[动态规划]Recaman's Sequence

micklongen

于 2019-02-19 13:06:03 发布

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分类专栏：数据结构和算法

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本文深入探讨了Recaman数列的定义及其生成规则，通过具体实例展示了数列的前几项，并提供了一段C语言代码实现，用于计算指定位置的数列值。文章适合对数学数列及算法实现感兴趣的读者。

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Recaman's Sequence

Time Limit:5s	Memory limit:32M
Accepted Submit:383	Total Submit:1245

The Recaman's sequence is defined by a(0)=0; for m>0, a(m)=a(m-1)-m if the resulting a(m) is positive and not already in the sequence, otherwise a(m)=a(m-1)+m.

The first few numbers in the Recaman's Sequence is 0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, ...

Given k, your task is to calculate a(k).

Input

The input consists of several test cases. Each line of the input contains an integer k where 0<=k<=500000.
The last line contains an integer -1, which should not be processed.

Output

For each k given in the input, print one line containing a(k) to the output.

Sample Input

7
10000
-1

Sample Output

20
18658

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

struct Entry
{
    int i;
    int val;
    int next;
};

int flag[1000000];
int out[500010];

int main()
{
    int i, val, t;

    memset(flag, 0, sizeof(flag));
    flag[0] = 1;
    out[0] = 0;
    for (i = 1; i <= 500000; ++i)
    {
        t = out[i - 1] - i;
        if ((t < 0) || (flag[t / 32] & (1 << (t & 0x1F))))
            t = out[i - 1] + i;

        out[i] = t;
        flag[t / 32] |= (1 << (t & 0x1F));
    }

    while (scanf("%d", &val) && (val >= 0))
        printf("%d\n", out[val]);

    return 0;
}