埃及分数 迭代加深搜索 IDA*

迭代加深搜索 IDA*
首先枚举当前选择的分数个数上限maxd，进行迭代加深
之后进行估价，假设当前分数之和为a,目标分数为b，当前考虑分数为1/c，那么如果1/c×（maxd - d）< a - b那么不可能得解，进行剪枝

1 #include <cstdio>
2 #include <cstring>
3 #include <algorithm>
4
5
6 const int maxn = 100;
7 const int inf = 2139062143;
8 int a, b;
9 int ans[maxn], cur[maxn];
10 int maxd = 0;
11
12
13 bool better(void) {
14     for (int i = maxd; i >= 1; i--) {
15         if (cur[i] < ans[i]) return (1);
16         else if (cur[i] > ans[i]) return (0);
17     }
18 }
19
20 int gcd(int x, int y) {
21     return (y == 0 ? x : gcd(y, x % y));
22 }
23
24 int getfirst(int aa, int bb) {
25     if (bb % aa == 0) return (bb / aa);
26     else return (bb / aa + 1);
27 }
28
29 void dfs(int d, int aa, int bb) {
30     if (d == maxd + 1) {
31         if (!aa && better()) memcpy(ans, cur, sizeof(int) * (maxd + 1));
32         return;
33     }
34     int fr = std :: max(getfirst(aa, bb), cur[d-1] + 1);
35     for (; ; fr++) {
36         if (aa * fr > (bb * (maxd - d + 1))) break;
37         cur[d] = fr;
38         int g = gcd(bb, fr);
39         int ta = (aa * fr - bb) / g;
40         int tb = (bb * fr / g);
41         dfs(d + 1, ta, tb);
42     }
43 }
44 int main () {
45     scanf("%d %d", &a, &b);
46     for (maxd = 1; ; maxd++) {
47         memset(ans, 127, sizeof(ans));
48         dfs(1, a, b);
49         if (ans[1] > 0 && ans[1] != inf) {
50             int cur = 1;
51             while (ans[cur] > 0 && ans[cur] != inf) {
52                 printf("%d ", ans[cur]);
53                 cur++;
54             }
55             break;
56         }
57     }
58
59     <
4000
span style="color:#0000ff;">return 0;
60 }