算法导论_分治法_最大子数组C++实现

只是机械实现，和算法导论的伪代码区别不大；复杂度分析 T(n)=2T(n/2)+O(n),由主定理（算法导论内容），时间复杂度为O(nlgn).

#include<iostream>
using namespace std;
//寻找跨越中点的最大子数组；
void find_crossing_subarray(int*a, int low, int mid, int high, int& start, int& end, int& max_sum) {
	int left_sum = INT32_MIN;
	int sum = 0;
	for (int i = mid; i >= low; i--) {
		sum += a[i];
		if (sum>left_sum) {
			start = i;
			left_sum = sum;
		}
	}
	int right_sum = INT32_MIN;
	sum = 0;
	for (int i = mid + 1; i <= high; i++) {
		sum += a[i];
		if (sum > right_sum) {
			end = i;
			right_sum = sum;
		}
	}
	max_sum = left_sum + right_sum;
}
void find_maximum_subarray(int*a, int low, int high, int&start, int&end, int&max_sum) {
	if (high == low) {
		start = low;
		end = high;
		max_sum = a[high];
	}
	else {
		int mid = (high + low) / 2;

		//查找中点左侧的最大子数组；
		int left_start, left_end, left_sum;
		find_maximum_subarray(a, low, mid, left_start, left_end, left_sum);
		//寻找中点右侧的最大子数组；
		int right_start, right_end, right_sum;
		find_maximum_subarray(a, mid + 1, high, right_start, right_end, right_sum);
		int cross_start, cross_end, cross_sum;
		//寻找跨越中点的最大子数组；
		find_crossing_subarray(a, low, mid, high, cross_start, cross_end, cross_sum);

		//将三种情况的最大值设为当前数组的最大子数组；
		if ((left_sum >= cross_sum) && (left_sum >= right_sum)) {
			start = left_start;
			end = left_end;
			max_sum = left_sum;
		}
		else if ((cross_sum >= left_sum) && (cross_sum >= right_sum)) {
			start = cross_start;
			end = cross_end;
			max_sum = cross_sum;
		}
		else {
			start = right_start;
			end = right_end;
			max_sum = right_sum;
		}
	}
}
int main() {
	int n;
	cin >> n;
	int a[1000];
	for (int i = 0; i < n; ++i) {
		cin >> a[i];
	}
	int max=0,start = 0,end = 0;
	find_maximum_subarray(a, 0, n - 1, start, end, max);
	cout << max << endl;
}