题解 | #蘑菇阵#

import java.util.Scanner;

public class Main {
    public static void main(String[] args){
        Scanner in = new Scanner(System.in);

        while(in.hasNext()){
            // solution1(in);
            solution2(in);
        }
    }

    /**
     * 动态规划
     *
     * dp[i][j]表示不碰到蘑菇走到位置(i,j)处的概率
     *
     * 简化
     * dp[i][j] = (j==m?1:0.5) * dp[i-1][j] + (i==n?1:0.5) * dp[i][j-1]
     *
     * @param in
     */
    private static void solution2(Scanner in){
        int n = in.nextInt();
        int m = in.nextInt();
        int k = in.nextInt();

        double[][] dp = new double[n+1][m+1];
        boolean[][] mushroom = new boolean[n+1][m+1];
        for(int i=1; i<=k; i++){
            mushroom[in.nextInt()][in.nextInt()] = true;
        }

        // 初始化 (1,1)有无蘑菇
        if(mushroom[1][1]){
            dp[1][1] = 0;
        }else{
            dp[1][1] = 1;
        }

        for(int i=1; i<=n; i++){
            for(int j=1; j<=m; j++){
                if(!(i==1 && j==1)){
                    if(mushroom[i][j]){
                        dp[i][j] = 0 * dp[i-1][j] + 0 * dp[i][j-1];
                    }else{
                        dp[i][j] = (j==m?1:0.5) * dp[i-1][j] + (i==n?1:0.5) * dp[i][j-1];
                    }
                }
            }
        }

        System.out.println(String.format("%.2f", dp[n][m]));
    }

    /**
     * 动态规划
     *
     * dp[i][j]表示不碰到蘑菇走到位置(i,j)处的概率
     *
     * @param in
     */
    private static void solution1(Scanner in){
        int n = in.nextInt();
        int m = in.nextInt();
        int k = in.nextInt();

        double[][] dp = new double[n+1][m+1];
        boolean[][] mushroom = new boolean[n+1][m+1];
        for(int i=1; i<=k; i++){
            mushroom[in.nextInt()][in.nextInt()] = true;
        }

        // 起始处(1,1) 有无蘑菇
        if(mushroom[1][1]){
            dp[1][1] = 0;
        }else{
            dp[1][1] = 1;
        }
        // 初始化第一列
        for(int i=2; i<=n; i++){
            if(mushroom[i][1]){
                dp[i][1] = 0 * dp[i-1][1];
            }else{
                if(m == 1){
                    dp[i][1] = 1 * dp[i-1][1];
                }else{
                    dp[i][1] = 0.5 * dp[i-1][1];
                }
            }
        }
        // 初始化第一行
        for(int i=2; i<=m; i++){
            if(mushroom[1][i]){
                dp[1][i] = 0 * dp[1][i-1];
            }else{
                if(n == 1){
                    dp[1][i] = 1 * dp[1][i-1];
                }else{
                    dp[1][i] = 0.5 * dp[1][i-1];
                }
            }
        }

        for(int i=2; i<=n; i++){
            for(int j=2; j<=m; j++){
                if(mushroom[i][j]){
                    dp[i][j] = 0 * dp[i-1][j] + 0 * dp[i][j-1];
                }else{
                    if(i==n && j==m){
                        dp[i][j] = 1 * dp[i-1][j] + 1 * dp[i][j-1];
                    }else if(i == n){
                        dp[i][j] = 0.5 * dp[i-1][j] + 1 * dp[i][j-1];
                    }else if(j == m){
                        dp[i][j] = 1 * dp[i-1][j] + 0.5 * dp[i][j-1];
                    }else{
                        dp[i][j] = 0.5 * dp[i-1][j] + 0.5 * dp[i][j-1];
                    }
                }
            }
        }

        System.out.println(String.format("%.2f", dp[n][m]));
    }
}