Maximum Sum Path in Two Arrays | GeeksforGeeks
Key Algorithm: Merge Sort, whenever the input are several sorted array, consider merge sort and binary search.
http://prismoskills.appspot.com/lessons/Arrays/Maximum_sum_path_in_two_arrays.jsp
http://comproguide.blogspot.com/2014/12/maximum-sum-path-in-two-sorted-arrays.html
==> we don't have to use while loop to handle duplicate same elements. as the code will just handle it.
Read full article from Maximum Sum Path in Two Arrays | GeeksforGeeks
Given two sorted arrays such the arrays may have some common elements. Find the sum of the maximum sum path to reach from beginning of any array to end of any of the two arrays. We can switch from one array to another array only at common elements.
Expected time complexity is O(m+n) where m is the number of elements in ar1[] and n is the number of elements in ar2[].
Examples:
Input: ar1[] = {2, 3, 7, 10, 12}, ar2[] = {1, 5, 7, 8}
Output: 35
35 is sum of 1 + 5 + 7 + 10 + 12.
We start from first element of arr2 which is 1, then we
move to 5, then 7. From 7, we switch to ar1 (7 is common)
and traverse 10 and 12.
The idea is to do something similar to merge process of merge sort. We need to calculate sums of elements between all common points for both arrays. Whenever we see a common point, we compare the two sums and add the maximum of two to the result. Following are detailed steps.
1) Initialize result as 0. Also initialize two variables sum1 and sum2 as 0. Here sum1 and sum2 are used to store sum of element in ar1[] and ar2[] respectively. These sums are between two common points.
2) Now run a loop to traverse elements of both arrays. While traversing compare current elements of ar1[] and ar2[].
2.a) If current element of ar1[] is smaller than current element of ar2[], then update sum1, else if current element of ar2[] is smaller, then update sum2.
2.b) If current element of ar1[] and ar2[] are same, then take the maximum of sum1 and sum2 and add it to the result. Also add the common element to the result.
int maxPathSum(int ar1[], int ar2[], int m, int n){ // initialize indexes for ar1[] and ar2[] int i = 0, j = 0; // Initialize result and current sum through ar1[] and ar2[]. int result = 0, sum1 = 0, sum2 = 0; // Below 3 loops are similar to merge in merge sort while (i < m && j < n) { // Add elements of ar1[] to sum1 if (ar1[i] < ar2[j]) sum1 += ar1[i++]; // Add elements of ar2[] to sum2 else if (ar1[i] > ar2[j]) sum2 += ar2[j++]; else // we reached a common point { // Take the maximum of two sums and add to result result += max(sum1, sum2); // Update sum1 and sum2 for elements after this // intersection point sum1 = 0, sum2 = 0; // Keep updating result while there are more common // elements while (i < m && j < n && ar1[i] == ar2[j]) // corner cases { result = result + ar1[i++]; j++; } } } // Add remaining elements of ar1[] while (i < m) sum1 += ar1[i++]; // Add remaining elements of ar2[] while (j < n) sum2 += ar2[j++]; // Add maximum of two sums of remaining elements result += max(sum1, sum2); return result;}http://prismoskills.appspot.com/lessons/Arrays/Maximum_sum_path_in_two_arrays.jsp
http://comproguide.blogspot.com/2014/12/maximum-sum-path-in-two-sorted-arrays.html
==> we don't have to use while loop to handle duplicate same elements. as the code will just handle it.
Read full article from Maximum Sum Path in Two Arrays | GeeksforGeeks
