POJ 1644

找找感觉准备夏令营

上来是一道DP问题，首先需要理解清楚题意。关于dp状态的定义，开始的设置过于复杂于是参考了一些解题博客做法，定义\(dp(i, j)\)为j次到达i的概率

#include <iostream>
#include <algorithm>
#include <queue>
#include <string>
#include <vector>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <string>
#include <stack>
#include <map>
#include <set>
#include <deque>
using namespace std;

const int maxm= 55;
const int maxt= 45;
const int INF= 0x3f3f3f3f;
const double eps= 1e-9;

int m, t;
char op[23];
int ins[maxm];
double dv[maxm][maxt];

int Next(int x, int d)
{
	x= x+d > m ? m : x+d;
	if (INF== ins[x]){
		return -x;
	}
	else{
		return min(max(x+ins[x], 0), m);
	}
}

int main(int argc, char const *argv[])
{
	int kase= 0;
	scanf("%d", &kase);

	while (kase--){
		double ans= 0;
		scanf("%d %d", &m, &t);
		for (int i= 1; i<= m; ++i){
			scanf("%s", op);			
			if ('L'== op[0]){
				ins[i]= INF;
			}
			else{
				sscanf(op, "%d", ins+i);
			}
		}
		// notice here, change m to make code simplify
		ins[++m]= ins[0]= 0;
		for (int i= 0; i<= m; ++i){
			for (int j= 0; j<= t; ++j){
				dv[i][j]= 0;
			}
		}
		dv[0][0]= 1;

		for (int j= 0; j< t; ++j){
			for (int i= 0; i< m; ++i){
				int p= Next(i, 1), q= Next(i, 2);
				if (p< 0){
					dv[-p][j+2]+= 0.5*dv[i][j];
				}
				else{
					dv[p][j+1]+= 0.5*dv[i][j];
				}
				if (q< 0){
					dv[-q][j+2]+= 0.5*dv[i][j];
				}
				else{
					dv[q][j+1]+= 0.5*dv[i][j];
				}
			}
		}
		for (int j= 0; j<= t; ++j){
			ans+= dv[m][j];
		}
		if (ans-0.5 > eps){
			printf("Bet for. %.4lf\n", ans);
		}
		else if (0.5-ans > eps){
			printf("Bet against. %.4lf\n", ans);
		}
		else{
			printf("Push. 0.5000\n");
		}
	}	

	return 0;
}