HDU 1003 Max Sum

题目链接：HDU 1003 Max Sum

题目大意：
求出\(n\)个数字中的最大子序列和，并且输出起始和终止位置。

题解：
典型的DP题。
定义dp[i]为以第i个数为结尾的子序列的和的最大值，则状态转移方程为：

\[\left\{ \begin{array}{l} dp[i] = num[i], i = 1 \\ dp[i] = max(dp[i - 1] + num[i], num[i]),i > 1 \end{array} \right. \]

#include <iostream>
#include <cstring>
using namespace std;
#define ms(a, b) memset(a, b, sizeof(a))
#define io_speed_up ios::sync_with_stdio(false),cin.tie(0),cout.tie(0)

int dp[100010], t, n, l, r, index, maxn;

int main() {
	io_speed_up;
	cin >> t;
	for (int kase = 1; kase <= t; ++kase) {
		cin >> n;
                ms(dp, 0);
		for (int i = 1; i <= n; ++i) {
			cin >> dp[i];
		}
		l = r = index = 1;
		maxn = dp[1];
		for (int i = 2; i <= n; ++i) {
			if (dp[i - 1] >= 0) {
				dp[i] += dp[i - 1];
			} else {
				index = i;
			}
			if (dp[i] > maxn) {
				l = index;
				r = i;
				maxn = dp[i];
			}
		}
		cout << "Case " << kase << ":" << endl;
		cout << maxn << ' ' << l << ' ' << r << endl;
		if (kase != t) {
			cout << endl;
		}
	}
	return 0;
}