01-複雜度2 Maximum Subsequence Sum（25 分）

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 Knumbers, 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

Sample Input:

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

Sample Output:

10 1 4

參考程式碼：（以下程式碼沒拿滿分，在“並列和對應相同i但是不同j，即尾是0”測試中顯示錯誤。）

#include<iostream>  
using namespace std;  
int *getmaxsum(int a[], int n, int m[]){  
    int thissum=0, maxsum=0;//當我把對陣列m的初始化工作,即m[0]={0};放到被調函式中時會出現如圖所示的問題，編譯時沒問題，輸入數值執行計算後跳出該視窗。  
    int i,num=0;  
    int flag = 0;//用於處理只有負數和零的子列，此時應輸出0 0 0，用flag標記子列中是否出現了0。  
    thissum = 0; maxsum = 0;  
  
    for (i = 0; i < n; i++)  
    {  
        thissum += a[i];  
        if (a[i] == 0)  
        {  
            flag = 1;  
        }  
        if (thissum > maxsum)  
        {  
              
            maxsum = thissum;  
            m[2] = a[i];  
            num += 1;  
            if (num == 1)  
                m[1] = a[i];  
        }  
        else if (thissum < 0)  
        {  
            thissum = 0;  
            num = 0;  
        }  
    }  
    m[0] = maxsum;  
      
    if (maxsum == 0 && flag == 1)//處理只有負數和0的情況  
    {  
        m[0] = 0;  
        m[1] = 0;  
        m[2] = 0;  
    }  
    if (maxsum == 0 && flag == 0)//處理只有負數的情況  
    {  
        m[0]=0;m[1]=  a[0]; m[2] = a[n - 1];  
    }  
      
    return m;  
}  
int main()  
{  
    int k;  
    int m[3] = { 0};  
    cin >> k;  
    int *a = new int[k];  
    for (int i = 0; i < k; i++)  
        cin >> a[i];  
    int *b = getmaxsum(a, k,m);  
    for (int r = 0; r < 3; r++)  
    {  
        if (r == 2)  
            cout << b[2];  
        else  
            cout << b[r] << " ";  
    }  
  
    delete[]a;  
      
    return 0;  
}  

當我把對陣列m的初始化工作放到被調函式中時會出現如下問題：

以下是同方法的滿分程式碼，從mooc評論區複製並更改的，主要是更改了陣列a的定義方式，由固定長度a[100]改成了如下方式，通過了“最大N”的測試，但我實在看不到我的和這段程式碼的區別。

#include<iostream>  
  
int Maxseq(int a[], int K);  
using namespace std;  
  
int  main()  
{  
    int K;  
      
    int Max;  
    //cout<<"請輸入序列長度"<<endl;  
    cin >> K;  
    int *a = new int[K];  
    for (int i = 0; i<K; i++)  
        cin >> a[i];  
    Max = Maxseq(a, K);  
    delete[]a;  
    return 0;  
  
}  
int Maxseq(int a[], int K)  
{  
    int ThisSum = 0, MaxSum = 0;  
    int start = 0, end = 0;  
    int count = 0;  
    int flag = 0;  
    int first = 0, last = 0;  
    for (int i = 0; i<K; i++)  
    {  
  
        ThisSum += a[i];  
        if (a[i] == 0)  
            flag = 1;  
        ++count;  
        if (ThisSum>MaxSum)  
        {  
            MaxSum = ThisSum;  
            end = i;  
            start = end - count + 1;  
  
        }  
  
        else if (ThisSum<0)  
        {  
            ThisSum = 0;  
            count = 0;  
        }  
    }  
    first = a[start];  
    last = a[end];  
    if (MaxSum == 0 && flag == 1)  
    {  
        first = 0;  
        last = 0;  
    }  
    if (MaxSum == 0 && flag == 0)  
    {  
        first = a[0];  
        last = a[K - 1];  
    }  
    cout << MaxSum << " " << first << " " << last << endl;  
  
    return MaxSum;  
}  

更新：呃呃，附上對比滿分程式碼之後的修改版，改了之後也是滿分了，修改了記錄子列最左的記錄方式。我不知道什麼資料能使兩段程式碼輸出的結果會不一樣。

#include<iostream>  
using namespace std;
int *getmaxsum(int a[], int n, int m[]) {
	int thissum = 0, maxsum = 0;//當我把對陣列m的初始化工作,即m[0]={0};放到被調函式中時會出現如吐所示的問題，編譯時沒問題，輸入數值執行計算後跳出該視窗。  
	int i, num = 0;
	int flag = 0;//用於處理只有負數和零的子列，此時應輸出0 0 0，用flag標記子列中是否出現了0。  
	thissum = 0; maxsum = 0;

	for (i = 0; i < n; i++)
	{
		thissum += a[i];
		if (a[i] == 0)
		{
			flag = 1;
		}
		++num;
		if (thissum > maxsum)
		{

			maxsum = thissum;
			m[2] = a[i];
			
			
			m[1] = a[i - num + 1];
		}
		else if (thissum < 0)
		{
			thissum = 0;
			num = 0;
		}
	}
	m[0] = maxsum;

	if (maxsum == 0 && flag == 1)//處理只有負數和0的情況  
	{
		m[0] = 0;
		m[1] = 0;
		m[2] = 0;
	}
	if (maxsum == 0 && flag == 0)//處理只有負數的情況  
	{
		m[0] = 0; m[1] = a[0]; m[2] = a[n - 1];
	}

	return m;
}
int main()
{
	int k;
	int m[3] = { 0 };
	cin >> k;
	int *a = new int[k];
	for (int i = 0; i < k; i++)
		cin >> a[i];
	int *b = getmaxsum(a, k, m);
	for (int r = 0; r < 3; r++)
	{
		if (r == 2)
			cout << b[2];
		else
			cout << b[r] << " ";
	}

	delete[]a;

	return 0;
}

更新：

我知道了，錯誤不是尾是0的狀況，是開頭是0的狀況。

輸入0  1  2  3  5  0  -7

我的程式碼輸出11 1 5

滿分程式碼輸出11 0 5

按照題目要求，最大和相同時輸出i，j最小的那一組，應該輸出11 0 5。我的記錄方式使子列首項不會是0。