The main idea is: dp[i][j] represent what is the maximum sum of two towers when the difference is j.
/***********Template Starts Here***********/ #include <cstdio> #include <cstring> #include <cmath> #include <algorithm> #include <map> #include <queue> #include <stack> #include <vector> #include <deque> #include <functional> #include <string> #include <iostream> #include <cctype> #include <set> #include <climits> #include <iomanip> #include <cassert> //#include <unordered_map> #define pb push_back #define nl puts ("") #define sp printf ( " " ) #define phl printf ( "hello\n" ) #define ff first #define ss second #define POPCOUNT __builtin_popcountll #define RIGHTMOST __builtin_ctzll #define LEFTMOST(x) (63-__builtin_clzll((x))) #define MP make_pair #define FOR(i,x,y) for(int i = (x) ; i <= (y) ; ++i) #define ROF(i,x,y) for(int i = (y) ; i >= (x) ; --i) #define CLR(x,y) memset(x,y,sizeof(x)) #define UNIQUE(V) (V).erase(unique((V).begin(),(V).end()),(V).end()) #define MIN(a,b) ((a)<(b)?(a):(b)) #define MAX(a,b) ((a)>(b)?(a):(b)) #define NUMDIGIT(x,y) (((int)(log10((x))/log10((y))))+1) #define SQ(x) ((x)*(x)) #define ABS(x) ((x)<0?-(x):(x)) #define FABS(x) ((x)+eps<0?-(x):(x)) #define ALL(x) (x).begin(),(x).end() #define LCM(x,y) (((x)/gcd((x),(y)))*(y)) #define SZ(x) ((int)(x).size()) #define NORM(x) if(x>=mod)x-=mod; using namespace std; typedef long long vlong; typedef unsigned long long uvlong; typedef pair < int, int > pii; typedef pair < vlong, vlong > pll; typedef vector<pii> vii; typedef vector<int> vi; const vlong inf = 2147383647; const double pi = 2 * acos ( 0.0 ); const double eps = 1e-9; #ifdef forthright48 #include <ctime> clock_t tStart = clock(); #define debug(args...) {dbg,args; cerr<<endl;} #define timeStamp printf("Execution Time: %.2fs\n", (double)(clock() - tStart)/CLOCKS_PER_SEC) #else #define debug(args...) // Just strip off all debug tokens #define timeStamp #endif struct debugger{ template<typename T> debugger& operator , (const T& v){ cerr<<v<<" "; return *this; } }dbg; //int knightDir[8][2] = { {-2,1},{-1,2},{1,2},{2,1},{2,-1},{-1,-2},{1,-2},{-2,-1} }; //int dir4[4][2] = {{-1,0},{0,1},{1,0},{0,-1}}; inline vlong gcd ( vlong a, vlong b ) { a = ABS ( a ); b = ABS ( b ); while ( b ) { a = a % b; swap ( a, b ); } return a; } vlong ext_gcd ( vlong A, vlong B, vlong *X, vlong *Y ){ vlong x2, y2, x1, y1, x, y, r2, r1, q, r; x2 = 1; y2 = 0; x1 = 0; y1 = 1; for (r2 = A, r1 = B; r1 != 0; r2 = r1, r1 = r, x2 = x1, y2 = y1, x1 = x, y1 = y ) { q = r2 / r1; r = r2 % r1; x = x2 - (q * x1); y = y2 - (q * y1); } *X = x2; *Y = y2; return r2; } inline vlong modInv ( vlong a, vlong m ) { vlong x, y; ext_gcd( a, m, &x, &y ); if ( x < 0 ) x += m; //modInv is never negative return x; } inline vlong power ( vlong a, vlong p ) { vlong res = 1, x = a; while ( p ) { if ( p & 1 ) res = ( res * x ); x = ( x * x ); p >>= 1; } return res; } inline vlong bigmod ( vlong a, vlong p, vlong m ) { vlong res = 1 % m, x = a % m; while ( p ) { if ( p & 1 ) res = ( res * x ) % m; x = ( x * x ) % m; p >>= 1; } return res; } /***********Template Ends Here***********/ /*********** Hasib Templates Starts Here**********/ #include<bits/stdc++.h> using namespace std; #define loop(i, n) for(int i=0; i<(n); i++) #define sf scanf #define pf printf #define fr first #define sc second #define ll long long #define dd double #define all(v) (v).begin(), (v).end() #define PI acos(-1.0) #define mem(ara, val) memset(ara, val, sizeof(ara)) #define paii pair<int, int> #define pall pair<ll, ll> #define read(nm) freopen(nm, "r", stdin) #define write(nm) freopen(nm, "w", stdout) #define vdump(x) cerr<<#x<<" = "<<x<<endl; #define dump(args...) cerr,args; cerr<<endl template<typename T> ostream& operator<<(ostream& out, vector<T> v) { out<<"[ "; loop(i, SZ(v)) { if(i) out<<", "; out<<v[i]; } out<<" ]"; return out; } template<typename T1, typename T2> ostream& operator<<(ostream &out, pair<T1, T2> p) { out<<"( "<<p.fr<<", "<<p.sc<<")"; return out; } template<typename T> ostream& operator,(ostream &out, T x) { out<<x<<" "; return out; } /**********Hasib Templates Ends Here**************/ /** * WARTNING for me: * Never use FOR * Never use pii, pll, vi, vi * Never use ff, ss, phl, sp, nl */ #define MAXX 57 #define MAXSUM 500007 int ara[MAXX]; int N; int dp[2][MAXSUM]; int solve() { mem(dp, -1); dp[0][0] = 0; int now, pre; now = 1, pre = 0; loop(i, N) { loop(j, MAXSUM) { if(dp[pre][j] != -1) { dp[now][j] = max(dp[now][j], dp[pre][j]); int diff = abs(j - ara[i]); dp[now][diff] = max(dp[now][diff], max(dp[pre][diff], dp[pre][ j ] + ara[i] )); //pf("dp[%d] = %d\n", diff, dp[now][diff]); diff = j + ara[i]; dp[now][diff] = max(dp[now][diff], max(dp[pre][diff], dp[pre][ j ] + ara[i] )); //pf("dp[%d] = %d\n", diff, dp[now][diff]); } } swap(now, pre); } return max(dp[now][0], dp[pre][0]); } int main () { #ifdef hasibpc read("input.txt"); //write("output.txt"); #endif // hasibpc int kases, kaseno = 0; sf("%d", &kases); while(kases--) { sf("%d", &N); loop(i, N) { sf("%d", &ara[i]); } sort(ara, ara+N); ///optimization đ int ret = solve(); if(ret != 0) { pf("Case %d: %d\n",++kaseno, ret/2); } else { pf("Case %d: impossible\n", ++kaseno); } } return 0; }