#include<bits/stdc++.h> #include<time.h> #define llu long long unsigned #define MAXSIZE 10000 #define pb push_back using namespace::std; typedef vector <int> vi; typedef pair < int, int > ii; typedef vector < ii > vii; typedef vector <vii> vvii; typedef vector < vi > vvi; //r2 keeps track of the no. of open window children of root of /**each**/ tree in the forest map <int, llu> r2; map <int, llu> aux_map; vi tree; vector <int> track; vector <bool> vs; class disjoint_sets { public : unordered_map <int, int > parent; unordered_map <int, int > rank; //constructor disjoint_sets(deque <int> &universe) { for(int x : universe)//for(auto it = universe.begin() ; it != universe.end() ; ++it) //: line no nodes req { parent[x] = x; rank[x] = 0; } } int find(int item) { if(parent[item] == item) return item; else return find(parent[item]); } void unite(int a, int b) { int a_parent = find(a); int b_parent = find(b); if(rank[a_parent] > rank[b_parent]) { parent[b_parent] = a_parent; rank[a_parent] += rank[b_parent]; } else if(rank[a_parent] < rank[b_parent]) { parent[a_parent] = b_parent; rank[b_parent] += rank[a_parent]; } else { parent[a_parent] = b_parent; rank[b_parent] ++; } } void disp() { for(pair < int, int > p : parent) //for(auto it = parent.begin() ; it != parent.end() ; ++it) cout<<p.second<<" "; } }; int dfs_fun(vvi &g, int x, vector <int> &key, vector <bool> &vs) //function for second query { vs[x] = true; int res = (key[x] == 1) ? 1 :0; for(auto it : g[x]) if(!vs[it]) { if(key[it] == 1) { vs[it] = true; return 1; } res = dfs_fun(g, it, key, vs); if(res) return res; } return res; } llu dfs(vvi &g, vector <bool> &vs, int v, vi &key) { vs[v] = true; llu c = 1; //contribution of the node on which dfs has been called, ...we'll return c-1 later if this nodes window is closed for(auto it = g[v].begin() ; it != g[v].end() ; ++it) if(!vs[*it]) c += dfs(g, vs, *it, key); //increment c by the no of open window nodes rooted at c if(key[v]) { r2[v] = c ; //map r2 keeps track of no. of open window nodes rooted at each node of the graph return c ; } { r2[v] = c-1 ; //if the node has its window closed,adjust its contribution which was initiated as 1 return c-1; } } void drought(vvi &g, vi &key, int V, vi &r1) { vs = vector<bool> (V+1, false); vs[0] = true; for(int i = 1 ; i <= V ; ++i) if(!vs[i]) { tree.pb(i); // the vector tree keeps track of root of each tree in the forest r1.pb(dfs(g, vs, i, key)); //the vector r1 stores the no of 'open window' nodes rooted at each root of the forest including the status of root } } long long unsigned calculate(vi tree, map<int, llu> &r2) { long long unsigned count = 0; for(auto it : tree) count += (r2[it]*(r2[it]-1))/2; return count; } int main() { // ios_base::sync_with_stdio(0); // cin.tie(0); srand(time(0)); track.reserve(50050); tree.reserve(50050); int V, E, s, d, w, st, auxi = 0; cout<<"\nenter the no of nodes and edges :\t "; cin>>V>>E; deque <int> aux; for(int i = 0; i < V ; ++i) aux.pb(i+1); disjoint_sets dso(aux); for(int i = 0 ; i <= V ; ++i) r2[i] = 0; tree.pb(0); vi r1; vi key(V+1); vvi g(V+1); //cout<<"\nenter the window status \n"; key[0] = 0; for(int i = 1 ; i <= V ; ++i) { st = rand()%2; key[i] = st; } /**cout<<"\nutilising rand(), the window status and links bw friends that have been formed are :\n";**/ for(int i = 1 ; i <= V ; ++i) cout<<key[i]<<' '; //cout<<"\nenter each edge\n"; int ct = E; for(int i = 0 ; i < ct ;) { s = 1 + rand()%V; do d = 1 + rand()%V; while(d==s); if(dso.find(s) != dso.find(d)) { dso.unite(s, d); cout<<"\n"<<s<<' '<<d; g[s].pb(d); g[d].pb(s); i++; } } drought(g, key, V, r1); // cout<<"\nno of open window children rooted @ a prticular node(including its own status) : node -> open window children "<<endl; // cout<<"\nigonre the case for 0"<<endl; // for(auto it : r2) // cout<<it.first<<" -> "<<it.second<<endl; ///****************************************************************************************************************************/ cout<<"\nanswer to query 1 is : \t"; cout<<calculate(tree, r2)<<endl; tree.pb(V+1); // last element of the vector tree contains V+1 to make the do while loop (to find answer to query 2)ahead functional auto it1 = tree.begin()+1; //root of the very first tree auto it2 = it1+1; //root of the next tree llu rubik = 0; vector <int> remaining; // cout<<"\n3 cases for second answer :"; // cout<<"\n1.element has at least 1 open window child also there is some open window node rooted at the same root at which the element is hence at least the way between these 2 nodes connects 'em"; // cout<<"\n2.element has its window open and has at least one open window child, hence the path bw them connects 'em"; // cout<<"\n3.else the node must have at least two open window nodes rooted @ itself"; while(*it1 != V+1) //for root of each tree in the forest do the following { llu x = *it1 ; //first element of the present tree llu root_id = r2[x]; //no. of open window nodes rooted @ node x while( x < *it2 ) //for each element of the tree rooted at it1 do the following { if(r2[x] > 0 && r2[x] < root_id) //element has at least 1 open window child also there is some open window node rooted at the same root at which the element is hence at least the way between these 2 nodes connects 'em {rubik++;} //cout<<"\t 1. "<<x<<endl;} else { if(key[x] == 1 && r2[x] > 1) //element has its window open and has at least one open window child, hence the path bw them connects 'em {rubik++;} //cout<<"\t 2. "<<x<<endl;} else //else for the element must have at least two open window nodes rooted @ itself remaining.pb(x); } //store these elements in a vector, w'll deal with those later, this requires another loop x++; } it1++; /*increment the tree*/ it2++; } // for(auto it : remaining) // cout<<"\n"<<"3. "<<it<<endl; for(auto it : remaining) { vs = vector<bool> (V+1, false); track = vector<int> (V+1, 0); int i = 0; while(count(begin(track), end(track), 1)<2 && i < g[it].size()) //loop till either we find at least 2 open window children rooted at concerned node 'x' (lying in remaining) or we visit all adj nodes of x { track.pb(dfs_fun(g, it, key, vs)); i++; } if(count(begin(track), end(track), 1)>=2) {rubik++;} //cout<<"\n"<<it<<" contributes towards the second answer";} } cout<<"\nthe result of query 2 is :\t"; cout<<rubik<<endl; return 0; }
5000 4999
