1007. Maximum Subsequence Sum (25)

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分类专栏： Advanced PAT C++

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本文探讨如何在给定整数序列中找到具有最大和的连续子序列，并输出该子序列的最大和及其首尾元素。

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1007. Maximum Subsequence Sum (25)

时间限制

400 ms

内存限制

65536 kB

代码长度限制

16000 B

判题程序

Standard

作者

CHEN, Yue

Given a sequence of K integers { N₁, N₂, ..., N_K }. A continuous subsequence is defined to be { N_i, N_i+1, ..., N_j } where 1 <= i <= j <= K. The Maximum Subsequence is the continuous subsequence which has the largest sum of its elements. For example, given sequence { -2, 11, -4, 13, -5, -2 }, its maximum subsequence is { 11, -4, 13 } with the largest sum being 20.

Now you are supposed to find the largest sum, together with the first and the last numbers of the maximum subsequence.

Input Specification:

Each input file contains one test case. Each case occupies two lines. The first line contains a positive integer K (<= 10000). The second line contains K numbers, separated by a space.

Output Specification:

For each test case, output in one line the largest sum, together with the first and the last numbers of the maximum subsequence. The numbers must be separated by one space, but there must be no extra space at the end of a line. In case that the maximum subsequence is not unique, output the one with the smallest indices i and j (as shown by the sample case). If all the K numbers are negative, then its maximum sum is defined to be 0, and you are supposed to output the first and the last numbers of the whole sequence.

Sample Input:

10
-10 1 2 3 4 -5 -23 3 7 -21

Sample Output:

10 1 4

//特殊测试用例，我目前想到的
//用例1：-1 0 -2 只有一个0，其余全是负数
//用例2：-1 -2 -3 -4 全是负数
//用例3:-1 -3 2 -5 只有一个正数

int main()
{
	int n;
	int num[10000] = {0};
	int max[10000] = { 0 };	//起点为i时，Max[i]存放和的最大值
	int maxloc[10000] = {0};//起点为i时，终点为maxloc[i],取得最大值
	cin >> n;
	int count = 0;
	for (int i = 0; i < n; i++)
	{		
		cin >> num[i];
		if (num[i] < 0)
			count++;
	}
	if (count == n)//一开始写代码没写上这种特殊情况，导致一个测试用例过不了
	{
		cout << 0 << " " << num[0] << " " << num[n-1];
	}
	else
	{
		for (int i = 0; i < n; i++)
		{
			int firstnum = num[i];
			int sum = firstnum;

			max[i] = sum;//一开始这里没有提前赋值，导致错误
			maxloc[i] = i;
			for (int j = i+1; j < n; j++)
			{
				int lastnum = num[j];
				int temp = sum + lastnum;
				if (temp>max[i])
				{
					max[i] = temp;
					maxloc[i] = j;
				}
				sum = temp;
			}
		}

		int maxvalue = max[0], maxl = 0;//注意这里一开始赋初值时，不要赋值0，而应该赋值为数组里面的首元素，这个地方导致一个测试用例不过，调了半天

		for (int i = 0; i < n; i++)
		{
			if (max[i]>maxvalue)
			{
				maxvalue = max[i];
				maxl = i;
			}
		}

		cout << maxvalue << " " <<num[maxl] << " " << num[maxloc[maxl]];
	}
	
	return 0;
}