Kadane\u2019s Algorithm:<\/strong><\/p>\nInitialize:\r\n max_so_far = 0\r\n max_ending_here = 0\r\n\r\nLoop for each element of the array\r\n (a) max_ending_here = max_ending_here + a[i]\r\n (b) if(max_ending_here < 0)\r\n max_ending_here = 0\r\n (c) if(max_so_far < max_ending_here)\r\n max_so_far = max_ending_here\r\nreturn max_so_far\r\n<\/pre>\n[ad type=”banner”]\nExplanation:<\/strong>
\nSimple idea of the Kadane’s algorithm is to look for all positive contiguous segments of the array (max_ending_here is used for this). And keep track of maximum sum contiguous segment among all positive segments (max_so_far is used for this). Each time we get a positive sum compare it with max_so_far and update max_so_far if it is greater than max_so_far<\/p>\n Lets take the example:\r\n {-2, -3, 4, -1, -2, 1, 5, -3}\r\n\r\n max_so_far = max_ending_here = 0\r\n\r\n for i=0, a[0] = -2\r\n max_ending_here = max_ending_here + (-2)\r\n Set max_ending_here = 0 because max_ending_here < 0\r\n\r\n for i=1, a[1] = -3\r\n max_ending_here = max_ending_here + (-3)\r\n Set max_ending_here = 0 because max_ending_here < 0\r\n\r\n for i=2, a[2] = 4\r\n max_ending_here = max_ending_here + (4)\r\n max_ending_here = 4\r\n max_so_far is updated to 4 because max_ending_here greater \r\n than max_so_far which was 0 till now\r\n\r\n for i=3, a[3] = -1\r\n max_ending_here = max_ending_here + (-1)\r\n max_ending_here = 3\r\n\r\n for i=4, a[4] = -2\r\n max_ending_here = max_ending_here + (-2)\r\n max_ending_here = 1\r\n\r\n for i=5, a[5] = 1\r\n max_ending_here = max_ending_here + (1)\r\n max_ending_here = 2\r\n\r\n for i=6, a[6] = 5\r\n max_ending_here = max_ending_here + (5)\r\n max_ending_here = 7\r\n max_so_far is updated to 7 because max_ending_here is \r\n greater than max_so_far\r\n\r\n for i=7, a[7] = -3\r\n max_ending_here = max_ending_here + (-3)\r\n max_ending_here = 4\r\n<\/pre>\nProgram:<\/strong><\/p>\n\n
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C++<\/span> <\/div> \/\/ C++ program to print largest contiguous array sum#include<iostream>#include<climits>using namespace std; int maxSubArraySum(int a[], int size){ int max_so_far = INT_MIN, max_ending_here = 0; for (int i = 0; i < size; i++) { max_ending_here = max_ending_here + a[i]; if (max_so_far < max_ending_here) max_so_far = max_ending_here; if (max_ending_here < 0) max_ending_here = 0; } return max_so_far;} \/*Driver program to test maxSubArraySum*\/int main(){ int a[] = {-2, -3, 4, -1, -2, 1, 5, -3}; int n = sizeof(a)\/sizeof(a[0]); int max_sum = maxSubArraySum(a, n); cout << "Maximum contiguous sum is " << max_sum; return 0;}<\/code><\/pre> <\/div>\nOutput :<\/strong><\/p>\nMaximum contiguous sum is 7<\/pre>\n[ad type=”banner”]\nAbove program can be optimized further, if we compare max_so_far with max_ending_here only if max_ending_here is greater than 0.<\/p>\n
C++<\/span> <\/div> int maxSubArraySum(int a[], int size){ int max_so_far = 0, max_ending_here = 0; for (int i = 0; i < size; i++) { max_ending_here = max_ending_here + a[i]; if (max_ending_here < 0) max_ending_here = 0; \/* Do not compare for all elements. Compare only when max_ending_here > 0 *\/ else if (max_so_far < max_ending_here) max_so_far = max_ending_here; } return max_so_far;}<\/code><\/pre> <\/div>\nTime Complexity: <\/strong>O(n)
\nAlgorithmic Paradigm: <\/strong>Dynamic Programming<\/p>\nThe implementation handles the case when all numbers in array are negative.<\/p>\n
C++<\/span> <\/div> #include<iostream>using namespace std; int maxSubArraySum(int a[], int size){ int max_so_far = a[0]; int curr_max = a[0]; for (int i = 1; i < size; i++) { curr_max = max(a[i], curr_max+a[i]); max_so_far = max(max_so_far, curr_max); } return max_so_far;} \/* Driver program to test maxSubArraySum *\/int main(){ int a[] = {-2, -3, 4, -1, -2, 1, 5, -3}; int n = sizeof(a)\/sizeof(a[0]); int max_sum = maxSubArraySum(a, n); cout << "Maximum contiguous sum is " << max_sum; return 0;}<\/code><\/pre> <\/div>\nOutput :<\/strong><\/p>\nMaximum contiguous sum is 7<\/pre>\n[ad type=”banner”]\nTo print the subarray with the maximum sum, we maintain indices whenever we get the maximum sum.<\/p>\n
C++<\/span> <\/div> \/\/ C++ program to print largest contiguous array sum#include<iostream>#include<climits>using namespace std; int maxSubArraySum(int a[], int size){ int max_so_far = INT_MIN, max_ending_here = 0, start =0, end = 0, s=0; for (int i=0; i< size; i++ ) { max_ending_here += a[i]; if (max_so_far < max_ending_here) { max_so_far = max_ending_here; start = s; end = i; } if (max_ending_here < 0) { max_ending_here = 0; s = i+1; } } cout << "Maximum contiguous sum is " << max_so_far << endl; cout << "Starting index "<< start << endl << "Ending index "<< end << endl;} \/*Driver program to test maxSubArraySum*\/int main(){ int a[] = {-2, -3, 4, -1, -2, 1, 5, -3}; int n = sizeof(a)\/sizeof(a[0]); int max_sum = maxSubArraySum(a, n); return 0;}<\/code><\/pre> <\/div>\nOutput :<\/strong><\/p>\nMaximum contiguous sum is 7\r\nStarting index 2\r\nEnding index 6<\/pre>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"C++ Programming – Largest Sum Contiguous Subarray – Dynamic Programming Write a program to find the sum of contiguous subarray within one-dimensional array<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[83515,1,70145],"tags":[79942,72845,72844,77101,79935,79940,79936,79929,79930,79938,77932,79933,79944,79943,72852,72855,79954,78229,72853,72851],"class_list":["post-26772","post","type-post","status-publish","format-standard","hentry","category-c-programming-3","category-coding","category-dynamic-programming","tag-contiguous-sequence","tag-definition-of-dynamic-programming","tag-dynamic-programming-software","tag-max-c","tag-max-subarray","tag-max-subarray-problem","tag-maximum-product-subarray","tag-maximum-subarray","tag-maximum-subarray-problem","tag-maximum-subarray-sum","tag-maximum-subsequence-sum","tag-maximum-sum-subarray","tag-non-contiguous","tag-php-array-sum","tag-problems-on-dynamic-programming","tag-simple-dynamic-programming-example","tag-sum-c","tag-sum-sum","tag-types-of-dynamic-programming","tag-youtube-dynamic-programming"],"_links":{"self":[{"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/posts\/26772","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=26772"}],"version-history":[{"count":0,"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/posts\/26772\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/media?parent=26772"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/categories?post=26772"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/tags?post=26772"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
![\"kadane](\"https:\/\/www.wikitechy.com\/technology\/wp-content\/uploads\/2017\/06\/kadane-Algorithm.png\")
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