Problem p00482 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <algorithm>
#include <stdio.h>
using namespace std;
int MOD = 100000;
char str[20][21];
int dp[2][3][1 << 20];
int main() {
  int a, b;
  scanf("%d%d", &a, &b);
  for (int i = 0; i < a; i++)
    scanf("%s", str[i]);
  int q = 0;
  for (int i = 0; i < a; i++)
    for (int j = 0; j < b; j++)
      if (str[i][j] == '?')
        q++;
  if (str[0][0] == 'J')
    dp[1][0][0] = 1;
  if (str[0][0] == 'O')
    dp[1][1][0] = 1;
  if (str[0][0] == 'I')
    dp[1][2][0] = 1;
  if (str[0][0] == '?')
    dp[1][0][0] = dp[1][1][0] = dp[1][2][0] = 1;
  for (int i = 0; i < a; i++) {
    if (i) {
      int e = (i * (b - 1) + 1) % 2;
      for (int k = 0; k < (1 << (b - 1)); k++) {
        if (str[i][0] == 'J') {
          dp[e][0][k] = dp[e][0][k] + dp[e][1][k] + dp[e][2][k];
        }
        if (str[i][0] == 'O') {
          dp[e][1][k] = dp[e][0][k] + dp[e][1][k] + dp[e][2][k];
        }
        if (str[i][0] == 'I') {
          if (k % 2 == 0)
            dp[e][2][k] = dp[e][0][k] + dp[e][1][k] + dp[e][2][k];
        }
        if (str[i][0] == '?') {
          int v = dp[e][0][k] + dp[e][1][k] + dp[e][2][k];
          int w = dp[e][0][k] + dp[e][1][k] + dp[e][2][k];
          if (k % 2 == 0)
            dp[e][2][k] = dp[e][0][k] + dp[e][1][k] + dp[e][2][k];
          dp[e][0][k] = v;
          dp[e][1][k] = w;
        }
      }
      // for(int k=0;k<(1<<(b-1));k++)printf("[%d,%d,%d]
      // ",dp[e][0][k],dp[e][1][k],dp[e][2][k]); printf("\n");
      for (int k = 0; k < (1 << (b - 1)); k++) {
        dp[e][0][k] %= MOD;
        dp[e][1][k] %= MOD;
        dp[e][2][k] %= MOD;
      }
    }
    for (int j = 0; j < b - 1; j++) {
      int e = (i * (b - 1) + j) % 2;
      for (int k = 0; k < (1 << (b - 1)); k++)
        dp[e][0][k] = dp[e][1][k] = dp[e][2][k] = 0;
      for (int k = 0; k < (1 << (b - 1)); k++) {
        int t = k / 2;
        if (str[i][j] == 'J' && str[i][j + 1] == 'J') {
          dp[e][0][t] += dp[!e][0][k];
        } else if (str[i][j] == 'J' && str[i][j + 1] == 'O')
          dp[e][1][(1 << (b - 2)) + t] += dp[!e][0][k];
        else if (str[i][j] == 'J' && str[i][j + 1] == 'I') {
          dp[e][2][t] += dp[!e][0][k];
        } else if (str[i][j] == 'J' && str[i][j + 1] == '?') {
          dp[e][1][(1 << (b - 2)) + t] += dp[!e][0][k];
          dp[e][0][t] += dp[!e][0][k];
          dp[e][2][t] += dp[!e][0][k];
        }

        else if (str[i][j] == 'O' && str[i][j + 1] == 'J') {
          dp[e][0][t] += dp[!e][1][k];
        } else if (str[i][j] == 'O' && str[i][j + 1] == 'O') {
          dp[e][1][t] += dp[!e][1][k];
        } else if (str[i][j] == 'O' && str[i][j + 1] == 'I') {
          dp[e][2][t] += dp[!e][1][k];
        } else if (str[i][j] == 'O' && str[i][j + 1] == '?') {
          dp[e][0][t] += dp[!e][1][k];
          dp[e][1][t] += dp[!e][1][k];
          dp[e][2][t] += dp[!e][1][k];
        } else if (k & 1) {
