【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。

 /* 4516 */
 #include <iostream>
 #include <string>
 #include <map>
 #include <queue>
 #include <set>
 #include <stack>
 #include <vector>
 #include <deque>
 #include <algorithm>
 #include <cstdio>
 #include <cmath>
 #include <ctime>
 #include <cstring>
 #include <climits>
 #include <cctype>
 #include <cassert>
 #include <functional>
 #include <iterator>
 #include <iomanip>
 using namespace std;
 //#pragma comment(linker,"/STACK:102400000,1024000")

 #define sti                set<int>
 #define stpii            set<pair<int, int> >
 #define mpii            map<int,int>
 #define vi                vector<int>
 #define pii                pair<int,int>
 #define vpii            vector<pair<int,int> >
 #define rep(i, a, n)     for (int i=a;i<n;++i)
 #define per(i, a, n)     for (int i=n-1;i>=a;--i)
 #define clr                clear
 #define pb                 push_back
 #define mp                 make_pair
 #define fir                first
 #define sec                second
 #define all(x)             (x).begin(),(x).end()
 #define SZ(x)             ((int)(x).size())
 #define lson            l, mid, rt<<1
 #define rson            mid+1, r, rt<<1|1
 #define LL                long long

 const int maxl = ;
 const int maxn = ;
 char s[maxl], ss[maxl];
 int A[][maxn], B[maxn], B_[maxn];
 int c[maxn], cn;

 bool check() {
     memset(B, , sizeof(B));
     B[] = ;
     B[] = c[];

     rep(i, , cn) {
         memset(B_, , sizeof(B_));
         rep(j, , maxn)
             B_[j] += B[j-];
         rep(j, , maxn)
             B_[j] += B[j] * c[i];
         memcpy(B, B_, sizeof(B));
     }

     rep(i, , maxn) {
         if (A[][i] != B[i])
             return false;
     }

     return true;
 }

 bool judge(int p, int i, int x) {
     LL ret = , base = ;

     for (int j=; j<=i; ++j) {
         ret += A[p][j] * base;
         base *= x;
     }

     return ret == ;
 }

 void reduce(int p, int i, int x) {
     int q = p + ;

     memcpy(B, A[p], sizeof(B));
     for (int j=i; j>; --j) {
         A[q][j-] = B[j];
         B[j-] -= B[j] * x;
     }
 }

 bool solve() {
     // init parameter
     int i = , a = , p = , q;
     int cnt = ;
     bool neg = false, flag = false;

     memset(A, , sizeof(A));
     cn = ;

     while () {
         if (s[i]=='+' || s[i]=='\0') {
             if (neg)
                 a = -a;
             if (flag && p==)
                 p = ;
             A[][p] += a;
             neg = false;
             flag = false;
             p = ;
             a = ;
             cnt = ;
         } else if (s[i] == '-') {
             neg = true;
         } else if (s[i] == 'x') {
             if (cnt == )
                 a = ;
             flag = true;
         } else if (s[i] == '^') {
             ;
         } else {
             if (flag)
                 p = p*+s[i]-'';
             else
                 a = a*+s[i]-'';
             ++cnt;
         }
         if (s[i] == '\0')
             break;
         ++i;
     }

     p = , q = ;
     int x, xx;

     while () {
         for (i=; i>=; --i) {
             if (A[p][i] != )
                 break;
         }
         if (i < )
             break;
         if (A[p][i] != )
             return false;
         if (i == )
             break;