enter the no of nodes and edges : 0 1 1 1 1 0 0 0 1 1 0 0 1 0 1 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 1 0 0 0 0 1 1 1 0 0 1 0 1 1 1 0 1 0 0 1 1 1 0 0 0 0 1 1 0 0 0 1 0 0 0 1 1 1 0 0 1 1 0 0 0 1 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 1 1 1 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 1 0 0 1 0 1 1 1 1 1 0 1 1 1 0 0 1 0 0 0 1 0 0 1 0 0 1 1 0 1 1 1 1 0 0 1 1 0 1 0 1 1 1 0 0 1 1 1 1 1 1 1 0 1 0 0 1 1 1 0 0 1 1 0 1 0 1 0 0 0 0 1 1 1 1 1 0 0 0 1 0 1 0 0 1 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 1 0 1 0 1 0 0 1 1 0 0 1 0 1 1 1 0 1 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0 0 0 1 0 1 1 0 0 1 0 0 1 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 1 0 0 1 1 0 1 1 1 0 1 0 0 1 1 0 0 0 0 0 1 0 0 0 1 1 0 1 1 1 0 0 0 0 1 1 1 1 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 0 1 0 1 1 0 0 0 1 1 0 1 0 0 1 1 1 0 0 0 0 0 0 1 1 0 0 0 1 1 1 1 0 1 0 1 0 1 1 1 0 0 1 1 0 0 0 0 1 1 0 1 1 0 0 0 0 0 0 1 1 0 1 0 1 1 1 1 0 1 1 1 1 0 0 1 0 0 1 1 1 0 0 0 0 0 1 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981 3030 4538 2768 3745 2259 2804 780 882 1543 4326 1970 3346 936 543 2909 1716 1495 4324 500 2702 4486 4382 3706 1505 241 3784 598 2943 3923 4711 3840 1001 262 1994 2594 3862 3447 1750 580 4094 625 2587 2695 1974 4679 4616 2672 908 4741 543 2 2642 2957 4257 4950 2599 2646 4832 1459 4672 4197 1037 776 2153 448 158 3224 796 4497 3714 2045 2896 1302 3214 4789 1247 3860 4248 1743 3591 2052 3975 2087 2476 3747 3500 2076 1571 1650 4127 1898 3736 4004 3404 2845 1038 3961 4205 1750 858 4292 1056 4701 2860 4112 3143 1182 1501 31 301 211 3622 4655 1263 1293 568 3155 4751 3217 1581 453 810 1397 368 2509 965 4854 4501 3661 1746 1416 4006 726 2719 3758 3306 2178 4929 3183 309 1774 1406 3319 2499 1752 1405 3805 3210 3403 706 2271 4076 4384 4212 3934 1513 4024 2252 980 4799 2457 4382 4809 2908 3471 3345 2469 4159 1382 2922 1660 2361 2772 913 4168 4440 4804 4457 1364 2302 2305 2037 1383 1545 3422 803 1338 4063 1777 2201 4799 3302 100 4892 4623 303 4642 1688 1060 1833 3015 1003 4494 3580 267 1813 2644 2274 2134 1378 251 940 2445 1827 3023 634 4027 4660 74 2271 1248 4884 714 3294 559 4483 4084 127 1538 4893 2609 4009 2499 4920 3558 1468 4226 3915 1944 3389 4490 214 674 407 178 3433 2937 4492 797 4197 3315 4565 1084 3375 28 4406 147 3331 3270 1883 117 3888 1068 3118 3057 1104 1327 3073 459 4606 2626 691 1946 3612 2429 2739 3390 1553 426 4686 3298 1492 824 260 3241 4086 569 4821 3309 4595 2199 1536 3177 3811 1097 1544 4081 4583 2500 2257 4427 3643 4447 701 1773 811 4454 1270 2155 3744 15 3287 3380 4990 1643 4673 1095 2691 2249 2390 4728 3430 1391 892 53 4188 3699 4261 2344 2452 4621 2177 2519 4508 1539 248 3481 403 2052 1583 932 3118 1313 239 295 4292 2681 3581 3983 3054 2623 2889 1219 427 1162 2941 1521 1530 4059 503 4104 3557 394 144 1161 4177 4286 1132 4187 1935 2291 4130 3836 3709 2336 3061 1152 4056 4408 673 1203 1592 2355 2491 1724 3902 1962 1171 3115 439 3144 1286 160 3124 2140 955 3898 3705 5000 928 3545 3430 902 4837 357 492 3019 4255 4000 337 2014 3941 1791 1819 735 790 4324 2870 1337 196 2769 482 1528 2498 2313 4670 1922 1945 4558 1624 445 3882 2410 3723 4258 1032 3229 2494 4416 3608 4259 4929 4833 4919 1470 2243 4993 2079 4626 2749 1610 3139 3098 4101 3120 3550 4880 2746 1313 3995 19 4230 2138 2486 1368 2233 3792 4205 1588 4881 3360 3804 2340 1744 3006 3339 1472 2885 2489 2962 3916 297 3776 2008 2387 873 4598 3801 4686 2430 2632 3219 4714 1392 4945 1734 1067 4547 2090 4012 3010 317 1284 4226 4836 1425 3594 1216 2927 2896 1003 936 4072 841 2265 3653 3443 4472 4135 3757 2180 3930 4580 2692 4033 2554 3150 351 3808 4648 4921 329 1130 2199 861 4609 1116 3476 1204 4981 605 3992 4137 590 3954 4285 762 4604 1562 