PAT 甲级 1007 Maximum Subsequence Sum

1007 Maximum Subsequence Sum （25 point(s)）

Given a sequence of K integers { N​1​​, N​2​​, ..., 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

Experiential Summing-up

This question involves dynamic programming and that is a classical problem of solving the maximum subsequence sum. We must pay attention to two requirements brought by rubric. Firstly, if maximum is a negative number, output 0 and the first and the last numbers of the whole sequence. This one is OK. The second request can be solved by traversal from subscript 0 to subscript k, Jump the loop as soon as find the element whose sum is equal to maxsum. That's all~

 (The purpose of using English to portray my solution is that to exercise the ability of my expression of English and accommodate PAT advanced level's style.We can make progress together by reading and comprehending it. Please forgive my basic grammar's and word's error. Of course, I would appreciated it if you can point out my grammar's and word's error in comment section.( •̀∀•́ ) Furthermore, Big Lao please don't laugh at me because I just a English beginner settle for CET6    _(:з」∠)_  )

Accepted Code

#include <cstdio>
#include <cstring>
const int maxn=10010;

struct node
{
	int start,end;
	int sum;
	int value;
}dp[maxn];
int main()
{
	int k;
	scanf("%d",&k);
	for(int i=0;i<k;++i)
	{
		scanf("%d",&dp[i].value);
	}
	int maxsum=dp[0].value;
	dp[0].sum=dp[0].value;
	dp[0].start=0;
	dp[0].end=0;
	for(int i=1;i<k;++i)
	{
		if(dp[i].value+dp[i-1].sum>=dp[i].value)
		{
			dp[i].sum=dp[i].value+dp[i-1].sum;
			dp[i].start=dp[i-1].start;
			dp[i].end=i;
		}
		else
		{
			dp[i].sum=dp[i].value;
			dp[i].start=i;
			dp[i].end=i;
		}
		maxsum=maxsum>dp[i].sum?maxsum:dp[i].sum;
	}
	if(maxsum<0)
	{
		printf("0 %d %d\n",dp[0].value,dp[k-1].value);
	}
	else
	{
		printf("%d ",maxsum);
		for(int i=0;i<k;++i)
		{
			if(maxsum==dp[i].sum)
			{
				printf("%d %d\n",dp[dp[i].start].value,dp[dp[i].end].value);
				break;
			}
		}
	}
	return 0;
}