefix_sum[i] + nums[i]

dp = [[float('inf')] * 3 for _ in range(n)]
for i in range(n):
dp[i][0] = prefix_sum[i+1]
for j in range(1, min(i+1, 3)):
for k in range(i):
dp[i][j] = min(dp[i][j], dp[k][j-1] + prefix_sum[i+1] - prefix_sum[k+1])

return dp[n-1][2]
```

This function takes an array of integers as input and returns the minimum possible sum of costs when the array is divided into 3 disjoint contiguous subarrays.

Question

This problem can be solved using dynamic programming. Here are the steps:

1. Initialize a 2D array dp of size n x 3, where dp[i][j] represents the minimum possible sum of costs when the array is divided into j+1 subarrays and the last subarray ends at index i. Fill this array with a large number (e.g., Integer.MAX_VALUE) as we want to find the minimum sum.

2. Iterate over the array from left to right. For each element, calculate the prefix sum from the start of the array to the current element. This prefix sum represents the cost of a subarray starting from the first element and ending at the current element.

3. For each element, update dp[i][j] for all j from 0 to 2. The new value of dp[i][j] is the minimum of its current value and dp[k][j-1] + prefix_sum[i] - prefix_sum[k], where k ranges from 0 to i-1. This represents the cost of dividing the array into j+1 subarrays, where the last subarray starts at index k+1 and ends at index i.

4. After filling the dp array, the minimum possible sum of costs is dp[n-1][2], which represents the cost of dividing the array into 3 subarrays.

5. Return dp[n-1][2] as the result.

Here is a Python code snippet that implements these steps:

```python
def minCost(nums):
    n = len(nums)
    prefix_sum = [0] * (n+1)
    for i in range(n):
        prefix_sum[i+1] = prefix_sum[i] + nums[i]

dp = [[float('inf')] * 3 for _ in range(n)]
    for i in range(n):
        dp[i][0] = prefix_sum[i+1]
        for j in range(1, min(i+1, 3)):
            for k in range(i):
                dp[i][j] = min(dp[i][j], dp[k][j-1] + prefix_sum[i+1] - prefix_sum[k+1])

return dp[n-1][2]
```

This function takes an array of integers as input and returns the minimum possible sum of costs when the array is divided into 3 disjoint contiguous subarrays.

Knowee AI · Accepted Answer