add first DP solution to longest subsequence

Author: DanOlaru

longestAscendingSubsequence/longestAscendingSubsequence.h

@@ -0,0 +1,22 @@
+#define MAXLEN 100
+
+#include <stdio.h>
+
+typedef int SubsequencesMatrix[2][MAXLEN];
+
+void printMaximumsMatrix(SubsequencesMatrix matrix, int len)
+{
+
+  for (int i = 0; i < len; i++)
+  {
+    printf("%d, ", matrix[0][i]);
+  }
+
+  printf("\n");
+
+  for (int i = 0; i < len; i++)
+  {
+    printf("%d, ", matrix[1][i]);
+  }
+  printf("\n");
+}

longestAscendingSubsequence/main

@@ -0,0 +1,40 @@
+#include "longestAscendingSubsequence.h"
+
+int main(int argc, char const *argv[])
+{
+  int sequence[MAXLEN] = {2, 4, 3, 5, 1, 7, 6, 9, 8};
+  int length = 0;
+  SubsequencesMatrix subsequences;
+
+  for (int i = 0; sequence[i] != '\0'; i++)
+  {
+    length++;
+    // printf("element %d = %d \n", i, sequence[i]);
+
+    if (i == 0)
+    {
+      subsequences[0][i] = 1;  // subsequence max length
+      subsequences[1][i] = -1; // subsequence last item index
+    }
+    else
+    {
+      int maxIndex = 0, maxLen = 1;
+
+      for (int j = 0; j < i; j++)
+      {
+        if ((sequence[j] < sequence[i]) && (subsequences[0][j] >= maxLen))
+        {
+          maxLen = subsequences[0][j] + 1;
+          maxIndex = j;
+        }
+      }
+
+      subsequences[0][i] = maxLen;
+      subsequences[1][i] = maxIndex;
+    }
+  }
+
+  printMaximumsMatrix(subsequences, length);
+
+  return 0;
+}