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  • Topcoder SRM654 DIV2 1000 SuccessiveSubtraction2

    题意：给你一个序列 这个序列代表是 a[1] - a[2] - ......-a[n] ，然后每一次更改其中的一个值，你只能在这个算式中最多加两个括号，问你使得这个算式得到的最大值是多少。

    解题思路：

    1）因为最多加两个括号  ，我们可以知道括号嵌套会负负得正所以相当于两个没有交集的括号，这里我们又想到连续字串和，但是字串和又可以嵌套，那怎么办，

    就正序求一遍，逆序再求一遍。

    解题代码：

      1 // BEGIN CUT HERE
  2 /*
  3 
  4 */
  5 // END CUT HERE
  6 #line 7 "SuccessiveSubtraction2.cpp"
  7 #include <cstdlib>
  8 #include <cctype>
  9 #include <cstring>
 10 #include <cstdio>
 11 #include <cmath>
 12 #include <algorithm>
 13 #include <vector>
 14 #include <string>
 15 #include <iostream>
 16 #include <sstream>
 17 #include <map>
 18 #include <set>
 19 #include <queue>
 20 #include <stack>
 21 #include <fstream>
 22 #include <numeric>
 23 #include <iomanip>
 24 #include <bitset>
 25 #include <list>
 26 #include <stdexcept>
 27 #include <functional>
 28 #include <utility>
 29 #include <ctime>
 30 using namespace std;
 31 
 32 #define PB push_back
 33 #define MP make_pair
 34 
 35 #define REP(i,n) for(i=0;i<(n);++i)
 36 #define FOR(i,l,h) for(i=(l);i<=(h);++i)
 37 #define FORD(i,h,l) for(i=(h);i>=(l);--i)
 38 
 39 typedef vector<int> VI;
 40 typedef vector<string> VS;
 41 typedef vector<double> VD;
 42 typedef long long LL;
 43 typedef pair<int,int> PII;
 44 #define maxn 2005
 45 int ary[maxn];
 46 int n;
 47 int dpz[maxn];
 48 int dpf[maxn];
 49 int solve()
 50 {
 51     memset(dpz,0,sizeof(dpz));
 52     memset(dpf,0,sizeof(dpf));
 53     int tsum = 0 ;
 54 //    for(int i = 1 ;i <= n;i ++)
 55 //        printf("%d ",ary[i]);
 56 //    printf("
");
 57     for(int i = 3;i <= n;i ++)
 58     {
 59         if(tsum < 0 )
 60             tsum =0 ;
 61         tsum += ary[i];
 62         dpz[i] = max(dpz[i],tsum);
 63     }
 64     tsum = 0 ;
 65     int ans = 0 ; 
 66     for(int i = n;i >= 3 ;i --)
 67     {
 68         if(tsum < 0 )
 69             tsum =0 ; 
 70         tsum += ary[i];
 71         dpf[i] = max(dpf[i+1],tsum);
 72         ans = max(dpf[i] + dpz[i-2],ans);
 73     }
 74     return ans ;
 75 }
 76 class SuccessiveSubtraction2
 77 {
 78         public:
 79         vector <int> calc(vector <int> a, vector <int> p, vector <int> v)
 80         {
 81            vector<int> ans ;    
 82            n = a.size();
 83            int sum =0 ;
 84            for(int i =0 ;i < n ;i ++)
 85            {
 86                ary[i+1] =a[i];
 87            }
 88            int k = p.size(); 
 89            for(int i =0 ;i < k ;i ++)
 90            {
 91               ary[p[i]+1] = v[i];
 92               sum = ary[1] *2; 
 93               for(int j = 1;j <= n;j ++)
 94                   sum -= ary[j];
 95               //printf("%d ",sum);
 96               sum += solve()*2;
 97               //printf("%d
",solve());
 98               ans.push_back(sum);
 99            }
100            return ans ;
101         }
102         
103 // BEGIN CUT HERE
104     public:
105     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(); }
106     private:
