// Given an NxN matrix of positive and negative integers, write code to find the sub-matrix with the largest possible sum
public static MaxSum FindMaxSumSubarray(int[] inArr)
{
int currMax = 0;
int currStartIndex = 0;
// initialize maxSum to -infinity, maxStart and maxEnd idx to 0.
MaxSum mx = new MaxSum(int.MinValue, 0, 0);
// travers through the array
for (int currEndIndex = 0; currEndIndex < inArr.Length; currEndIndex++)
{
// add element value to the current max.
currMax += inArr[currEndIndex];
// if current max is more that the last maxSum calculated, set the maxSum and its idx
if (currMax > mx.maxSum)
{
mx.maxSum = currMax;
mx.maxStartIdx = currStartIndex;
mx.maxEndIdx = currEndIndex;
}
if (currMax < 0) // if currMax is -ve, change it back to 0
{
currMax = 0;
currStartIndex = currEndIndex + 1;
}
}
return(mx);
}
public static MaxSumMatrix FindMaxSumSubmatrix(int[,] inMtrx)
{
MaxSumMatrix maxSumMtrx = new MaxSumMatrix();
// Step 1. Create SumMatrix - do the cumulative columnar summation
// S[i,j] = S[i-1,j]+ inMtrx[i-1,j];
int m = inMtrx.GetUpperBound(0) + 2;
int n = inMtrx.GetUpperBound(1) + 1;
int[,] sumMatrix = new int[m, n];
for (int i = 1; i < m; i++)
{
for (int j = 0; j < n; j++)
{
sumMatrix[i, j] = sumMatrix[i - 1, j] + inMtrx[i - 1, j];
}
}
PrintMatrix(sumMatrix);
// Step 2. Create rowSpans starting each rowIdx. For these row spans, create a 1-D array r_ij
for (int x = 0; x < n; x++)
{
for (int y = x; y < n; y++)
{
int[] r_ij = new int[n];
for (int k = 0; k < n; k++)
{
r_ij[k] = sumMatrix[y + 1, k] - sumMatrix[x, k];
}
// Step 3. Find MaxSubarray of this r_ij. If the sum is greater than the last recorded sum =>
// capture Sum, colStartIdx, ColEndIdx.
// capture current x as rowTopIdx, y as rowBottomIdx.
MaxSum currMaxSum = KadanesAlgo.FindMaxSumSubarray(r_ij);
if (currMaxSum.maxSum > maxSumMtrx.sum)
{
maxSumMtrx.sum = currMaxSum.maxSum;
maxSumMtrx.colStart = currMaxSum.maxStartIdx;
maxSumMtrx.colEnd = currMaxSum.maxEndIdx;
maxSumMtrx.rowStart = x;
maxSumMtrx.rowEnd = y;
}
}
}
return(maxSumMtrx);
}
static void TestKadanesAlgo()
{
int[] arr = new int[] { 2, -1, 2, -1, 4, -5 };//{ 7, 3, -4, 8, -9, 1, 5};
MaxSum mx = KadanesAlgo.FindMaxSumSubarray(arr);
Console.WriteLine("maxSum = {0}, startIdx = {1}, endIdx = {2}", mx.maxSum, mx.maxStartIdx, mx.maxEndIdx);
arr = new int[] { 4, 7, 4, -2, 8, -10 };
mx = KadanesAlgo.FindMaxSumSubarray(arr);
Console.WriteLine("maxSum = {0}, startIdx = {1}, endIdx = {2}", mx.maxSum, mx.maxStartIdx, mx.maxEndIdx);
arr = new int[] { 6, 6, 6, -3, 12, -15 };
mx = KadanesAlgo.FindMaxSumSubarray(arr);
Console.WriteLine("maxSum = {0}, startIdx = {1}, endIdx = {2}", mx.maxSum, mx.maxStartIdx, mx.maxEndIdx);
arr = new int[] { 8, 5, 8, -4, 16, -20 };
mx = KadanesAlgo.FindMaxSumSubarray(arr);
Console.WriteLine("maxSum = {0}, startIdx = {1}, endIdx = {2}", mx.maxSum, mx.maxStartIdx, mx.maxEndIdx);
arr = new int[] { 10, 4, 10, -5, 20, -25 };
mx = KadanesAlgo.FindMaxSumSubarray(arr);
Console.WriteLine("maxSum = {0}, startIdx = {1}, endIdx = {2}", mx.maxSum, mx.maxStartIdx, mx.maxEndIdx);
arr = new int[] { 8, 3, 8, -6, 24, -30 };
mx = KadanesAlgo.FindMaxSumSubarray(arr);
Console.WriteLine("maxSum = {0}, startIdx = {1}, endIdx = {2}", mx.maxSum, mx.maxStartIdx, mx.maxEndIdx);
// -----------
arr = new int[] { 7, 3, -14, 8, -9, 1, 5 };
mx = KadanesAlgo.FindMaxSumSubarray(arr);
Console.WriteLine("maxSum = {0}, startIdx = {1}, endIdx = {2}", mx.maxSum, mx.maxStartIdx, mx.maxEndIdx);
arr = new int[] { -7, -3, -14, -8, -9, -1, -5 };
mx = KadanesAlgo.FindMaxSumSubarray(arr);
Console.WriteLine("maxSum = {0}, startIdx = {1}, endIdx = {2}", mx.maxSum, mx.maxStartIdx, mx.maxEndIdx);
arr = new int[] { -7, -3, -14, -8, -9, -1, 0 };
mx = KadanesAlgo.FindMaxSumSubarray(arr);
Console.WriteLine("maxSum = {0}, startIdx = {1}, endIdx = {2}", mx.maxSum, mx.maxStartIdx, mx.maxEndIdx);
arr = new int[] { -7, 12, 3, 4, 8, -9, -1, -5, 11, 9 };
mx = KadanesAlgo.FindMaxSumSubarray(arr);
Console.WriteLine("maxSum = {0}, startIdx = {1}, endIdx = {2}", mx.maxSum, mx.maxStartIdx, mx.maxEndIdx);
}
// NOT WORKING
public static MaxSum FindMaxLengthSubarrayWithSumX(int[] inArr, int requiredSum)
{
int currMax = 0;
int currStartIndex = 0;
// initialize maxSum to -infinity, maxStart and maxEnd idx to 0.
MaxSum mx = new MaxSum(int.MinValue, 0, 0);
MaxSum xctSum = new MaxSum(requiredSum, -1, -1);
// travers through the array
for (int currEndIndex = 0; currEndIndex < inArr.Length; currEndIndex++)
{
// add element value to the current max.
currMax += inArr[currEndIndex];
// if current max is more that the last maxSum calculated, set the maxSum and its idx
if (currMax > mx.maxSum)
{
mx.maxSum = currMax;
mx.maxStartIdx = currStartIndex;
mx.maxEndIdx = currEndIndex;
}
if (currMax == xctSum.maxSum &&
(currEndIndex - currStartIndex) > (xctSum.maxEndIdx - xctSum.maxStartIdx))
{
xctSum.maxStartIdx = currStartIndex;
xctSum.maxEndIdx = currEndIndex;
mx = new MaxSum(int.MinValue, 0, 0);
currMax = 0;
currStartIndex = currEndIndex + 1;
}
//if (currMax < 0) // if currMax is -ve, change it back to 0
//{
// currMax = 0;
// currStartIndex = currEndIndex + 1;
//}
}
return(xctSum);
}