Dynamic-Programming/OptimalGameStrategy1(DP).cpp at master · robinrst/Dynamic-Programming · GitHub

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#include        "algorithm"
#include        "iostream"
#include        "numeric"
#include        "iomanip"
#include        "cstring"
#include        "math.h"
#include        "bitset"
#include        "string"
#include        "vector"
#include        "ctime"
#include        "queue"
#include        "stack"
#include        "map"
#include        "set"

#include        "ext/pb_ds/assoc_container.hpp" // Common file
#include        "ext/pb_ds/tree_policy.hpp" // Including tree_order_statistics_node_update
#include        "ext/pb_ds/detail/standard_policies.hpp"

using namespace std;
using namespace __gnu_pbds;


#define          f first
#define          lgn 25
#define          endl '\n'
#define          sc second
#define          pb push_back
#define          N (int)2e3+5
#define          PI acos(-1.0)
#define          int long long
#define          vi vector<int>
#define          mod 1000000007
#define          ld long double
#define          eb emplace_back
#define          mii map<int,int>
#define          vpii vector<pii>
#define          pii pair<int,int>
#define          pq priority_queue
#define          BLOCK (int)sqrt(N)
#define          test(x) while(x--)
#define          all(x) begin(x),end(x)
#define          allr(x) rbegin(x),rend(x)
#define          fo(i,a,n) for(int i=a;i<n;i++)
#define          rfo(i,n,a) for(int i=n;i>=a;i--)
#define          FAST ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define          time() cerr << "Time : " << (double)clock() / (double)CLOCKS_PER_SEC << "s\n"
#define 		 bug(...)       __f (#__VA_ARGS__, __VA_ARGS__)

typedef tree< int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update >
OS ;

template <typename Arg1>
void __f (const char* name, Arg1&& arg1) { cout << name << " : " << arg1 << endl; }
template <typename Arg1, typename... Args>
void __f (const char* names, Arg1&& arg1, Args&&... args)
{
     const char* comma = strchr (names + 1, ',');
     cout.write (names, comma - names) << " : " << arg1 << " | "; __f (comma + 1, args...);
}

const int inf = 0x3f3f3f3f;
const int INF = 0x3f3f3f3f3f3f3f3f;

int n,m,k,q;
string s;
int a[N] , dp[N][N]; // dp[i][j] -> maximum score we can achieved in range from i to j

void go()
{
	cin >> n;

	fo(i,1,n+1) cin >> a[i];

	fo(i,1,n+1) dp[i][i] = a[i]; // len = 1
	fo(i,1,n) dp[i][i+1] = max( a[i] , a[i+1] ); // len = 2

	for( int gap = 2; gap <= n; gap++)
	{
		for( int i = 1; i + gap <= n; i++)
		{
			int j = i + gap;

			int xx = a[i] + min( { dp[i+2][j] , dp[i+1][j-1] }); // if we take ith element the next range for opponent will be (i+1,j) ,
																// as he is also play optimally so he will also choose maximum he can get
																// in that range so , let it takes i+1 element then we have option of (i+2,j)
																// and if he take jth element then we have option of (i+1,j-1) so we will take the
																// minimum of both ranges because maximum is taken by opponent because he was also playing optimally
			int yy = a[j] + min( { dp[i][j-2] , dp[i+1][j-1] });

			dp[i][j] = max( xx , yy );

		}
	}

	cout << dp[1][n] << endl;
}

int32_t main()
{
	FAST;
	int t=1;
	// cin>>t;
	test(t) go();
}