扩展欧几里得的应用。
1 /* 1356 */ 2 #include <iostream> 3 #include <sstream> 4 #include <string> 5 #include <map> 6 #include <queue> 7 #include <set> 8 #include <stack> 9 #include <vector> 10 #include <deque> 11 #include <bitset> 12 #include <algorithm> 13 #include <cstdio> 14 #include <cmath> 15 #include <ctime> 16 #include <cstring> 17 #include <climits> 18 #include <cctype> 19 #include <cassert> 20 #include <functional> 21 #include <iterator> 22 #include <iomanip> 23 using namespace std; 24 //#pragma comment(linker,"/STACK:102400000,1024000") 25 26 #define sti set<int> 27 #define stpii set<pair<int, int> > 28 #define mpii map<int,int> 29 #define vi vector<int> 30 #define pii pair<int,int> 31 #define vpii vector<pair<int,int> > 32 #define rep(i, a, n) for (int i=a;i<n;++i) 33 #define per(i, a, n) for (int i=n-1;i>=a;--i) 34 #define clr clear 35 #define pb push_back 36 #define mp make_pair 37 #define fir first 38 #define sec second 39 #define all(x) (x).begin(),(x).end() 40 #define SZ(x) ((int)(x).size()) 41 #define lson l, mid, rt<<1 42 #define rson mid+1, r, rt<<1|1 43 44 int a, b, d; 45 46 int e_gcd(int n, int m, int& x, int& y) { 47 if (m == 0) { 48 x = 1; 49 y = 0; 50 return n; 51 } 52 53 int ret = e_gcd(m, n%m, y, x); 54 y -= n/m*x; 55 56 return ret; 57 } 58 59 void solve() { 60 int x, y; 61 bool flag = false; 62 63 if (a < b) { 64 swap(a, b); 65 flag = true; 66 } 67 68 int g = e_gcd(a, b, x, y); 69 int mn = 1e9; 70 int mn_ = 1e9; 71 a /= g; 72 b /= g; 73 x = d/g*x; 74 y = d/g*y; 75 int Beg = -x/b-1; 76 int End = y/a+1; 77 int xx, yy; 78 int tmp, tmp_; 79 int ansx = 0, ansy = 0; 80 81 rep(i, Beg, End+1) { 82 xx = abs(x+b*i); 83 yy = abs(y-a*i); 84 tmp = xx + yy; 85 tmp_ = a*xx + b*yy; 86 if (tmp < mn) { 87 mn = tmp; 88 mn_ = tmp_; 89 ansx = xx; 90 ansy = yy; 91 } else if (tmp==mn && tmp_<mn_) { 92 mn_ = tmp_; 93 ansx = xx; 94 ansy = yy; 95 } 96 } 97 98 if (flag) 99 swap(ansx, ansy); 100 printf("%d %d ", ansx, ansy); 101 } 102 103 int main() { 104 ios::sync_with_stdio(false); 105 #ifndef ONLINE_JUDGE 106 freopen("data.in", "r", stdin); 107 freopen("data.out", "w", stdout); 108 #endif 109 110 while (scanf("%d %d %d",&a,&b,&d)!=EOF) { 111 if(a==0 && b==0 && d==0) 112 break; 113 solve(); 114 } 115 116 #ifndef ONLINE_JUDGE 117 printf("time = %d. ", (int)clock()); 118 #endif 119 120 return 0; 121 }