最大子数组和
作者:互联网
题目:最大子数组和
1.题目描述
所谓的最大子数组问题,指的是:给定一个数组A,寻找A的和最大的非空连续子数组。比如,数组 A = [-2, -3, 4, -1, -2, 1, 5, -3], 最大子数组应为[4, -1, -2, 1, 5],其和为7。
2.解题思路
2.1 动态规划
2.2 分治法
3.代码
3.1 动态规划
#include <iostream>
using namespace std;
void Max_subarray(int A[],int array_start,int array_end)
{
int sum = 0;
int Max = -999999;
int high,low;
int currentHigh,currentLow;
for (int i = array_start;i <= array_end; i++)
{ high = i;
sum = sum + A[i];
if (A[i] > sum)
{
sum = A[i];
low = i;
}
if (sum > Max)
{
Max = sum;
currentLow = low;
currentHigh = high;
}
}
cout << currentLow << " " << currentHigh << " " << Max << endl;
}
int main()
{
int A[16] = {-13, -3, 25, 20, -3, -16, -23, 18, 110, -7, -12, -5, -22, 15, -4, 7};
Max_subarray(A,5,15);
return 0;
return 0;
}
3.2 分治法
#include <iostream>
using namespace std;
typedef struct
{
int subarray_start;
int subarray_end;
int subarray_max;
}result;
result Find_max_crossing_subarray(int A[],int array_start,int array_mid,int array_end)
{
result cross_result;
int left_sum = -999999;
int right_sum = -999999;
int max_left;
int max_right;
cout << array_start << " " << array_mid << ' ' << array_end << endl;
int sum = 0;
for (int i = array_mid; i >= array_start; i--)
{
sum = sum + A[i];
if (sum > left_sum)
{
left_sum = sum;
max_left = i;
}
}
sum = 0;
for (int i = array_mid + 1; i <= array_end; i++)
{
sum = sum + A[i];
if (sum > right_sum)
{
right_sum = sum;
max_right = i;
}
}
cross_result.subarray_start = max_left;
cross_result.subarray_end = max_right;
cross_result.subarray_max = left_sum + right_sum;
cout << max_left << ' ' << max_right << " " << left_sum + right_sum << endl;
cout << "-----" << endl;
return cross_result;
}
result Max_subarray(int A[],int array_start,int array_end)
{
if (array_start == array_end)
{
result end_start;
end_start.subarray_start = array_start;
end_start.subarray_end = array_end;
end_start.subarray_max = A[array_end];
return end_start;
}
result left_result,right_result,cross_result;
int mid = (array_start + array_end) / 2;
left_result = Max_subarray(A,array_start,mid);
right_result = Max_subarray(A,mid+1,array_end);
cross_result = Find_max_crossing_subarray(A,array_start,mid,array_end);
if (left_result.subarray_max >= right_result.subarray_max && left_result.subarray_max >= cross_result.subarray_max)
return left_result;
else if (right_result.subarray_max >= left_result.subarray_max && right_result.subarray_max >= cross_result.subarray_max)
return right_result;
else
return cross_result;
}
int main()
{
int A[16] = {-13, -3, 25, 20, -3, -16, -23, 18, 110, -7, -12, -5, -22, 15, -4, 7};
result my_result;
my_result = Max_subarray(A,0,15);
cout << my_result.subarray_start << " " << my_result.subarray_end << " " << my_result.subarray_max;
return 0;
}
标签:right,最大,int,max,sum,result,数组,subarray 来源: https://blog.csdn.net/a13333978782/article/details/114677622