#include <cstdio> #include <iostream> #include <algorithm> #include <cstring> #include <vector> #include <set> #include <map> #include <cmath> #include <list> #include <ctime> #include <sstream> #include <queue> #include <stack> #include <bitset> #include <unordered_set> #include <unordered_map> using namespace std; typedef vector<int> vi; typedef pair<int,int> pii; typedef long long ll; typedef short int sint; #define FOR(x, b, e) for(int x=(b); x<=(e); ++x) #define FORD(x, b, e) for(int x=((int)(b))-1; x>=(e); --x) #define REP(x, n) for(int x=0; x<(n); ++x) #define ALL(c) c.begin(),c.end() #define SIZE(x) ((int)((x).size())) #define PB push_back #define ST first #define ND second // #define DEBUG 0 #define debug(x) {if (DEBUG)cerr <<#x <<" = " <<x <<endl; } #define debugv(x) {if (DEBUG) {cerr <<#x <<" = "; FOREACH(it, (x)) cerr <<*it <<", "; cout <<endl; }} #define REMAX(a,b) (a)=max((a),(b)); #define REMIN(a,b) (a)=min((a),(b)); #define wez(n) int (n); scanf("%d",&(n)); #define wez2(n,m) int (n),(m); scanf("%d %d",&(n),&(m)); ll nwd(ll x, ll y) { if (y == 0) { return x; } return nwd(y, x % y); } struct num { ll l, m; num() { } num(ll x): l(x), m(1) {} num(ll x, ll y) { ll dziel = nwd(x, y); l = x / dziel; m = y / dziel; } bool operator < (const num &b) const { return l * b.m < b.l * m; } bool operator==(const num& b) const { return l == b.l && m == b.m; } }; num operator-(const num& a, const num& b) { return num(a.l * b.m - b.l * a.m, a.m * b.m); } num operator+(const num& a, const num& b) { return num(a.l*b.m + b.l*a.m, a.m * b.m); } num operator*(const num &a, const num& b) { return num(a.l * b.l, a.m * b.m); } num operator/(const num& a, const num& b) { return num(a.l * b.m, a.m * b.l); } typedef long double number; typedef pair<number, number> event; const int N = 100101; const number eps = 1e-7; int n, n1, n2; event ea[N], eb[N], tea[N], teb[N]; event lacz(const event& a, const event& b) { return {(a.ND * a.ST + b.ST * b.ND)/(a.ND + b.ND), a.ND + b.ND}; } void printOne(int idx, int limit, const event* tab) { for (int i = idx; i < limit; ++i) { printf("{t: %Lf, l: %Lf} ", tab[i].ST, tab[i].ND); } printf("\n"); } void printState(int ida, int idb) { printf("A: "); printOne(ida, n1, ea); printf("B: "); printOne(idb, n2, eb); } bool eq(const number& a, const number&b) { return abs(a - b) < eps; } void testcase(bool DEBUG) { ll s1 = 0, s2 = 0; scanf("%d", &n); map<int, ll> wyd; for (int i = 0; i < n; ++i) { int l, a, b; scanf("%d %d %d", &l, &a, &b); s1 += (ll)a * l; s2 += (ll)b * l; wyd[a] += l; wyd[b] -= l; } if (s1 != s2) { printf("NIE\n"); return; } n1 = 0, n2 = 0; for (auto elem : wyd) { if (elem.ND == 0) { continue; } if (elem.ND > 0) { ea[n1++] = {elem.ST, elem.ND}; } else { eb[n2++] = {elem.ST, -elem.ND}; } } sort(ea, ea + n1); sort(eb, eb + n2); int ida = 0, idb = 0; while (ida < n1 && idb < n2) { if (DEBUG)printf("ida: %d, idb: %d\n", ida, idb); if (DEBUG)printState(ida, idb); if (eq(ea[ida].ND, 0.)) { ++ida; } else if (eb[idb].ST + eps < ea[ida].ST) { if (DEBUG) printf("first early return\n"); printf("NIE\n"); return; } else if (eq(ea[ida].ST, eb[idb].ST)) { if (eq(ea[ida].ND, eb[idb].ND)) { if (DEBUG) printf("both same, taking out\n"); ++ida; ++idb; } else if (ea[ida].ND < eb[idb].ND) { if (DEBUG) printf("same, less litres on first\n"); eb[idb].ND = eb[idb].ND - ea[ida].ND; ++ida; } else { if (DEBUG) printf("same, less litres on second\n"); ea[ida].ND = ea[ida].ND - eb[idb].ND; ++idb; } } else { if (ida + 1 < n1) { auto nalane = lacz(ea[ida], ea[ida + 1]); // if (DEBUG) printf("If joined first 1and2, temp: %lld/%lld\n", nalane.ST.l, nalane.ST.m); if (nalane.ST + eps < eb[idb].ST || eq(nalane.ST, eb[idb].ST)) { if (DEBUG) printf("Joining both first is smaller than second, join\n"); ea[ida + 1] = nalane; ++ida; } else { // hard hard hard case auto szuk = (ea[ida].ND*(eb[idb].ST - ea[ida].ST)/(ea[ida + 1].ST - eb[idb].ST)); // if (DEBUG) printf("would need (%lld/%lld) of second\n", szuk.l, szuk.m); // tyle potrzeba litrow ea[ida + 1]; if (ea[ida + 1].ND + eps < szuk) { // SHOULD NEVER HAPPEN if (DEBUG) printf("3rd early return\n"); printf("NIE\n"); return; } else { // if (DEBUG) printf("joining (%lld/%lld) to first and removing from further\n", szuk.l, szuk.m); ea[ida] = {eb[idb].ST, ea[ida].ND + szuk}; ea[ida+1]={ea[ida+1].ST, ea[ida + 1].ND - szuk}; } } } else { if (DEBUG) printf("second early return\n"); printf("NIE\n"); return; } } } while (ida < n1 && eq(ea[ida].ND, 0.)) { ++ida; } if (ida == n1 && idb == n2) { printf("TAK\n"); } else { printf("NIE\n"); } } int main() { int t; scanf("%d", &t); // t=1; FOR(q, 1, t) { testcase(false); } return 0; }
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 | #include <cstdio> #include <iostream> #include <algorithm> #include <cstring> #include <vector> #include <set> #include <map> #include <cmath> #include <list> #include <ctime> #include <sstream> #include <queue> #include <stack> #include <bitset> #include <unordered_set> #include <unordered_map> using namespace std; typedef vector<int> vi; typedef pair<int,int> pii; typedef long long ll; typedef short int sint; #define FOR(x, b, e) for(int x=(b); x<=(e); ++x) #define FORD(x, b, e) for(int x=((int)(b))-1; x>=(e); --x) #define REP(x, n) for(int x=0; x<(n); ++x) #define ALL(c) c.begin(),c.end() #define SIZE(x) ((int)((x).size())) #define PB push_back #define ST first #define ND second // #define DEBUG 0 #define debug(x) {if (DEBUG)cerr <<#x <<" = " <<x <<endl; } #define debugv(x) {if (DEBUG) {cerr <<#x <<" = "; FOREACH(it, (x)) cerr <<*it <<", "; cout <<endl; }} #define REMAX(a,b) (a)=max((a),(b)); #define REMIN(a,b) (a)=min((a),(b)); #define wez(n) int (n); scanf("%d",&(n)); #define wez2(n,m) int (n),(m); scanf("%d %d",&(n),&(m)); ll nwd(ll x, ll y) { if (y == 0) { return x; } return nwd(y, x % y); } struct num { ll l, m; num() { } num(ll x): l(x), m(1) {} num(ll x, ll y) { ll dziel = nwd(x, y); l = x / dziel; m = y / dziel; } bool operator < (const num &b) const { return l * b.m < b.l * m; } bool operator==(const num& b) const { return l == b.l && m == b.m; } }; num operator-(const num& a, const num& b) { return num(a.l * b.m - b.l * a.m, a.m * b.m); } num operator+(const num& a, const num& b) { return