{"id":26220,"date":"2017-10-26T20:31:40","date_gmt":"2017-10-26T15:01:40","guid":{"rendered":"https:\/\/www.wikitechy.com\/technology\/?p=26220"},"modified":"2017-10-26T20:31:40","modified_gmt":"2017-10-26T15:01:40","slug":"c-programming-maximum-sum-increasing-subsequence","status":"publish","type":"post","link":"https:\/\/www.wikitechy.com\/technology\/c-programming-maximum-sum-increasing-subsequence\/","title":{"rendered":"C Programming – Maximum Sum Increasing Subsequence"},"content":{"rendered":"

Given an array of n positive integers. Write a program to find the sum of maximum sum subsequence of the given array such that the intgers in the subsequence are sorted in increasing order.<\/span> For example, if input is {1, 101, 2, 3, 100, 4, 5}, then output should be 106 (1 + 2 + 3 + 100), if the input array is {3, 4, 5, 10}, then output should be 22 (3 + 4 + 5 + 10) and if the input array is {10, 5, 4, 3}, then output should be 10<\/p>\n

Solution<\/strong>
\nThis problem is a variation of standard Longest Increasing Subsequence (LIS) problem. We need a slight change in the Dynamic Programming solution of LIS problem. All we need to change is to use sum as a criteria instead of length of increasing subsequence.<\/p>\n

Following are C implementations for Dynamic Programming solution of the problem.<\/p>\n

C<\/span> <\/div> 
\/* Dynamic Programming implementation of Maximum Sum IncreasingSubsequence (MSIS) problem *\/#include<stdio.h> \/* maxSumIS() returns the maximum sum of increasing subsequence    in arr[] of size n *\/int maxSumIS( int arr[], int n ){    int i, j, max = 0;    int msis[n];     \/* Initialize msis values for all indexes *\/    for ( i = 0; i < n; i++ )        msis[i] = arr[i];     \/* Compute maximum sum values in bottom up manner *\/    for ( i = 1; i < n; i++ )        for ( j = 0; j < i; j++ )            if ( arr[i] > arr[j] && msis[i] < msis[j] + arr[i])                msis[i] = msis[j] + arr[i];     \/* Pick maximum of all msis values *\/    for ( i = 0; i < n; i++ )        if ( max < msis[i] )            max = msis[i];     return max;} \/* Driver program to test above function *\/int main(){    int arr[] = {1, 101, 2, 3, 100, 4, 5};    int n = sizeof(arr)\/sizeof(arr[0]);    printf("Sum of maximum sum increasing subsequence is %d\\n",           maxSumIS( arr, n ) );    return 0;}<\/code><\/pre> <\/div>\n
Output:<\/p>\n
Sum of maximum sum increasing subsequence is 106<\/pre>\n
Time Complexity: O(n^2)<\/p>\n[ad type=”banner”]\n","protected":false},"excerpt":{"rendered":"
C Programming – Maximum Sum Increasing Subsequence – Dynamic Programming Given an array of n positive integers. To find the sum of maximum sum <\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[69969,69866,1,70145],"tags":[72847,72842,72845,70483,72841,72848,72840,72849,72846,72843,72854,77933,72844,72850,72839,77941,77935,77934,77932,77928,77929,77931,77942,77936,77937,77927,72852,72855,72853,72851],"class_list":["post-26220","post","type-post","status-publish","format-standard","hentry","category-algorithm","category-c-programming","category-coding","category-dynamic-programming","tag-concept-of-dynamic-programming","tag-define-dynamic-programming","tag-definition-of-dynamic-programming","tag-dynamic-programming","tag-dynamic-programming-c","tag-dynamic-programming-code-generation-algorithm","tag-dynamic-programming-definition","tag-dynamic-programming-in-c","tag-dynamic-programming-in-data-structure","tag-dynamic-programming-problems","tag-dynamic-programming-set-1","tag-dynamic-programming-set-15","tag-dynamic-programming-software","tag-explain-dynamic-programming","tag-how-to-solve-dynamic-programming-problems","tag-increasing-subsequence-with-maximum-sum-in-c-code","tag-largest-sum-non-contiguous-subarray","tag-maximum-increasing-subsequence","tag-maximum-subsequence-sum","tag-maximum-sum-alternating-subsequence","tag-maximum-sum-increasing-subsequence-dynamic-programming","tag-maximum-sum-increasing-subsequence-nlogn","tag-maximum-sum-subarray-divide-and-conquer-in-c-code","tag-maximum-sum-subarray-dynamic-programming","tag-maximum-sum-subsequence-dynamic-programming","tag-printing-maximum-sum-increasing-subsequence","tag-problems-on-dynamic-programming","tag-simple-dynamic-programming-example","tag-types-of-dynamic-programming","tag-youtube-dynamic-programming"],"_links":{"self":[{"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/posts\/26220","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/comments?post=26220"}],"version-history":[{"count":0,"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/posts\/26220\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/media?parent=26220"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/categories?post=26220"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/tags?post=26220"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}