1007. Maximum Subsequence Sum (25)

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.

10-10 1 2 3 4 -5 -23 3 7 -21Sample Output:
10 1 4
#include<cstdio>#include<algorithm>using namespace std;const int maxn = 10010;int N[maxn];int d[maxn];int main(){	int K;	scanf("%d", &K);	for (int i = 0; i < K; i++)	{		scanf("%d", &N[i]);	}	d[0] = N[0];//邊界	for (int i = 1; i < K; i++)	{		d[i] = max(N[i], d[i - 1]+N[i]);//狀態轉移方程	}	int k=0;//由于是d[i]表示下標為i的數為尾的最大連續子序列的和，也就是說N[i]必須在其中	//那么d[K-1]不一定是最大的，需要對d[]進行遍歷找最大的，并記錄下標	for (int i = 0; i < K; i++)	{		if (d[i] > d[k])		{			k = i;		}	}	int sum = d[k];	int j = k;//j用來求最大子序列和的第一個數	if (sum != 0)//這個地方得注意下，若sum就等于0，j不需要自增	{		while (sum != 0)		{			sum -= N[j];			j--;		}		j++;	}	if (d[k] < 0)		PRintf("0 %d %d/n", N[0], N[K-1]);	else		printf("%d %d %d/n", d[k], N[j], N[k]);//注意題目說的是序列中的元素而不是下標	return 0;}