【HDOJ】4516 威威猫系列故事——因式分解

可解的算法太多了，采用的算法是试x的值。注意题目的输入x^3-2x^2不会写成x^3+-2x^2。一直RE在这儿。

  1 /* 4516 */
  2 #include <iostream>
  3 #include <string>
  4 #include <map>
  5 #include <queue>
  6 #include <set>
  7 #include <stack>
  8 #include <vector>
  9 #include <deque>
 10 #include <algorithm>
 11 #include <cstdio>
 12 #include <cmath>
 13 #include <ctime>
 14 #include <cstring>
 15 #include <climits>
 16 #include <cctype>
 17 #include <cassert>
 18 #include <functional>
 19 #include <iterator>
 20 #include <iomanip>
 21 using namespace std;
 22 //#pragma comment(linker,"/STACK:102400000,1024000")
 23 
 24 #define sti                set<int>
 25 #define stpii            set<pair<int, int> >
 26 #define mpii            map<int,int>
 27 #define vi                vector<int>
 28 #define pii                pair<int,int>
 29 #define vpii            vector<pair<int,int> >
 30 #define rep(i, a, n)     for (int i=a;i<n;++i)
 31 #define per(i, a, n)     for (int i=n-1;i>=a;--i)
 32 #define clr                clear
 33 #define pb                 push_back
 34 #define mp                 make_pair
 35 #define fir                first
 36 #define sec                second
 37 #define all(x)             (x).begin(),(x).end()
 38 #define SZ(x)             ((int)(x).size())
 39 #define lson            l, mid, rt<<1
 40 #define rson            mid+1, r, rt<<1|1
 41 #define LL                long long
 42 
 43 const int maxl = 505;
 44 const int maxn = 10;
 45 char s[maxl], ss[maxl];
 46 int A[40][maxn], B[maxn], B_[maxn];
 47 int c[maxn], cn;
 48 
 49 bool check() {
 50     memset(B, 0, sizeof(B));
 51     B[1] = 1;
 52     B[0] = c[0];
 53         
 54     rep(i, 1, cn) {
 55         memset(B_, 0, sizeof(B_));
 56         rep(j, 1, maxn)
 57             B_[j] += B[j-1];
 58         rep(j, 0, maxn)
 59             B_[j] += B[j] * c[i];
 60         memcpy(B, B_, sizeof(B));
 61     }
 62     
 63     rep(i, 0, maxn) {
 64         if (A[0][i] != B[i])
 65             return false;
 66     }
 67     
 68     return true;
 69 }
 70 
 71 bool judge(int p, int i, int x) {
 72     LL ret = 0, base = 1;
 73     
 74     for (int j=0; j<=i; ++j) {
 75         ret += A[p][j] * base;
 76         base *= x;
 77     }
 78     
 79     return ret == 0;
 80 }
 81 
 82 void reduce(int p, int i, int x) {
 83     int q = p + 1;
 84     
 85     memcpy(B, A[p], sizeof(B));
 86     for (int j=i; j>0; --j) {
 87         A[q][j-1] = B[j];
 88         B[j-1] -= B[j] * x;
 89     }
 90 }
 91 
 92 bool solve() {
 93     // init parameter
 94     int i = 0, a = 0, p = 0, q;
 95     int cnt = 0;
 96     bool neg = false, flag = false;
 97     
 98     memset(A, 0, sizeof(A));
 99     cn = 0;
100     
101     while (1) {
102         if (s[i]=='+' || s[i]=='\0') {
103             if (neg)
104                 a = -a;
105             if (flag && p==0)
106                 p = 1;
107             A[0][p] += a;
108             neg = false;
109             flag = false;
110             p = 0;
111             a = 0;
112             cnt = 0;
113         } else if (s[i] == '-') {
114             neg = true;
115         } else if (s[i] == 'x') {
116             if (cnt == 0)
117                 a = 1;
118             flag = true;
119         } else if (s[i] == '^') {
120             ;
121         } else {
122             if (flag)
123                 p = p*10+s[i]-'0';
124             else
125                 a = a*10+s[i]-'0';
126             ++cnt;
127         }        
128         if (s[i] == '\0')
129             break;
130         ++i;
131     }
132     
133     p = 0, q = 1;
134     int x, xx;
135     
136     while (1) {
137         for (i=5; i>=0; --i) {
138             if (A[p][i] != 0)
139                 break;
140         }
141         if (i < 0)
142             break;
143         if (A[p][i] != 1)
144             return false;
145         if (i == 0)
146             break;
147         
148         a = A[p][0];
149         if (a == 0) {
150             c[cn] = 0;
151             while (i > 0) {
152                 A[q][i-1] = A[p][i];
153                 --i;
154             }
155             flag = true;
156         } else if (a > 0) {
157             flag = false;
158             for (x=1; x*x<=a; ++x) {
159                 if (a%x == 0) {
160                     if (judge(p, i, -x)) {
161                         reduce(p, i, x);
162                         flag = true;
163                         c[cn] = x;
164                         break;
165                     } else if (judge(p, i, x)) {
166                         reduce(p, i, -x);
167                         flag = true;
168                         c[cn] = -x;
169                         break;
170                     }
171                     xx = a/x;
172                     if (xx != x) {
173                         if (judge(p, i, -xx)) {
174                             reduce(p, i, xx);
175                             flag = true;
176                             c[cn] = xx;
177                             break;
178                         } else if (judge(p, i, xx)) {
179                             reduce(p, i, -xx);
180                             flag = true;
181                             c[cn] = -xx;
182                             break;
183                         }
184                     }
185                 }
186             }
187         } else {
188             flag = false;
189             a = -a;
190             for (x=1; x*x<=a; ++x) {
191                 if (a%x == 0) {
192                     if (judge(p, i, x)) {
193                         reduce(p, i, -x);
194                         c[cn] = -x;
195                         flag = true;
196                         break;
197                     } else if (judge(p, i, -x)) {
198                         reduce(p, i, x);
199                         c[cn] = x;
200                         flag = true;
201                         break;
202                     }
203                     xx = a/x;
204                     if (xx != x) {
205                         if (judge(p, i, xx)) {
206                             reduce(p, i, -xx);
207                             flag = true;
208                             c[cn] = -xx;
209                             break;
210                         } else if (judge(p, i, -xx)) {
211                             reduce(p, i, xx);
212                             flag = true;
213                             c[cn] = xx;
214                             break;
215                         }
216                     }
217                 }
218             }
219         }
220         
221         if (!flag)
222             return false;
223         
224         ++cn;
225         ++p;
226         ++q;
227     }
228     
229     return cn>0;
230 }
231 
232 void change() {
233     int l = 0;
234     int i = 0;
235     int len = strlen(s);
236     
237     while (i < len) {
238         if (s[i] == '-') {
239             if (i && s[i-1]!='+')
240                 ss[l++] = '+';
241         }
242         ss[l++] = s[i++];
243     }
244         
245     ss[l]  = '\0';
246     strcpy(s, ss);
247 }
248 
249 int main() {
250     ios::sync_with_stdio(false);
251     #ifndef ONLINE_JUDGE
252         freopen("data.in", "r", stdin);
253         freopen("data.out", "w", stdout);
254     #endif
255     
256     int t;
257     bool flag;
258     
259     scanf("%d", &t);
260     rep(tt, 1, t+1) {
261         scanf("%s", s);
262         change();
263         flag = solve();
264         printf("Case #%d: ", tt);
265         if (flag) {
266             sort(c, c+cn);
267             rep(i, 0, cn) {
268                 if (c[i] == 0)
269                     printf("x");
270                 else if (c[i] > 0)
271                     printf("(x+%d)", c[i]);
272                 else
273                     printf("(x-%d)", -c[i]);
274             }
275             putchar('\n');
276             #ifndef ONLINE_JUDGE
277                 if (!check())
278                     puts("wrong");
279             #endif
280         } else {
281             puts("-1");
282         }
283     }
284     
285     #ifndef ONLINE_JUDGE
286         printf("time = %d.\n", (int)clock());
287     #endif
288     
289     return 0;
290 }

