hdu 4193 - Non-negative Partial Sums(滚动数列)

题意：

给定一个由n个整数组成的整数序列，可以滚动，滚动的意思就是前面k个数放到序列末尾去。问有几种滚动方法使得前面任意个数的和>=0.

思路：

先根据原来的数列求sum数组，找到最低点，然后再以最低点为始点，求解题目答案，（每求解一始点i，符合要求的条件为：sum[i]>=minx,[minx是i<x<=n中的最小值],之所以不用考虑前面的，就是因为我们的预处理是的所有的x<i的sum[x]的值满足sum[x]>=sum[i]）

代码如下：

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <cstring>
#include <cstdlib>
#include <stack>
#include <queue>
#include <vector>
#include <algorithm>
#include <set>
#include <map>

#define M 1000005
#define mod 1000000007
#define INF 0x7fffffff
#define eps 1e-8
#define LL long long
#define LLU unsigned long long

using namespace std;

int a[M], n, mini;
LL sum[M], minx;
int main ()
{
	while(scanf("%d", &n) && n)
	{
		minx = INF;
		sum[0] = 0;
		for(int i= 1; i <= n; ++i)
		{
			scanf("%d", &a[i]);
			sum[i] = sum[i-1]+a[i];
			if(minx>sum[i])
			{
				minx = sum[i];
				mini = i;
			}
		}
		sum[0] = 0;
		int c = 0;
		for(int i = mini+1; i <= n; ++i)
			sum[++c] = sum[c-1]+a[i];
		for(int i = 1; i <= mini; ++i)
			sum[++c] = sum[c-1]+a[i];
		minx = sum[n];
		int ans = 0;
		for(int i = n-1; i >= 0; --i)
		{
			if(sum[i]<=minx)
			{
				ans += 1;
				minx = sum[i];
			}
		}
		printf("%d\n", ans);
	}
	return 0;
}

　　

单调队列的思路是比较简单的，

 

就是确定一个始点以后，然后在队列中找最小的值，满足要求的条件为：minx-sum[i]>=0

代码如下：

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <cstring>
#include <cstdlib>
#include <stack>
#include <queue>
#include <vector>
#include <algorithm>
#include <set>
#include <map>

#define M 1000005
#define mod 1000000007
#define INF 0x7fffffff
#define eps 1e-8
#define LL long long
#define LLU unsigned long long

using namespace std;
int n, head, rear, a[M];
LL sum[2*M], deq[2*M];
void insert(int x)
{
	while(head<=rear && sum[deq[rear]]>=sum[x]) --rear;
	deq[++rear] = x;
}
LL push(int x)
{
	while(deq[head]<=x-n) ++head;
	return sum[deq[head]];
}
int main ()
{
	while(scanf("%d", &n) && n)
	{
		head = 1; rear = 0;
		for(int i = 1; i <= n; ++i)
			scanf("%d", &a[i]);
		sum[0] = 0;
		for(int i = 1; i <= n; ++i)
			sum[i] = sum[i-1]+a[i];
		for(int i = n+1; i <= 2*n; ++i)
			sum[i] = sum[i-1]+a[i-n];
		for(int i = 1; i < n; ++i)
			insert(i);
		int ans = 0;
		for(int i = n; i < 2*n; ++i)
		{
			insert(i);
			if(push(i)-sum[i-n]>=0) ++ans;
		}
		printf("%d\n", ans);
	}
	return 0;
}