          if (str[i][j] == '?' && str[i][j + 1] == 'J') {
            dp[e][0][t] += dp[!e][0][k] + dp[!e][1][k];
          } else if (str[i][j] == '?' && str[i][j + 1] == 'O') {
            dp[e][1][t] += dp[!e][1][k];
            dp[e][1][(1 << (b - 2)) + t] += dp[!e][0][k];
          } else if (str[i][j] == '?' && str[i][j + 1] == 'I') {
            dp[e][2][t] += dp[!e][0][k] + dp[!e][1][k];
          } else if (str[i][j] == '?' && str[i][j + 1] == '?') {
            dp[e][0][t] += dp[!e][0][k] + dp[!e][1][k];
            dp[e][1][(1 << (b - 2)) + t] += dp[!e][0][k];
            dp[e][1][t] += dp[!e][1][k];
            dp[e][2][t] += dp[!e][0][k] + dp[!e][1][k];
          }
        } else {
          if (str[i][j] == '?' && str[i][j + 1] == 'J') {
            dp[e][0][t] += dp[!e][0][k] + dp[!e][1][k] + dp[!e][2][k];
          } else if (str[i][j] == '?' && str[i][j + 1] == 'O') {
            dp[e][1][t] += dp[!e][1][k] + dp[!e][2][k];
            dp[e][1][(1 << (b - 2)) + t] += dp[!e][0][k];
          } else if (str[i][j] == '?' && str[i][j + 1] == 'I') {
            dp[e][2][t] += dp[!e][0][k] + dp[!e][1][k] + dp[!e][2][k];
          } else if (str[i][j] == '?' && str[i][j + 1] == '?') {
            dp[e][0][t] += dp[!e][0][k] + dp[!e][1][k] + dp[!e][2][k];
            dp[e][1][(1 << (b - 2)) + t] += dp[!e][0][k];
            dp[e][1][t] += dp[!e][1][k] + dp[!e][2][k];
            dp[e][2][t] += dp[!e][0][k] + dp[!e][1][k] + dp[!e][2][k];
          } else if (str[i][j] == 'I' && str[i][j + 1] == 'J') {
            dp[e][0][t] += dp[!e][2][k];
          } else if (str[i][j] == 'I' && str[i][j + 1] == 'O') {
            dp[e][1][t] += dp[!e][2][k];
          } else if (str[i][j] == 'I' && str[i][j + 1] == 'I') {
            dp[e][2][t] += dp[!e][2][k];
          } else if (str[i][j] == 'I' && str[i][j + 1] == '?') {
            dp[e][0][t] += dp[!e][2][k];
            dp[e][1][t] += dp[!e][2][k];
            dp[e][2][t] += dp[!e][2][k];
          }
        }
      }
      // for(int k=0;k<(1<<(b-1));k++)printf("[%d,%d,%d]
      // ",dp[e][0][k],dp[e][1][k],dp[e][2][k]); printf("\n");
      for (int k = 0; k < (1 << (b - 1)); k++) {
        dp[e][0][k] %= MOD;
        dp[e][1][k] %= MOD;
        dp[e][2][k] %= MOD;
      }
    }
  }
  int ret = 0;
  for (int i = 0; i < (1 << (b - 1)); i++)
    ret = (ret + dp[(a * (b - 1) - 1) % 2][0][i] +
           dp[(a * (b - 1) - 1) % 2][1][i] + dp[(a * (b - 1) - 1) % 2][2][i]) %
          MOD;
  int pow = 1;
  for (int i = 0; i < q; i++)
    pow = pow * 3 % MOD;
  ret = (pow - ret) % MOD;
  if (ret < 0)
    ret += MOD;
  printf("%d\n", ret);
}

Fixed submission:
#include <algorithm>
#include <stdio.h>
using namespace std;
int MOD = 100000;
char str[20][21];
int dp[2][3][1 << 20];
int main() {
  int a, b;
  scanf("%d%d", &a, &b);
  for (int i = 0; i < a; i++)
    scanf("%s", str[i]);
  int q = 0;
  for (int i = 0; i < a; i++)
    for (int j = 0; j < b; j++)
      if (str[i][j] == '?')