测试数据和答案。

 1 from random import randint
 2 import shutil
 3 
 4 def GenEle(k):
 5     if k == 0:
 6         return "x"
 7     elif k>0:
 8         return "(x+%d)" % (k)
 9     else:
10         return "(x-%d)" % (-k)
11         
12 
13 def GenLine():
14     src, ans = "", ""
15     k = randint(1, 5)
16     L = []
17     for i in xrange(k):
18         x = randint(-10, 10)
19         L.append(x)
20     L = sorted(L)
21     ans = "".join(map(GenEle, L))
22     a = [0 for i in xrange(6)]
23     a[1] = 1
24     a[0] = L[0]
25     for i in xrange(1, k):
26         b = [0 for j in xrange(6)]
27         for j in xrange(1, 6):
28             b[j] += a[j-1]
29         for j in xrange(0, 6):
30             b[j] += a[j] * L[i]
31         a = b
32     i = 5
33     while i>=0:
34         if a[i]>0:
35             break
36         i -= 1
37     srcList = []
38     while i>=0:
39         line = ""
40         if a[i] < 0:
41             line += "-"
42             a[i] = -a[i]
43         if i==0 or a[i]!=1:
44             line += str(a[i])
45         if i==1:
46             line += "x"
47         elif i>1:
48             line += "x^%d" % i
49         i -= 1
50         srcList.append(line) 
51     src = "+".join(srcList)
52     return src, ans
53 
54 
55 def GenDataIn():
56     bound = 10**2
57     ansList = []
58     with open("data.in", "w") as fout:
59         t = 50
60         fout.write("%d\n" % (t))
61         for tt in xrange(t):
62             line, ans = GenLine()
63             fout.write(line + "\n")
64             ansList.append(ans)
65     with open("F:\code_today\data.in", "w") as fout:
66         for i,ans in enumerate(ansList):
67             line = "Case #%d: %s\n" % (i+1, ans)
68             fout.write(line)
69     
70         
71 def MovDataIn():
72     desFileName = "F:\workspace\cpp_hdoj\data.in"
73     shutil.copyfile("data.in", desFileName)
74 
75 if __name__ == "__main__":
76     GenDataIn()
77     MovDataIn()
78     
79

 



posted on 2015-12-20 21:22  Bombe  阅读(261)  评论(0)  编辑  收藏  举报

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