107     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(); }
108     void verify_case(int Case, const vector <int> &Expected, const vector <int> &Received) { cerr << "Test Case #" << Case << "..."; if (Expected == Received) cerr << "PASSED" << endl; else { cerr << "FAILED" << endl; cerr << "	Expected: " << print_array(Expected) << endl; cerr << "	Received: " << print_array(Received) << endl; } }
109     void test_case_0() { int Arr0[] = {1, 2, 3, 4, 5}; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arr1[] = {1, 2, 0, 4, 3}; vector <int> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[0]))); int Arr2[] = {3, 9, -10, 5, 1}; vector <int> Arg2(Arr2, Arr2 + (sizeof(Arr2) / sizeof(Arr2[0]))); int Arr3[] = {10, 16, 5, 5, 2 }; vector <int> Arg3(Arr3, Arr3 + (sizeof(Arr3) / sizeof(Arr3[0]))); verify_case(0, Arg3, calc(Arg0, Arg1, Arg2)); }
110     void test_case_1() { int Arr0[] = {-100, -100, -100, -100, -100}; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arr1[] = {0, 1, 2, 3, 4}; vector <int> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[0]))); int Arr2[] = {0, 0, 0, 0, 0}; vector <int> Arg2(Arr2, Arr2 + (sizeof(Arr2) / sizeof(Arr2[0]))); int Arr3[] = {400, 300, 200, 100, 0 }; vector <int> Arg3(Arr3, Arr3 + (sizeof(Arr3) / sizeof(Arr3[0]))); verify_case(1, Arg3, calc(Arg0, Arg1, Arg2)); }
111     void test_case_2() { int Arr0[] = {83, 0, 25, 21}; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arr1[] = {0, 3, 2, 1, 3, 1, 2}; vector <int> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[0]))); int Arr2[] = {10, -90, 33, 52, -100, 0, 45}; vector <int> Arg2(Arr2, Arr2 + (sizeof(Arr2) / sizeof(Arr2[0]))); int Arr3[] = {56, 125, 133, 81, 91, 143, 155 }; vector <int> Arg3(Arr3, Arr3 + (sizeof(Arr3) / sizeof(Arr3[0]))); verify_case(2, Arg3, calc(Arg0, Arg1, Arg2)); }
112     void test_case_3() { int Arr0[] = {1}; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arr1[] = {0, 0, 0, 0}; vector <int> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[0]))); int Arr2[] = {10, -10, 100, -100}; vector <int> Arg2(Arr2, Arr2 + (sizeof(Arr2) / sizeof(Arr2[0]))); int Arr3[] = {10, -10, 100, -100 }; vector <int> Arg3(Arr3, Arr3 + (sizeof(Arr3) / sizeof(Arr3[0]))); verify_case(3, Arg3, calc(Arg0, Arg1, Arg2)); }
113     void test_case_4() { int Arr0[] = {-11, -4, 28, 38, 21, -29, -45, 11, -58, -39, 92, 35, -56, -6, 29, -2, 61, 10, -29, -63}; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arr1[] = {19, 5, 3, 10, 4, 18, 5, 2, 0, 15}; vector <int> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[0]))); int Arr2[] = {-19, 21, 7, -66, 38, -39, -22, 24, -32, 13}; vector <int> Arg2(Arr2, Arr2 + (sizeof(Arr2) / sizeof(Arr2[0]))); int Arr3[] = {451, 443, 412, 440, 457, 467, 468, 464, 443, 458 }; vector <int> Arg3(Arr3, Arr3 + (sizeof(Arr3) / sizeof(Arr3[0]))); verify_case(4, Arg3, calc(Arg0, Arg1, Arg2)); }
114 
115 // END CUT HERE
116 
117 };
118 
119 // BEGIN CUT HERE
120 int main()
121 {
122         SuccessiveSubtraction2 ___test;
123         ___test.run_test(-1);
124         return 0;
125 }
126 // END CUT HERE
    View Code

