3. The largest subarray and [MaximumContinuousSubArray]

【Question]:

Enter an integer array, and the array contains positive and negative numbers. One or more consecutive integers in the array form a sub-array. Each sub-array has a sum. Calculate the maximum sum of all sub-arrays. the time complexity is O (n ).

For example, the input array is 1,-2, 3, 10,-4, 7, 2,-5, and the maximum sub-array is 3, 10,-4, 7, 2, so the output is the sum of 18 of the Child array.

【Dynamic Planning]:

C ++ Code

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/* See Http://www.cppblog.com/jake1036/archive/2013/04/10/144726.html Http://en.wikipedia.org/wiki/Maximum_subarray_problem F (I): max subsequence value ending at I F (I) = max (f (I-1) + a [I], a [I]) Max f (I) (I = 0,... N-1) N = 8 -4, 3, 12,-7, 20,-1,-14, 4 3, 12,-7, 20 ---> 28 */ Int dp_forward () { // Time o (n) // Base case F [0] = a [0]; Int maxi = f [0]; For (int I = 1; I <N; I ++) { F [I] = max (f [I-1] + a [I], a [I]); If (maxi <f [I]) { Maxi = f [I]; } } Return maxi; } Int dp_forward2 () { // Base case Int f = a [0]; Int maxi = a [0]; For (int I = 1; I <N; I ++) { // F = max (f + a [I], a [I]); If (f <0) { F = a [I]; } Else { F + = a [I]; } If (maxi <f) { Maxi = f; } } Return maxi; }

【Reference]:

Http://zhedahht.blog.163.com/blog/static/254111742007219147591/

Http://blog.csdn.net/v_JULY_v/article/details/6444021