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Optimal Strategy for a Game

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13.Dynamic-programming/Optimal Strategy for a Game
- OptimalStrategyForAGameBottomUp.cpp

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	`1`	`+/* Amit Bansal - @amitbansal7 */`
	`2`	`+#include <bits/stdc++.h>`
	`3`	`+using namespace std;`
	`4`	`+`
	`5`	`+/*`
	`6`	`+Optimal Strategy for a Game. Consider a row of n coins of values v(1) ... v(n), where n is even. We play`
	`7`	`+a game against an opponent by alternating turns. In each turn, a player selects either the first or last`
	`8`	`+coin from the row, removes it from the row permanently, and receives the value of the coin. Determine`
	`9`	`+the maximum possible amount of money we can definitely win if we move first.`
	`10`	`+*/`
	`11`	`+int main()`
	`12`	`+{`
	`13`	`+ int C[] = {20, 30, 2, 2, 2, 10};`
	`14`	`+ int c = sizeof(C) / sizeof(C[0]);`
	`15`	`+`
	`16`	`+ pair<int, int>DP[c][c];`
	`17`	`+`
	`18`	`+ for (int i = 0; i < c; i++)`
	`19`	`+ DP[i][i] = make_pair(C[i], 0);`
	`20`	`+`
	`21`	`+ for (int l = 2; l <= c; l++)`
	`22`	`+ {`
	`23`	`+ for (int i = 0; i < c - l + 1; i++)`
	`24`	`+ {`
	`25`	`+ int j = i + l - 1;`
	`26`	`+`
	`27`	`+ int a = C[i] + DP[i + 1][j].second;`
	`28`	`+ int b = C[j] + DP[i][j - 1].second;`
	`29`	`+`
	`30`	`+ if (a > b)`
	`31`	`+ DP[i][j] = make_pair(a, DP[i + 1][j].first);`
	`32`	`+`
	`33`	`+ else`
	`34`	`+ DP[i][j] = make_pair(b, DP[i][j - 1].first);`
	`35`	`+ }`
	`36`	`+ }`
	`37`	`+ printf("Player 1 gets : %d\nPlayer 2 gets : %d\n", DP[0][c - 1].first, DP[0][c - 1].second);`
	`38`	`+`
	`39`	`+`
	`40`	`+ return 0;`
	`41`	`+}`

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