The Painter's Partition Problem Part II

(http://leetcode.com/2011/04/the-painters-partition-problem-part-ii.html)

This is Part II of the artical: The Painter's Partition Problem. Please read Part I for more background information.

Solution:

Assume that you are assigning continuous section of board to each painter such that its total length must not exceed a predefined maximum, cost_max. Then, you are able to find the number of painters that is required, x. Following are some key obervations:

• The lowest possible value for cost_max must be the maximum element in A (name this as lo).
• The highest possible value for cost_max must be the entire sum of A (name this as hi).
• As cost_max increases, x decreases. The opposite also holds true.

Now, the question translates directly into:

• How do we use binary search to find the minimum of cost_max while satifying the condition x=k? The search space will be the range of [lo, hi].

int getMax(int A[], int n)
{
    int max = INT_MIN;
    for (int i = ; i < n; i++)
    {
        if (A[i] > max)
            max = A[i];
    }
    return max;
}

int getSum(int A[], int n)
{
        int total = ;
        for (int i = ; i < n; i++)
            total += A[i];
        return total;
}

int getRequiredPainters(int A[], int n, int maxLengthPainter)
{
    int total =;
    int numPainters = ;
    for (int i = ; i < n; i++)
    {
        total += A[i];
        if (total > maxLengthPerPainter)
        {
            total = A[i];
            numPainters++;
        }
    }
    return numPainters;
}

int partition(int A[], int n, int k)
{
    if (A == NULL || n <=  || k <= )
        return -;

    int lo = getMax(A, n);
    int hi = getSum(A, n);

    while (lo < hi)
    {
        int mid = lo + (hi-lo)/;
        int requiredPainters = getRequiredPainter(A, n, mid);
        if (requiredPainters <= k)
            hi = mid;
        else
            lo = mid+;
    }
    return lo;
}

The complexity of this algorithm is O(N log(∑A_i)), which is quite efficient. Furthermore, it does not require any extra space, unlike the DP solution which requires O(kN) space.