         a = A[p][];
         if (a == ) {
             c[cn] = ;
             while (i > ) {
                 A[q][i-] = A[p][i];
                 --i;
             }
             flag = true;
         } else if (a > ) {
             flag = false;
             for (x=; x*x<=a; ++x) {
                 if (a%x == ) {
                     if (judge(p, i, -x)) {
                         reduce(p, i, x);
                         flag = true;
                         c[cn] = x;
                         break;
                     } else if (judge(p, i, x)) {
                         reduce(p, i, -x);
                         flag = true;
                         c[cn] = -x;
                         break;
                     }
                     xx = a/x;
                     if (xx != x) {
                         if (judge(p, i, -xx)) {
                             reduce(p, i, xx);
                             flag = true;
                             c[cn] = xx;
                             break;
                         } else if (judge(p, i, xx)) {
                             reduce(p, i, -xx);
                             flag = true;
                             c[cn] = -xx;
                             break;
                         }
                     }
                 }
             }
         } else {
             flag = false;
             a = -a;
             for (x=; x*x<=a; ++x) {
                 if (a%x == ) {
                     if (judge(p, i, x)) {
                         reduce(p, i, -x);
                         c[cn] = -x;
                         flag = true;
                         break;
                     } else if (judge(p, i, -x)) {
                         reduce(p, i, x);
                         c[cn] = x;
                         flag = true;
                         break;
                     }
                     xx = a/x;
                     if (xx != x) {
                         if (judge(p, i, xx)) {
                             reduce(p, i, -xx);
                             flag = true;
                             c[cn] = -xx;
                             break;
                         } else if (judge(p, i, -xx)) {
                             reduce(p, i, xx);
                             flag = true;
                             c[cn] = xx;
                             break;
                         }
                     }
                 }
             }
         }

         if (!flag)
             return false;

         ++cn;
         ++p;
         ++q;
     }

     return cn>;
 }

 void change() {
     int l = ;
     int i = ;
     int len = strlen(s);

     while (i < len) {
         if (s[i] == '-') {
             if (i && s[i-]!='+')
                 ss[l++] = '+';
         }
         ss[l++] = s[i++];
     }

     ss[l]  = '\0';
     strcpy(s, ss);
 }

 int main() {
     ios::sync_with_stdio(false);
     #ifndef ONLINE_JUDGE
         freopen("data.in", "r", stdin);
         freopen("data.out", "w", stdout);
     #endif

     int t;
     bool flag;

     scanf("%d", &t);
     rep(tt, , t+) {
         scanf("%s", s);
         change();
         flag = solve();
         printf("Case #%d: ", tt);
         if (flag) {
             sort(c, c+cn);
             rep(i, , cn) {
                 if (c[i] == )
                     printf("x");
                 else if (c[i] > )
                     printf("(x+%d)", c[i]);
                 else
                     printf("(x-%d)", -c[i]);
             }
             putchar('\n');
             #ifndef ONLINE_JUDGE
                 if (!check())
                     puts("wrong");
             #endif
         } else {
             puts("-1");
         }
     }

     #ifndef ONLINE_JUDGE
         printf("time = %d.\n", (int)clock());
     #endif

     return ;
 }

测试数据和答案。

 from random import randint
 import shutil

 def GenEle(k):
     if k == 0:
         return "x"
     elif k>0:
         return "(x+%d)" % (k)
     else:
         return "(x-%d)" % (-k)

 def GenLine():
     src, ans = "", ""
     k = randint(1, 5)
     L = []
     for i in xrange(k):
         x = randint(-10, 10)
         L.append(x)
     L = sorted(L)
     ans = "".join(map(GenEle, L))
     a = [0 for i in xrange(6)]
     a[1] = 1
     a[0] = L[0]
     for i in xrange(1, k):
         b = [0 for j in xrange(6)]
         for j in xrange(1, 6):
             b[j] += a[j-1]
         for j in xrange(0, 6):
             b[j] += a[j] * L[i]
         a = b
     i = 5
     while i>=0:
         if a[i]>0:
             break
         i -= 1
     srcList = []
     while i>=0:
         line = ""
         if a[i] < 0:
             line += "-"
             a[i] = -a[i]
         if i==0 or a[i]!=1:
             line += str(a[i])
         if i==1:
             line += "x"
         elif i>1:
             line += "x^%d" % i
         i -= 1
         srcList.append(line)
     src = "+".join(srcList)
     return src, ans

 def GenDataIn():
     bound = 10**2
     ansList = []
     with open("data.in", "w") as fout:
         t = 50
         fout.write("%d\n" % (t))
         for tt in xrange(t):
             line, ans = GenLine()
             fout.write(line + "\n")
             ansList.append(ans)
     with open("F:\code_today\data.in", "w") as fout:
         for i,ans in enumerate(ansList):
             line = "Case #%d: %s\n" % (i+1, ans)
             fout.write(line)

 def MovDataIn():
     desFileName = "F:\workspace\cpp_hdoj\data.in"
     shutil.copyfile("data.in", desFileName)

 if __name__ == "__main__":
     GenDataIn()
     MovDataIn()