        q++;
  if (str[0][0] == 'J')
    dp[1][0][0] = 1;
  if (str[0][0] == 'O')
    dp[1][1][0] = 1;
  if (str[0][0] == 'I')
    dp[1][2][0] = 1;
  if (str[0][0] == '?')
    dp[1][0][0] = dp[1][1][0] = dp[1][2][0] = 1;
  for (int i = 0; i < a; i++) {
    if (i) {
      int e = (i * (b - 1) + 1) % 2;
      for (int k = 0; k < (1 << (b - 1)); k++) {
        if (str[i][0] == 'J') {
          dp[e][0][k] = dp[e][0][k] + dp[e][1][k] + dp[e][2][k];
        }
        if (str[i][0] == 'O') {
          dp[e][1][k] = dp[e][0][k] + dp[e][1][k] + dp[e][2][k];
        }
        if (str[i][0] == 'I') {
          if (k % 2 == 0)
            dp[e][2][k] = dp[e][0][k] + dp[e][1][k] + dp[e][2][k];
        }
        if (str[i][0] == '?') {
          int v = dp[e][0][k] + dp[e][1][k] + dp[e][2][k];
          int w = dp[e][0][k] + dp[e][1][k] + dp[e][2][k];
          if (k % 2 == 0)
            dp[e][2][k] = dp[e][0][k] + dp[e][1][k] + dp[e][2][k];
          dp[e][0][k] = v;
          dp[e][1][k] = w;
        }
      }
      // for(int k=0;k<(1<<(b-1));k++)printf("[%d,%d,%d]
      // ",dp[e][0][k],dp[e][1][k],dp[e][2][k]); printf("\n");
      for (int k = 0; k < (1 << (b - 1)); k++) {
        dp[e][0][k] %= MOD;
        dp[e][1][k] %= MOD;
        dp[e][2][k] %= MOD;
      }
    }
    for (int j = 0; j < b - 1; j++) {
      int e = (i * (b - 1) + j) % 2;
      for (int k = 0; k < (1 << (b - 1)); k++)
        dp[e][0][k] = dp[e][1][k] = dp[e][2][k] = 0;
      for (int k = 0; k < (1 << (b - 1)); k++) {
        if (dp[!e][0][k] + dp[!e][1][k] + dp[!e][2][k] == 0)
          continue;
        int t = k / 2;
        if (str[i][j] == 'J' && str[i][j + 1] == 'J') {
          dp[e][0][t] += dp[!e][0][k];
        } else if (str[i][j] == 'J' && str[i][j + 1] == 'O')
          dp[e][1][(1 << (b - 2)) + t] += dp[!e][0][k];
        else if (str[i][j] == 'J' && str[i][j + 1] == 'I') {
          dp[e][2][t] += dp[!e][0][k];
        } else if (str[i][j] == 'J' && str[i][j + 1] == '?') {
          dp[e][1][(1 << (b - 2)) + t] += dp[!e][0][k];
          dp[e][0][t] += dp[!e][0][k];
          dp[e][2][t] += dp[!e][0][k];
        }

        else if (str[i][j] == 'O' && str[i][j + 1] == 'J') {
          dp[e][0][t] += dp[!e][1][k];
        } else if (str[i][j] == 'O' && str[i][j + 1] == 'O') {
          dp[e][1][t] += dp[!e][1][k];
        } else if (str[i][j] == 'O' && str[i][j + 1] == 'I') {
          dp[e][2][t] += dp[!e][1][k];
        } else if (str[i][j] == 'O' && str[i][j + 1] == '?') {
          dp[e][0][t] += dp[!e][1][k];
          dp[e][1][t] += dp[!e][1][k];
          dp[e][2][t] += dp[!e][1][k];
        } else if (k & 1) {
