Question: A sequence of n integers (possibly negative numbers) a[1],a[2],a[3],..., A[n], and the maximum value of the sub-segments of the sequence, such as A[i]+a[i+1]+...+a[j], is obtained. When the given integer is negative, the defined sub-segment and is 0, according to this definition, the optimal value is: Max{0,a[i]+a[i+1]+...+a[j]},1<=i<=j<=n For example, when (A[1],a[2],a[3],a[4],a[5],a[6] ) = ( -2,11,-4,13,-5,-2), the maximum sub-segment and is 20.
Divided into three cases, divided by the middle, 1. All on the left, 2. All on the right 3. Across the middle mid (which is easy to find)
The situation can be recursive according to the original problem
//MaxChildArray.cpp:Defines the entry point for the console application.//#include"stdafx.h"#include<VECTOR>#include<iostream>using namespacestd;//return value,result[0]-> lindex result[1]-> rindex result[2]-> sum (lindex,rindex)Vector<int> Getmaxacross (vector<int> & V,intMidintBeginintend) { intLsum =0, maxlsum=-9999; intRsum =0, maxrsum=-9999; Vector<int> Result (3,0); inti =0; for(i = mid;i>=begin;i--) {lsum+=V[i]; if(Maxlsum <lsum) {Maxlsum=lsum; result[0] =i; } } for(i = mid+1; i<=end;i++) {rsum+=V[i]; if(Maxrsum <rsum) {Maxrsum=rsum; result[1] =i; }} result[2] = maxlsum+maxrsum; returnresult;} Vector<int> Getmaxchildarray (vector<int> & V,intBeginintend) {Vector<int> Result (3,0); if(Begin = =end) {//recursive cutoff point result[0] =begin; result[1] =end; result[2] =V[end]; returnresult; } intMid = (begin+end)/2; Vector<int> lresult =Getmaxchildarray (V,begin,mid); Vector<int> Rresult = Getmaxchildarray (v,mid+1, end); Vector<int> Midresult =Getmaxacross (v,mid,begin,end); if(lresult[2] >= rresult[2] && lresult[2] >= midresult[2]) returnlresult; if(rresult[2] >= lresult[2] && rresult[2] >= midresult[2]) returnRresult; returnMidresult;}intMainintargcChar*argv[]) { intArray[] = {-2, One,-4, -,-5,-2}; Vector<int> Elements (array,array+sizeof(array)/sizeof(int)); Vector<int> result = Getmaxchildarray (elements,0,sizeof(array)/sizeof(int)-1); cout<<"Leftindex ="<<result[0]<<Endl; cout<<"Rightindex ="<<result[1]<<Endl; cout<<"Maxsubarray ="<<result[2]<<Endl; inti; CIN>>i; return 0;}
Divide-and-conquer method to find the maximum field and