1708 3255 1422 2894 1924 1925 1455 2884 2539 4112 662 3655 3035 1277 933 16 650 914 2672 324 4282 1902 4976 4429 2636 613 3765 2776 1056 3843 3846 2658 2970 1261 4384 4763 4861 1619 3239 292 2647 2213 4885 4793 1299 2076 4050 1533 1953 2288 2781 2292 4820 3107 530 3769 4639 3321 881 3842 3619 1528 2323 1121 497 2977 1655 3887 78 1437 3507 1558 57 4216 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4509 3681 4079 4952 1895 1502 4682 4340 4221 3925 3877 4689 3683 796 1411 116 3451 4043 1644 1643 3424 1361 4696 2160 3732 3873 4145 4704 2593 4077 2631 3797 1201 3179 1073 2236 2350 2598 2830 4051 1015 4713 269 556 340 4781 2999 898 4123 1738 4002 1006 4834 4829 258 3137 2931 1083 1299 145 2157 3007 805 2523 2655 92 4552 4031 4638 1226 2661 4684 191 4719 3465 393 3559 3362 572 665 4850 3095 2649 4880 1933 522 3900 2694 2075 2828 1112 909 4137 48 3296 1343 3791 4927 1854 1563 2579 3939 4457 3028 214 2380 1166 3283 1581 237 1038 554 4452 2671 1078 4878 1888 4461 3075 2506 4934 1648 2071 2501 1075 4487 723 3644 1103 688 3117 2963 424 3473 3837 1017 205 3972 4256 3706 46 240 4537 2464 4349 341 432 4012 4256 950 2888 102 3726 49 533 3251 812 2866 4309 1909 4215 4827 684 4687 2784 2217 2349 742 2661 3888 4867 1637 4672 2598 3067 3363 1117 660 1237 4985 2185 4745 355 346 2732 3442 1430 3483 1239 1169 213 2754 364 4038 1679 1341 3304 893 161 3097 4665 4909 3796 1118 3512 1243 3508 3486 4617 4048 3689 567 4715 4730 476 4294 1307 3795 3052 4028 1450 400 700 1586 3679 3109 3594 2163 1150 2685 3799 335 1540 4610 1279 1429 1219 1144 643 504 1628 3970 1050 4951 2392 3634 272 915 3173 1839 4341 2329 1897 2261 3590 4386 2375 3878 2411 1295 4633 390 2379 1860 2573 3326 3763 2989 3611 891 2151 4470 3800 2903 3523 3619 1800 4441 3513 233 4446 1730 4525 702 111 4372 3538 4768 4528 3427 3571 1465 2290 363 32 4595 2034 429 39 3929 733 1683 1804 3377 1233 1145 1788 2788 3611 2132 4847 4522 371 850 4554 628 3163 3207 3369 4216 1027 1189 1667 963 2761 315 4779 4891 3366 4927 4308 2458 4277 58 3253 1569 239 102 407 4717 2007 2374 4272 2472 363 4566 1096 903 1516 3395 4420 51 660 2947 4958 998 4984 3273 4555 4402 3595 418 4790 2320 960 236 3428 271 3079 2165 1433 920 4503 404 3962 1269 2798 877 3563 1363 353 4913 2438 551 1471 1884 2264 1988 484 1025 3968 3878 2019 3246 3272 3099 3940 677 1592 4323 2217 2173 3415 3666 3265 1028 2655 897 3660 3355 4099 1644 1663 2610 1879 1978 1050 2287 2738 2222 4157 3543 4193 3113 1770 3758 1574 4941 3880 3199 1900 1647 814 1802 426 2621 4643 2998 1777 504 2562 2340 4194 25 513 1144 3901 2565 2864 3615 1359 2511 4935 2484 1327 1718 218 2956 4924 2210 4797 1176 478 2809 3641 1056 1527 2088 4514 2483 3264 1321 3278 75 539 2676 1223 3912 860 925 794 1351 1705 4238 1213 1969 2506 421 3546 4772 1495 3759 1191 566 4339 2298 2384 580 3037 1122 4773 552 1540 2242 4840 3887 4908 1742 3723 3629 4496 3166 712 785 83 109 244 1636 3851 4956 454 3009 4479 2426 2541 3292 3447 3034 682 373 3671 2934 3532 866 4706 3695 4187 3037 2164 2858 350 1120 4733 1483 87 1344 3724 1555 2838 2243 1167 3826 3301 1154 369 2321 4209 4906 1742 4890 922 3628 935 2056 1912 3251 4914 599 2375 3451 452 3190 103 1290 3682 4653 3781 4117 2038 4417 1450 3229 1693 763 4832 2509 3088 1118 982 1861 4517 2808 4586 2175 4276 4655 521 3270 1768 2945 361 3574 2023 answer to query 1 is : 3221991 the result of query 2 is : 3691