解題區/解題區 - UVa

UVa 751 - Triangle War

contents

  1. 1. Problem
  2. 2. Sample Input
  3. 3. Sample Output
  4. 4. Solution

Problem

兩名玩家進行放邊的操作，當其中一名玩家成功創建一個三角形，則可以再放入一邊，直到該操作無法創建一個新的三角形，則進行輪替。最大化自己與對方的分數差異。

一開始先模擬兩名玩家的操作過程。

Sample Input

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6 10
2 4
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Sample Output

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Game 1: B wins.
Game 2: A wins.
Game 3: A wins.
Game 4: B wins.

Solution

這題很妙，總之先定義狀態 dp(盤面狀況，剩餘三角形) = 最大化差異。

那麼轉移方程要看操作是否造成輪替，如果仍然為自己，則把下一步的最大化結果累加上來，反之扣除。

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#include <stdio.h>
#include <string.h>
#include <queue>
#include <set>
#include <algorithm>
using namespace std;
int dp[1<<18][11];
char used[1<<18][11] = {};
int trans[11][11], tri[10];
int countTri(int state) {
    int ret = 0;
    for (int i = 0; i < 9; i++) {
        if ((state&tri[i]) == tri[i])
            ret++;
    }
    return ret;
}
int dfs(int state, int score) {
    if (used[state][score])		return dp[state][score];
    used[state][score] = 1;
    
    int ret = 0, nstate, had = 9 - score, c, t;
    for (int i = 0; i < 18; i++) {
        if ((state>>i)&1) {
            nstate = state ^ (1<<i); // used it.
            c = countTri(((1<<18)-1)^nstate);
            if (c > had) { // create new
                t = c - had + dfs(nstate, score - (c - had));
                ret = max(ret, t);
            } else {
                t = score - dfs(nstate, score);
                ret = max(ret, t);
            }
        }
    }
    dp[state][score] = ret;
    return ret;
}
int main() {	
//	freopen("in.txt", "r+t", stdin);
//	freopen("out.txt", "w+t", stdout); 
    trans[1][2] = 0, trans[1][3] = 1;
    trans[2][3] = 2;
    trans[2][4] = 3, trans[2][5] = 4, trans[3][5] = 5, trans[3][6] = 6;
    trans[4][5] = 7, trans[5][6] = 8;
    trans[4][7] = 9, trans[4][8] = 10, trans[5][8] = 11, trans[5][9] = 12, trans[6][9] = 13, trans[6][10] = 14;
    trans[7][8] = 15, trans[8][9] = 16, trans[9][10] = 17;
    tri[0] = (1<<0)|(1<<1)|(1<<2);
    tri[1] = (1<<3)|(1<<4)|(1<<7);
    tri[2] = (1<<2)|(1<<4)|(1<<5);
    tri[3] = (1<<5)|(1<<6)|(1<<8);
    tri[4] = (1<<9)|(1<<10)|(1<<15);
    tri[5] = (1<<7)|(1<<10)|(1<<11);
    tri[6] = (1<<11)|(1<<12)|(1<<16);
    tri[7] = (1<<8)|(1<<12)|(1<<13);
    tri[8] = (1<<13)|(1<<14)|(1<<17);
    int testcase, cases = 0;
    int n, x, y;
    scanf("%d", &testcase);
    while (testcase--) {
        scanf("%d", &n);
        
        int state = 0, A = 0, B = 0, turn = 0;
        for (int i = 0; i < n; i++) {
            scanf("%d %d", &x, &y);
            if (x > y)	swap(x, y);
            int c = countTri(state|(1<<trans[x][y])) - countTri(state);
            if (c) {
                if (turn == 0)		A += c;
                else				B += c;
            } else {
                turn = !turn;
            }
            state |= 1<<trans[x][y];
        }
//		printf("score %d %d\n", A, B);
        state = ((1<<18)-1)^state; // unused: 1
        int had = A + B;
        int mx = dfs(state, 9 - had);
        if (turn == 0)	A += mx, B += 9 - had - mx;
        else			B += mx, A += 9 - had - mx;
        printf("Game %d: %s wins.\n", ++cases, A > B ? "A" : "B");
    }
    return 0;
}
/*
4
6
2 4
4 5
5 9
3 6
2 5
3 5
7
2 4
4 5
5 9
3 6
2 5
3 5
7 8
6
1 2
2 3
1 3
2 4
2 5
4 5
10
1 2
2 5
3 6
5 8
4 7
6 10
2 4
4 5
4 8
7 8
*/