topcoder srm 610
div1 250pt:
题意:100*100的01矩阵，找出来面积最大的“类似国际象棋棋盘”的子矩阵。
解法：枚举矩阵宽(水平方向)的起点和终点，然后利用尺取法来找到每个固定宽度下的最大矩阵，不断更新答案。
1 // BEGIN CUT HERE 2 3 // END CUT HERE 4 #line 5 "TheMatrix.cpp" 5 #include<cstdio> 6 #include<sstream> 7 #include<cstring> 8 #include<cstdlib> 9 #include<ctime> 10 #include<cmath> 11 #include<cassert> 12 #include<iostream> 13 #include<string> 14 #include<vector> 15 #include<map> 16 #include<set> 17 #include<queue> 18 #include<stack> 19 #include<algorithm> 20 using namespace std; 21 typedef long long ll; 22 typedef pair<int,int> pii; 23 class TheMatrix 24 { 25 public: 26 bool check(vector<string>& s,int start,int end,int row){ 27 for(int i = start + 1;i <=end;i++) 28 if(s[row][i]==s[row][i-1])return false; 29 return true; 30 } 31 bool ok(vector<string>& s,int start,int end,int row){ 32 for(int i=start;i<=end;i++) 33 if(s[row][i]==s[row-1][i])return false; 34 return true; 35 } 36 int MaxArea(vector <string> s){ 37 //$CARETPOSITION$ 38 int answer = 0; 39 int n=s.size(),m=s[0].size(); 40 for(int i=0;i<m;i++) 41 for(int j=0;j<m;j++){ 42 int down=0,up=0; 43 for(down=0;down<n;down++){ 44 if(check(s,i,j,down)){ 45 up=down+1; 46 while(up<n&&ok(s,i,j,up))up++; 47 int area=(j-i+1)*(up-down); 48 answer=max(answer,area); 49 down=up-1; 50 } 51 } 52 } 53 return answer; 54 } 55 56 // BEGIN CUT HERE 57 public: 58 void run_test(int Case) { if ((Case == -1) || (Case == 0)) test_case_0(); if ((Case == -1) || (Case == 1)) test_case_1(); if ((Case == -1) || (Case == 2)) test_case_2(); if ((Case == -1) || (Case == 3)) test_case_3(); if ((Case == -1) || (Case == 4)) test_case_4(); if ((Case == -1) || (Case == 5)) test_case_5(); if ((Case == -1) || (Case == 6)) test_case_6(); if ((Case == -1) || (Case == 7)) test_case_7(); } 59 private: 60 template <typename T> string print_array(const vector<T> &V) { ostringstream os; os << "{ "; for (typename vector<T>::const_iterator iter = V.begin(); iter != V.end(); ++iter) os << '\"' << *iter << "\","; os << " }"; return os.str(); } 61 void verify_case(int Case, const int &Expected, const int &Received) { cerr << "Test Case #" << Case << "..."; if (Expected == Received) cerr << "PASSED" << endl; else { cerr << "FAILED" << endl; cerr << "\tExpected: \"" << Expected << '\"' << endl; cerr << "\tReceived: \"" << Received << '\"' << endl; } } 62 void test_case_0() { string Arr0[] = {"1", 63 "0"}; vector <string> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arg1 = 2; verify_case(0, Arg1, MaxArea(Arg0)); } 64 void test_case_1() { string Arr0[] = {"0000"}; vector <string> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arg1 = 1; verify_case(1, Arg1, MaxArea(Arg0)); } 65 void test_case_2() { string Arr0[] = {"01"}; vector <string> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arg1 = 2; verify_case(2, Arg1, MaxArea(Arg0)); } 66 void test_case_3() { string Arr0[] = {"001", 67 "000", 68 "100"}; vector <string> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arg1 = 2; verify_case(3, Arg1, MaxArea(Arg0)); } 69 void test_case_4() { string Arr0[] = {"0"}; vector <string> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arg1 = 1; verify_case(4, Arg1, MaxArea(Arg0)); } 70 void test_case_5() { string Arr0[] = {"101", 71 "010"}; vector <string> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arg1 = 6; verify_case(5, Arg1, MaxArea(Arg0)); } 72 void test_case_6() { string Arr0[] = {"101", 73 "011", 74 "101", 75 "010"}; vector <string> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arg1 = 8; verify_case(6, Arg1, MaxArea(Arg0)); } 76 void test_case_7() { string Arr0[] = {"11001110011000110001111001001110110011010110001011", 77 "10100100010111111011111001011110101111010011100001", 78 "11101111001110100110010101101100011100101000010001", 79 "01000010001010101100010011111000100100110111111000", 80 "10110100000101100000111000100001011101111101010010", 81 "00111010000011100001110110010011010110010011100100", 82 "01100001111101001101001101100001111000111001101010", 83 "11010000000011011010100010000000111011001001100101", 84 "10100000000100010100100011010100110110110001000001", 85 "01101010101100001100000110100110100000010100100010", 86 "11010000001110111111011010011110001101100011100010", 87 "11101111000000011010011100100001100011111111110111", 88 "11000001101100100011000110111010011001010100000001", 89 "00100001111001010000101101100010000001100100001000", 90 "01001110110111101011010000111111101011000110010111", 91 "01001010000111111001100000100010101100100101010100", 92 "11111101001101110011011011011000111001101100011011", 93 "10000100110111000001110110010000000000111100101101", 94 "01010011101101101110000011000110011111001111011100", 95 "01101010011111010000011001111101011010011100001101", 96 "11011000011000110010101111100000101011011111101100", 97 "11100001001000110010100011001010101101001010001100", 98 "11011011001100111101001100111100000101011101101011", 99 "11110111100100101011100101111101000111001111110111", 100 "00011001100110111100111100001100101001111100001111", 101 "10001111100101110111001111100000000011110000100111", 102 "10101010110110100110010001001010000111100110100011", 103 "01100110100000001110101001101011001010001101110101", 104 "10110101110100110110101001100111110000101111100110", 105 "01011000001001101110100001101001110011001001110001", 106 "00100101010001100110110101001010010100001011000011", 107 "00011101100100001010100000000011000010100110011100", 108 "11001001011000000101111111000000110010001101101110", 109 "10101010110110010000010011001100110101110100111011", 110 "01101001010111010001101000100011101001110101000110", 111 "00110101101110110001110101110010100100110000101101", 112 "11010101000111010011110011000001101111010011110011", 113 "10010000010001110011011101001110110010001100011100", 114 "00111101110001001100101001110100110010100110110000", 115 "00010011011000101000100001101110111100100000010100", 116 "01101110001101000001001000001011101010011101011110", 117 "00000100110011001011101011110011011101100001110111", 118 "00110011110000011001011100001110101010100110010110", 119 "00111001010011011111010100000100100000101101110001", 120 "10101101101110111110000011111011001011100011110001", 121 "00101110010101111000001010110100001110111011100011", 122 "01111110010100111010110001111000111101110100111011"}; vector <string> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arg1 = 12; verify_case(7, Arg1, MaxArea(Arg0)); } 123 124 // END CUT HERE 125 126 }; 127 // BEGIN CUT HERE 128 int main(){ 129 TheMatrix ___test; 130 ___test.run_test(-1); 131 return 0; 132 } 133 // END CUT HERE
div1 500pt:
题意：有个人有个飞机，起初有F升油，有很多个任务，第i个任务消耗duration[i]油，完成之后得到refuel[i]升油，求最多能完成的任务数。
解法：先按照refuel降序排列，然后背包。
why?
对于两个任务，refuel大的在前面做一定要优于在后面做。假设现在剩余F升油，有两个任务a,b,其中duration[a] > duration[b],如果a先做，那么做完之后会剩余F - duration[a] + refuel[a]升油，如果b先做，会剩余F - duration[b] + refuel[b]升油，也就是说，如果两个都能做完的话，至少要保证F-duration[a]-duraion[b]+refuel[a/b]>=0,
显然先做refuel大的更可能完成。