num(a.l*b.m + b.l*a.m, a.m * b.m); } num operator*(const num &a, const num& b) { return num(a.l * b.l, a.m * b.m); } num operator/(const num& a, const num& b) { return num(a.l * b.m, a.m * b.l); } typedef long double number; typedef pair<number, number> event; const int N = 100101; const number eps = 1e-7; int n, n1, n2; event ea[N], eb[N], tea[N], teb[N]; event lacz(const event& a, const event& b) { return {(a.ND * a.ST + b.ST * b.ND)/(a.ND + b.ND), a.ND + b.ND}; } void printOne(int idx, int limit, const event* tab) { for (int i = idx; i < limit; ++i) { printf("{t: %Lf, l: %Lf} ", tab[i].ST, tab[i].ND); } printf("\n"); } void printState(int ida, int idb) { printf("A: "); printOne(ida, n1, ea); printf("B: "); printOne(idb, n2, eb); } bool eq(const number& a, const number&b) { return abs(a - b) < eps; } void testcase(bool DEBUG) { ll s1 = 0, s2 = 0; scanf("%d", &n); map<int, ll> wyd; for (int i = 0; i < n; ++i) { int l, a, b; scanf("%d %d %d", &l, &a, &b); s1 += (ll)a * l; s2 += (ll)b * l; wyd[a] += l; wyd[b] -= l; } if (s1 != s2) { printf("NIE\n"); return; } n1 = 0, n2 = 0; for (auto elem : wyd) { if (elem.ND == 0) { continue; } if (elem.ND > 0) { ea[n1++] = {elem.ST, elem.ND}; } else { eb[n2++] = {elem.ST, -elem.ND}; } } sort(ea, ea + n1); sort(eb, eb + n2); int ida = 0, idb = 0; while (ida < n1 && idb < n2) { if (DEBUG)printf("ida: %d, idb: %d\n", ida, idb); if (DEBUG)printState(ida, idb); if (eq(ea[ida].ND, 0.)) { ++ida; } else if (eb[idb].ST + eps < ea[ida].ST) { if (DEBUG) printf("first early return\n"); printf("NIE\n"); return; } else if (eq(ea[ida].ST, eb[idb].ST)) { if (eq(ea[ida].ND, eb[idb].ND)) { if (DEBUG) printf("both same, taking out\n"); ++ida; ++idb; } else if (ea[ida].ND < eb[idb].ND) { if (DEBUG) printf("same, less litres on first\n"); eb[idb].ND = eb[idb].ND - ea[ida].ND; ++ida; } else { if (DEBUG) printf("same, less litres on second\n"); ea[ida].ND = ea[ida].ND - eb[idb].ND; ++idb; } } else { if (ida + 1 < n1) { auto nalane = lacz(ea[ida], ea[ida + 1]); // if (DEBUG) printf("If joined first 1and2, temp: %lld/%lld\n", nalane.ST.l, nalane.ST.m); if (nalane.ST + eps < eb[idb].ST || eq(nalane.ST, eb[idb].ST)) { if (DEBUG) printf("Joining both first is smaller than second, join\n"); ea[ida + 1] = nalane; ++ida; } else { // hard hard hard case auto szuk = (ea[ida].ND*(eb[idb].ST - ea[ida].ST)/(ea[ida + 1].ST - eb[idb].ST)); // if (DEBUG) printf("would need (%lld/%lld) of second\n", szuk.l, szuk.m); // tyle potrzeba litrow ea[ida + 1]; if (ea[ida + 1].ND + eps < szuk) { // SHOULD NEVER HAPPEN if (DEBUG) printf("3rd early return\n"); printf("NIE\n"); return; } else { // if (DEBUG) printf("joining (%lld/%lld) to first and removing from further\n", szuk.l, szuk.m); ea[ida] = {eb[idb].ST, ea[ida].ND + szuk}; ea[ida+1]={ea[ida+1].ST, ea[ida + 1].ND - szuk}; } } } else { if (DEBUG) printf("second early return\n"); printf("NIE\n"); return; } } } while (ida < n1 && eq(ea[ida].ND, 0.)) { ++ida; } if (ida == n1 && idb == n2) { printf("TAK\n"); } else { printf("NIE\n"); } } int main() { int t; scanf("%d", &t); // t=1; FOR(q, 1, t) { testcase(false); } return 0; } |