最大连续和

// 练习.cpp: 定义控制台应用程序的入口点。
//

#include "stdafx.h"

#include<iostream>
#include<algorithm>
#include<stdio.h>
#include<string.h>
#include<math.h>
#include<stdlib.h>
#include<time.h>
#include<windows.h>

using namespace std;

int Max(int a, int b) {
	return a > b ? a : b;
}

//暴力枚举

int maxsum1(int a[], int n) {
	int sum = 0;
	int max = 0;
	for (int i = 0; i < n; i++) {
		for (int j = i; j < n; j++) {
			sum = 0;
			for (int k = i; k <= j; k++)
				sum += a[k];
			if (max < sum)
				max = sum;
		}
	}
	return max;
}

//递推前缀

int maxsum2(int a[], int n)
{
	int s[100];
	int max = 0;
	s[0] = a[0];
	for (int i = 1; i < n; i++)
		s[i] = s[i - 1] + a[i];
	for (int i = 0; i < n; i++) {
		for (int j = i; j < n; j++) {
			int t = i == 0 ? s[j] : s[j] - s[i - 1];
			max = Max(max, t);
		}
	}
	return max;
}

//分治法
      
int maxsum3(int a[], int left, int right) {    //左闭右开
	int i, m, v, L, R, max;
	if (right - left == 1) return a[left];
	m = left + (right - left) / 2;             //第一步，划分成[left,m),[m,right)
	max = Max(maxsum3(a, left, m), maxsum3(a, m, right));
	                                           //第二步，递归求解
	v = 0; L = a[m - 1];                       //第三步，合并
	for (i = m - 1; i >= left; i--)
		L = Max(L, v += a[i]);
	v = 0; R = a[m];
	for (i = m; i < right; i++)
		R = Max(R, v += a[i]);
	return Max(max, L + R);
}

int main()
{
	int n;
	int a[100];
	cin >> n;
	for (int i = 0; i < n; i++) {
		cin >> a[i];
	}
	int s1 = maxsum1(a, n);
	int s2 = maxsum2(a, n);
	int s3 = maxsum3(a, 0, n);
	cout << s1 << endl;
	cout << s2 << endl;
	cout << s3 << endl;
	system("pause");
	return 0;
}