     2）分段dp， dp[i][0-4] 表示 i处于 （第一段 第一个空格内  两个空格间隙  第二个空格内  最后一段） 这五种状态

    解题代码：

      1 // BEGIN CUT HERE
  2 /*
  3 
  4 */
  5 // END CUT HERE
  6 #line 7 "SuccessiveSubtraction2.cpp"
  7 #include <cstdlib>
  8 #include <cctype>
  9 #include <cstring>
 10 #include <cstdio>
 11 #include <cmath>
 12 #include <algorithm>
 13 #include <vector>
 14 #include <string>
 15 #include <iostream>
 16 #include <sstream>
 17 #include <map>
 18 #include <set>
 19 #include <queue>
 20 #include <stack>
 21 #include <fstream>
 22 #include <numeric>
 23 #include <iomanip>
 24 #include <bitset>
 25 #include <list>
 26 #include <stdexcept>
 27 #include <functional>
 28 #include <utility>
 29 #include <ctime>
 30 using namespace std;
 31 
 32 #define PB push_back
 33 #define MP make_pair
 34 
 35 #define REP(i,n) for(i=0;i<(n);++i)
 36 #define FOR(i,l,h) for(i=(l);i<=(h);++i)
 37 #define FORD(i,h,l) for(i=(h);i>=(l);--i)
 38 
 39 typedef vector<int> VI;
 40 typedef vector<string> VS;
 41 typedef vector<double> VD;
 42 typedef long long LL;
 43 typedef pair<int,int> PII;
 44 #define maxn 2005
 45 int ary[maxn];
 46 int n;
 47 int dp[maxn][6];
 48 int solve()
 49 {
 50     int ans = -1e9; 
 51     memset(dp,0,sizeof(dp));
 52     for(int i = 1;i <= n;i ++)
 53         for(int j = 0 ;j <= 4; j ++)
 54             dp[i][j] = -1e9;
 55     dp[1][0] = ary[1];
 56     dp[2][0] = ary[1]-ary[2];
 57     for(int i = 3 ;i <= n;i ++)
 58     {
 59         dp[i][0] = dp[i-1][0] - ary[i] ;
 60         dp[i][1] = max(dp[i-1][1]+ary[i],dp[i-1][0]+ary[i]);
 61         dp[i][2] = max(dp[i-1][2]-ary[i],dp[i-1][1]-ary[i]);
 62         dp[i][3] = max(dp[i-1][3]+ary[i],dp[i-1][2]+ary[i]);
 63         dp[i][4] = max(dp[i-1][4]-ary[i],dp[i-1][3]-ary[i]);
 64     }
 65     for(int i= 0 ;i <= 4;i ++)
 66     {
 67        ans = max(ans,dp[n][i])    ;
 68     }
 69     return ans ;
 70 }
 71 class SuccessiveSubtraction2
 72 {
 73         public:
 74         vector <int> calc(vector <int> a, vector <int> p, vector <int> v)
 75         {
 76            vector<int> ans ;    
 77            n = a.size();
 78            int sum =0 ;
 79            for(int i =0 ;i < n ;i ++)
 80            {
 81                ary[i+1] =a[i];
 82            }
 83            int k = p.size(); 
 84            for(int i =0 ;i < k ;i ++)
 85            {
 86               ary[p[i]+1] = v[i];
 87               ans.push_back(solve());
 88            }
 89            return ans ;
 90         }
 91         
 92 // BEGIN CUT HERE
 93     public:
 94     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(); }
 95     private:
 96     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(); }
 97     void verify_case(int Case, const vector <int> &Expected, const vector <int> &Received) { cerr << "Test Case #" << Case << "..."; if (Expected == Received) cerr << "PASSED" << endl; else { cerr << "FAILED" << endl; cerr << "	Expected: " << print_array(Expected) << endl; cerr << "	Received: " << print_array(Received) << endl; } }
 98     void test_case_0() { int Arr0[] = {1, 2, 3, 4, 5}; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arr1[] = {1, 2, 0, 4, 3}; vector <int> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[0]))); int Arr2[] = {3, 9, -10, 5, 1}; vector <int> Arg2(Arr2, Arr2 + (sizeof(Arr2) / sizeof(Arr2[0]))); int Arr3[] = {10, 16, 5, 5, 2 }; vector <int> Arg3(Arr3, Arr3 + (sizeof(Arr3) / sizeof(Arr3[0]))); verify_case(0, Arg3, calc(Arg0, Arg1, Arg2)); }
 99     void test_case_1() { int Arr0[] = {-100, -100, -100, -100, -100}; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arr1[] = {0, 1, 2, 3, 4}; vector <int> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[0]))); int Arr2[] = {0, 0, 0, 0, 0}; vector <int> Arg2(Arr2, Arr2 + (sizeof(Arr2) / sizeof(Arr2[0]))); int Arr3[] = {400, 300, 200, 100, 0 }; vector <int> Arg3(Arr3, Arr3 + (sizeof(Arr3) / sizeof(Arr3[0]))); verify_case(1, Arg3, calc(Arg0, Arg1, Arg2)); }
100     void test_case_2() { int Arr0[] = {83, 0, 25, 21}; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arr1[] = {0, 3, 2, 1, 3, 1, 2}; vector <int> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[0]))); int Arr2[] = {10, -90, 33, 52, -100, 0, 45}; vector <int> Arg2(Arr2, Arr2 + (sizeof(Arr2) / sizeof(Arr2[0]))); int Arr3[] = {56, 125, 133, 81, 91, 143, 155 }; vector <int> Arg3(Arr3, Arr3 + (sizeof(Arr3) / sizeof(Arr3[0]))); verify_case(2, Arg3, calc(Arg0, Arg1, Arg2)); }
101     void test_case_3() { int Arr0[] = {1}; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arr1[] = {0, 0, 0, 0}; vector <int> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[0]))); int Arr2[] = {10, -10, 100, -100}; vector <int> Arg2(Arr2, Arr2 + (sizeof(Arr2) / sizeof(Arr2[0]))); int Arr3[] = {10, -10, 100, -100 }; vector <int> Arg3(Arr3, Arr3 + (sizeof(Arr3) / sizeof(Arr3[0]))); verify_case(3, Arg3, calc(Arg0, Arg1, Arg2)); }
102     void test_case_4() { int Arr0[] = {-11, -4, 28, 38, 21, -29, -45, 11, -58, -39, 92, 35, -56, -6, 29, -2, 61, 10, -29, -63}; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arr1[] = {19, 5, 3, 10, 4, 18, 5, 2, 0, 15}; vector <int> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[0]))); int Arr2[] = {-19, 21, 7, -66, 38, -39, -22, 24, -32, 13}; vector <int> Arg2(Arr2, Arr2 + (sizeof(Arr2) / sizeof(Arr2[0]))); int Arr3[] = {451, 443, 412, 440, 457, 467, 468, 464, 443, 458 }; vector <int> Arg3(Arr3, Arr3 + (sizeof(Arr3) / sizeof(Arr3[0]))); verify_case(4, Arg3, calc(Arg0, Arg1, Arg2)); }
103 
104 // END CUT HERE
105 
106 };
107 
108 // BEGIN CUT HERE
109 int main()
110 {
111         SuccessiveSubtraction2 ___test;
112         ___test.run_test(-1);
113         return 0;
114 }
115 // END CUT HERE
    View Code
    没有梦想，何谈远方
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  • 原文地址：https://www.cnblogs.com/zyue/p/4369000.html
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