Hdoj 1003.Max Sum 题解
Problem Description
Given a sequence a[1],a[2],a[3]......a[n], your job is to calculate the max sum of a sub-sequence. For example, given (6,-1,5,4,-7), the max sum in this sequence is 6 + (-1) + 5 + 4 = 14.
Input
The first line of the input contains an integer T(1<=T<=20) which means the number of test cases. Then T lines follow, each line starts with a number N(1<=N<=100000), then N integers followed(all the integers are between -1000 and 1000).
Output
For each test case, you should output two lines. The first line is "Case #:", # means the number of the test case. The second line contains three integers, the Max Sum in the sequence, the start position of the sub-sequence, the end position of the sub-sequence. If there are more than one result, output the first one. Output a blank line between two cases.
Sample Input
2
5 6 -1 5 4 -7
7 0 6 -1 1 -6 7 -5
Sample Output
Case 1:
14 1 4
Case 2:
7 1 6
Author
Ignatius.L
思路
最大连续子序列和问题,状态转移方程式:
\(f[i] = max(f[i-1]+a[i],a[i])\)
可以得出代码如下
代码
#include<bits/stdc++.h>
using namespace std;
const int INF = 1<<30;
int a[100001];
int main()
{
int n;
cin >> n;
for(int q=1;q<=n;q++)
{
int len;
cin >> len;
int maxsum = -INF;
int currentsum = 0;
int l = 0,r = 0;
int tmp = 1;
for(int i=1;i<=len;i++)
{
cin >> a[i];
if(currentsum >= 0)
currentsum += a[i];
else
{
currentsum = a[i];
tmp = i;
}
if(currentsum > maxsum)
{
maxsum = currentsum;
l = tmp;
r = i;
}
}
cout << "Case " << q << ":\n";
cout << maxsum << " " << l << " " << r << endl;
if(q!=n) cout << endl;
}
return 0;
}
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