URAL 2018 The Debut Album (DP)

Posted 2020-09-15 dwtfukgv

题意：给出n长度的数列，其实1的连续个数不超过a，2的连续个数不超过b。

析：dp[i][j][k] 表示前 i 个数，以 j 结尾，并且连续了k个长度，要用滚动数组，要不然MLE。

代码如下：

#pragma comment(linker, "/STACK:1024000000,1024000000")
#include <cstdio>
#include <string>
#include <cstdlib>
#include <cmath>
#include <iostream>
#include <cstring>
#include <set>
#include <queue>
#include <algorithm>
#include <vector>
#include <map>
#include <cctype>
#include <cmath>
#include <stack>
#include <sstream>
#define debug() puts("++++");
#define gcd(a, b) __gcd(a, b)
#define lson l,m,rt<<1
#define rson m+1,r,rt<<1|1
#define freopenr freopen("in.txt", "r", stdin)
#define freopenw freopen("out.txt", "w", stdout)
using namespace std;

typedef long long LL;
typedef unsigned long long ULL;
typedef pair<int, int> P;
const int INF = 0x3f3f3f3f;
const LL LNF = 1e16;
const double inf = 0x3f3f3f3f3f3f;
const double PI = acos(-1.0);
const double eps = 1e-8;
const int maxn = 1e5 + 10;
const int mod = 1e9 + 7;
const int dr[] = {-1, 0, 1, 0};
const int dc[] = {0, 1, 0, -1};
const char *de[] = {"0000", "0001", "0010", "0011", "0100", "0101", "0110", "0111", "1000", "1001", "1010", "1011", "1100", "1101", "1110", "1111"};
int n, m;
const int mon[] = {0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};
const int monn[] = {0, 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};
inline bool is_in(int r, int c){
  return r >= 0 && r < n && c >= 0 && c < m;
}
LL dp[2][2][310];

int main(){
  int a, b;
  cin >> n >> a >> b;
  dp[0][0][1] = dp[0][1][1] = 1;
  int cnt = 1;
  LL sum1 = 1, sum2 = 1;
  for(int i = 1; i < n; ++i, cnt ^= 1){
    dp[cnt][0][1] = sum1;
    dp[cnt][1][1] = sum2;
    swap(sum1, sum2);
    for(int j = 2; j <= a; ++j){
      dp[cnt][0][j] = dp[cnt^1][0][j-1];
      sum2 = (sum2 + dp[cnt][0][j]) % mod;
    }
    for(int j = 2; j <= b; ++j){
      dp[cnt][1][j] = dp[cnt^1][1][j-1];
      sum1 = (sum1 + dp[cnt][1][j]) % mod;
    }
  }
  LL ans = (sum1 + sum2) % mod;
  cout << ans << endl;
  return 0;
}