UVa 11078 Open Credit System (序列前后最大差)

11078 - Open Credit System

Time limit: 3.000 seconds

http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=460&page=show_problem&problem=2019

In an open credit system, the students can choose any course they like, but there is a problem. Some of the students are more senior than other students. The professor of such a course has found quite a number of such students who came from senior classes (as if they came to attend the pre requisite course after passing an advanced course). But he wants to do justice to the new students. So, he is going to take a placement test (basically an IQ test) to assess the level of difference among the students. He wants to know the maximum amount of score that a senior student gets more than any junior student. For example, if a senior student gets 80 and a junior student gets 70, then this amount is 10. Be careful that we don't want the absolute value. Help the professor to figure out a solution.

Input
Input consists of a number of test cases T (less than 20). Each case starts with an integer n which is the number of students in the course. This value can be as large as 100,000 and as low as 2. Next n lines contain n integers where the i'th integer is the score of the i'th student. All these integers have absolute values less than 150000. If i < j, then i'th student is senior to the j'th student.

Output
For each test case, output the desired number in a new line. Follow the format shown in sample input-output section.

Sample Input             Output for Sample Input

3 2 100 20 4 4 3 2 1 4 1 2 3 4

80 3 -1

找一个序列前后的最大差值。

首先判断这个序列是不是严格递增的，是的话就找最小的差值。

若序列有相等或递减的部分，每次都做差比较。

完整代码：

/*0.108s*/
/*快于《训练指南》上的代码，且空间复杂度为O(1)*/

#include<cstdio>

int main(void)
{
	int t, n, max, min, last, now, diff, maxdiff;
	bool isNegative;///关键！！
	scanf("%d", &t);
	while (t--)
	{
		scanf("%d%d%d", &n, &last, &now);
		--n;
		maxdiff = last - now;
		if (maxdiff < 0)
		{
			isNegative = true;
			last = now;
		}
		else
		{
			isNegative = false;
			max = last, min = now;
		}
		while (--n)
		{
			scanf("%d", &now);
			if (isNegative)
			{
				diff = last - now ;
				if (diff >= 0)
				{
					isNegative = false;///此时序列产生了递减子序列
					maxdiff = diff;
					max = last, min = now;
				}
				else if (diff > maxdiff)
				{
					maxdiff = diff;
					last = now;
				}
			}
			else
			{
				if (now < min)
				{
					min = now;
					if (max - min > maxdiff)
						maxdiff = max - min;
				}
				else if (now > max)
					max = min = now;///都更新
			}
		}
		printf("%d\n", maxdiff);
	}
	return 0;
}