1 // BEGIN CUT HERE 2 3 // END CUT HERE 4 #line 5 "AlbertoTheAviator.cpp" 5 #include<cstdio> 6 #include<cstring> 7 #include<cstdlib> 8 #include<ctime> 9 #include<cmath> 10 #include<sstream> 11 #include<cassert> 12 #include<iostream> 13 #include<string> 14 #include<vector> 15 #include<map> 16 #include<set> 17 #include<queue> 18 #include<stack> 19 #include<algorithm> 20 using namespace std; 21 typedef long long ll; 22 typedef pair<int,int> pii; 23 int dp[55][5050]; 24 pii hs[55]; 25 bool cmp(pii a,pii b){ 26 return a.first > b.first; 27 } 28 class AlbertoTheAviator 29 { 30 public: 31 int MaximumFlights(int F, vector <int> duration, vector <int> refuel){ 32 //$CARETPOSITION$ 33 int n = duration.size(); 34 for(int i = 0;i < n;i++){ 35 hs[i].first = refuel[i]; 36 hs[i].second = duration[i]; 37 } 38 sort(hs,hs+n,cmp); 39 memset(dp,-1,sizeof(dp)); 40 dp[0][F] = 0; 41 for(int i = 0;i < n;i++){ 42 for(int j=0;j<=5000;j++)dp[i+1][j]=dp[i][j]; 43 for(int j=hs[i].second;j <= 5000;j++){ 44 if(dp[i][j] == -1)continue; 45 dp[i+1][j-hs[i].second+hs[i].first]=max(dp[i+1][j-hs[i].second+hs[i].first],dp[i][j]+1); 46 } 47 } 48 49 50 int answer = 0; 51 for(int i = 0;i <= 5000;i++) 52 answer = max(answer,dp[n][i]); 53 return answer; 54 55 56 57 } 58 59 // BEGIN CUT HERE 60 public: 61 void run_test(int Case) { if ((Case == -1) || (Case == 0)) test_case_0(); if ((Case == -1) || (Case == 1)) test_case_1(); if ((Case == -1) || (Case == 2)) test_case_2(); if ((Case == -1) || (Case == 3)) test_case_3(); if ((Case == -1) || (Case == 4)) test_case_4(); if ((Case == -1) || (Case == 5)) test_case_5(); } 62 private: 63 template <typename T> string print_array(const vector<T> &V) { ostringstream os; os << "{ "; for (typename vector<T>::const_iterator iter = V.begin(); iter != V.end(); ++iter) os << '\"' << *iter << "\","; os << " }"; return os.str(); } 64 void verify_case(int Case, const int &Expected, const int &Received) { cerr << "Test Case #" << Case << "..."; if (Expected == Received) cerr << "PASSED" << endl; else { cerr << "FAILED" << endl; cerr << "\tExpected: \"" << Expected << '\"' << endl; cerr << "\tReceived: \"" << Received << '\"' << endl; } } 65 void test_case_0() { int Arg0 = 10; int Arr1[] = {10}; vector <int> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[0]))); int Arr2[] = {0}; vector <int> Arg2(Arr2, Arr2 + (sizeof(Arr2) / sizeof(Arr2[0]))); int Arg3 = 1; verify_case(0, Arg3, MaximumFlights(Arg0, Arg1, Arg2)); } 66 void test_case_1() { int Arg0 = 10; int Arr1[] = {8, 4}; vector <int> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[0]))); int Arr2[] = {0, 2}; vector <int> Arg2(Arr2, Arr2 + (sizeof(Arr2) / sizeof(Arr2[0]))); int Arg3 = 2; verify_case(1, Arg3, MaximumFlights(Arg0, Arg1, Arg2)); } 67 void test_case_2() { int Arg0 = 12; int Arr1[] = {4, 8, 2, 1}; vector <int> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[0]))); int Arr2[] = {2, 0, 0, 0}; vector <int> Arg2(Arr2, Arr2 + (sizeof(Arr2) / sizeof(Arr2[0]))); int Arg3 = 3; verify_case(2, Arg3, MaximumFlights(Arg0, Arg1, Arg2)); } 68 void test_case_3() { int Arg0 = 9; int Arr1[] = {4, 6}; vector <int> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[0]))); int Arr2[] = {0, 1}; vector <int> Arg2(Arr2, Arr2 + (sizeof(Arr2) / sizeof(Arr2[0]))); int Arg3 = 2; verify_case(3, Arg3, MaximumFlights(Arg0, Arg1, Arg2)); } 69 void test_case_4() { int Arg0 = 100; int Arr1[] = {101}; vector <int> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[0]))); int Arr2[] = {100}; vector <int> Arg2(Arr2, Arr2 + (sizeof(Arr2) / sizeof(Arr2[0]))); int Arg3 = 0; verify_case(4, Arg3, MaximumFlights(Arg0, Arg1, Arg2)); } 70 void test_case_5() { int Arg0 = 1947; int Arr1[] = {2407, 2979, 1269, 2401, 3227, 2230, 3991, 2133, 3338, 356, 2535, 3859, 3267, 365}; vector <int> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[0]))); int Arr2[] = {2406, 793, 905, 2400, 1789, 2229, 1378, 2132, 1815, 355, 72, 3858, 3266, 364}; vector <int> Arg2(Arr2, Arr2 + (sizeof(Arr2) / sizeof(Arr2[0]))); int Arg3 = 3; verify_case(5, Arg3, MaximumFlights(Arg0, Arg1, Arg2)); } 71 72 // END CUT HERE 73 74 }; 75 // BEGIN CUT HERE 76 int main(){ 77 AlbertoTheAviator ___test; 78 ___test.run_test(-1); 79 return 0; 80 } 81 // END CUT HERE
