usaco3.3.5 A Game

一 原题

A Game
IOI'96 - Day 1

Consider the following two-player game played with a sequence of N positive integers (2 <= N <= 100) laid onto a 1 x N game board. Player 1 starts the game. The players move alternately by selecting a number from either the left or the right end of the gameboar. That number is then deleted from the board, and its value is added to the score of the player who selected it. A player wins if his sum is greater than his opponents.

Write a program that implements the optimal strategy. The optimal strategy yields maximum points when playing against the "best possible" opponent. Your program must further implement an optimal strategy for player 2.

PROGRAM NAME: game1

INPUT FORMAT

Line 1:N, the size of the boardLine 2-etc:N integers in the range (1..200) that are the contents of the game board, from left to right

SAMPLE INPUT (file game1.in)

64 7 2 95 2

OUTPUT FORMAT

Two space-separated integers on a line: the score of Player 1 followed by the score of Player 2.

SAMPLE OUTPUT (file game1.out)

18 11

二 分析

动态规划。dp[i][j]表示在区间[i, j]内先手能获得的最高分数。

三 代码

运行结果：

USER: Qi Shen [maxkibb3]TASK: game1LANG: C++Compiling...Compile: OKExecuting...   Test 1: TEST OK [0.000 secs, 4264 KB]   Test 2: TEST OK [0.000 secs, 4264 KB]   Test 3: TEST OK [0.000 secs, 4264 KB]   Test 4: TEST OK [0.000 secs, 4264 KB]   Test 5: TEST OK [0.000 secs, 4264 KB]   Test 6: TEST OK [0.000 secs, 4264 KB]   Test 7: TEST OK [0.000 secs, 4264 KB]   Test 8: TEST OK [0.000 secs, 4264 KB]   Test 9: TEST OK [0.000 secs, 4264 KB]   Test 10: TEST OK [0.000 secs, 4264 KB]   Test 11: TEST OK [0.000 secs, 4264 KB]   Test 12: TEST OK [0.000 secs, 4264 KB]   Test 13: TEST OK [0.000 secs, 4264 KB]   Test 14: TEST OK [0.000 secs, 4264 KB]   Test 15: TEST OK [0.000 secs, 4264 KB]   Test 16: TEST OK [0.000 secs, 4264 KB]All tests OK.
Your program ('game1') produced all correct answers!  This is yoursubmission #2 for this problem.  Congratulations!

AC代码：

/*ID:maxkibb3LANG:C++PROG:game1*/#include<cstdio>#include<algorithm>using namespace std;const int MAXN = 105;int n;int a[MAXN];int sum[MAXN][MAXN];int dp[MAXN][MAXN];int main() {    freopen("game1.in", "r", stdin);    freopen("game1.out", "w", stdout);    scanf("%d", &n);    for(int i = 0; i < n; i++) {        scanf("%d", &a[i]);        sum[i][i] = a[i];        dp[i][i] = a[i];    }    for(int i = 0; i < n; i++) {        for(int j = i + 1; j < n; j++) {            sum[i][j] = sum[i][j - 1];            sum[i][j] += a[j];        }    }    for(int i = 1; i < n; i++) {        for(int j = 0; j < n - i; j++) {            dp[j][j + i] = max(a[j] + sum[j + 1][j + i] - dp[j + 1][j + i],                           a[j + i] + sum[j][j + i - 1] - dp[j][j + i - 1]);        }    }    printf("%d %d\n", dp[0][n - 1], sum[0][n - 1] - dp[0][n - 1]);    return 0;}