          if (str[i][j] == '?' && str[i][j + 1] == 'J') {
            dp[e][0][t] += dp[!e][0][k] + dp[!e][1][k];
          } else if (str[i][j] == '?' && str[i][j + 1] == 'O') {
            dp[e][1][t] += dp[!e][1][k];
            dp[e][1][(1 << (b - 2)) + t] += dp[!e][0][k];
          } else if (str[i][j] == '?' && str[i][j + 1] == 'I') {
            dp[e][2][t] += dp[!e][0][k] + dp[!e][1][k];
          } else if (str[i][j] == '?' && str[i][j + 1] == '?') {
            dp[e][0][t] += dp[!e][0][k] + dp[!e][1][k];
            dp[e][1][(1 << (b - 2)) + t] += dp[!e][0][k];
            dp[e][1][t] += dp[!e][1][k];
            dp[e][2][t] += dp[!e][0][k] + dp[!e][1][k];
          }
        } else {
          if (str[i][j] == '?' && str[i][j + 1] == 'J') {
            dp[e][0][t] += dp[!e][0][k] + dp[!e][1][k] + dp[!e][2][k];
          } else if (str[i][j] == '?' && str[i][j + 1] == 'O') {
            dp[e][1][t] += dp[!e][1][k] + dp[!e][2][k];
            dp[e][1][(1 << (b - 2)) + t] += dp[!e][0][k];
          } else if (str[i][j] == '?' && str[i][j + 1] == 'I') {
            dp[e][2][t] += dp[!e][0][k] + dp[!e][1][k] + dp[!e][2][k];
          } else if (str[i][j] == '?' && str[i][j + 1] == '?') {
            dp[e][0][t] += dp[!e][0][k] + dp[!e][1][k] + dp[!e][2][k];
            dp[e][1][(1 << (b - 2)) + t] += dp[!e][0][k];
            dp[e][1][t] += dp[!e][1][k] + dp[!e][2][k];
            dp[e][2][t] += dp[!e][0][k] + dp[!e][1][k] + dp[!e][2][k];
          } else if (str[i][j] == 'I' && str[i][j + 1] == 'J') {
            dp[e][0][t] += dp[!e][2][k];
          } else if (str[i][j] == 'I' && str[i][j + 1] == 'O') {
            dp[e][1][t] += dp[!e][2][k];
          } else if (str[i][j] == 'I' && str[i][j + 1] == 'I') {
            dp[e][2][t] += dp[!e][2][k];
          } else if (str[i][j] == 'I' && str[i][j + 1] == '?') {
            dp[e][0][t] += dp[!e][2][k];
            dp[e][1][t] += dp[!e][2][k];
            dp[e][2][t] += dp[!e][2][k];
          }
        }
      }
      // for(int k=0;k<(1<<(b-1));k++)printf("[%d,%d,%d]
      // ",dp[e][0][k],dp[e][1][k],dp[e][2][k]); printf("\n");
      for (int k = 0; k < (1 << (b - 1)); k++) {
        dp[e][0][k] %= MOD;
        dp[e][1][k] %= MOD;
        dp[e][2][k] %= MOD;
      }
    }
  }
  int ret = 0;
  for (int i = 0; i < (1 << (b - 1)); i++)
    ret = (ret + dp[(a * (b - 1) - 1) % 2][0][i] +
           dp[(a * (b - 1) - 1) % 2][1][i] + dp[(a * (b - 1) - 1) % 2][2][i]) %
          MOD;
  int pow = 1;
  for (int i = 0; i < q; i++)
    pow = pow * 3 % MOD;
  ret = (pow - ret) % MOD;
  if (ret < 0)
    ret += MOD;
  printf("%d\n", ret);
}