Description#
An attendance record for a student can be represented as a string where each character signifies whether the student was absent, late, or present on that day. The record only contains the following three characters:
'A': Absent.'L': Late.'P': Present.
Any student is eligible for an attendance award if they meet both of the following criteria:
- The student was absent (
'A') for strictly fewer than 2 days total. - The student was never late (
'L') for 3 or more consecutive days.
Given an integer n, return the number of possible attendance records of length n that make a student eligible for an attendance award. The answer may be very large, so return it modulo 109 + 7.
Example 1:
Input: n = 2
Output: 8
Explanation: There are 8 records with length 2 that are eligible for an award:
"PP", "AP", "PA", "LP", "PL", "AL", "LA", "LL"
Only "AA" is not eligible because there are 2 absences (there need to be fewer than 2).
Example 2:
Input: n = 1
Output: 3
Example 3:
Input: n = 10101
Output: 183236316
Constraints:
Solutions#
Solution 1#
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| class Solution:
def checkRecord(self, n: int) -> int:
@cache
def dfs(i, j, k):
if i >= n:
return 1
ans = 0
if j == 0:
ans += dfs(i + 1, j + 1, 0)
if k < 2:
ans += dfs(i + 1, j, k + 1)
ans += dfs(i + 1, j, 0)
return ans % mod
mod = 10**9 + 7
ans = dfs(0, 0, 0)
dfs.cache_clear()
return ans
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| class Solution {
private final int mod = (int) 1e9 + 7;
private int n;
private Integer[][][] f;
public int checkRecord(int n) {
this.n = n;
f = new Integer[n][2][3];
return dfs(0, 0, 0);
}
private int dfs(int i, int j, int k) {
if (i >= n) {
return 1;
}
if (f[i][j][k] != null) {
return f[i][j][k];
}
int ans = dfs(i + 1, j, 0);
if (j == 0) {
ans = (ans + dfs(i + 1, j + 1, 0)) % mod;
}
if (k < 2) {
ans = (ans + dfs(i + 1, j, k + 1)) % mod;
}
return f[i][j][k] = ans;
}
}
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| int f[100010][2][3];
const int mod = 1e9 + 7;
class Solution {
public:
int checkRecord(int n) {
this->n = n;
memset(f, -1, sizeof(f));
return dfs(0, 0, 0);
}
int dfs(int i, int j, int k) {
if (i >= n) {
return 1;
}
if (f[i][j][k] != -1) {
return f[i][j][k];
}
int ans = dfs(i + 1, j, 0);
if (j == 0) {
ans = (ans + dfs(i + 1, j + 1, 0)) % mod;
}
if (k < 2) {
ans = (ans + dfs(i + 1, j, k + 1)) % mod;
}
return f[i][j][k] = ans;
}
private:
int n;
};
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| func checkRecord(n int) int {
f := make([][][]int, n)
for i := range f {
f[i] = make([][]int, 2)
for j := range f[i] {
f[i][j] = make([]int, 3)
for k := range f[i][j] {
f[i][j][k] = -1
}
}
}
const mod = 1e9 + 7
var dfs func(i, j, k int) int
dfs = func(i, j, k int) int {
if i >= n {
return 1
}
if f[i][j][k] != -1 {
return f[i][j][k]
}
ans := dfs(i+1, j, 0)
if j == 0 {
ans = (ans + dfs(i+1, j+1, 0)) % mod
}
if k < 2 {
ans = (ans + dfs(i+1, j, k+1)) % mod
}
f[i][j][k] = ans
return ans
}
return dfs(0, 0, 0)
}
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Solution 2#
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| class Solution:
def checkRecord(self, n: int) -> int:
mod = int(1e9 + 7)
dp = [[[0, 0, 0], [0, 0, 0]] for _ in range(n)]
# base case
dp[0][0][0] = dp[0][0][1] = dp[0][1][0] = 1
for i in range(1, n):
# A
dp[i][1][0] = (dp[i - 1][0][0] + dp[i - 1][0][1] + dp[i - 1][0][2]) % mod
# L
dp[i][0][1] = dp[i - 1][0][0]
dp[i][0][2] = dp[i - 1][0][1]
dp[i][1][1] = dp[i - 1][1][0]
dp[i][1][2] = dp[i - 1][1][1]
# P
dp[i][0][0] = (dp[i - 1][0][0] + dp[i - 1][0][1] + dp[i - 1][0][2]) % mod
dp[i][1][0] = (
dp[i][1][0] + dp[i - 1][1][0] + dp[i - 1][1][1] + dp[i - 1][1][2]
) % mod
ans = 0
for j in range(2):
for k in range(3):
ans = (ans + dp[n - 1][j][k]) % mod
return ans
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| class Solution {
private static final int MOD = 1000000007;
public int checkRecord(int n) {
long[][][] dp = new long[n][2][3];
// base case
dp[0][0][0] = 1;
dp[0][0][1] = 1;
dp[0][1][0] = 1;
for (int i = 1; i < n; i++) {
// A
dp[i][1][0] = (dp[i - 1][0][0] + dp[i - 1][0][1] + dp[i - 1][0][2]) % MOD;
// L
dp[i][0][1] = dp[i - 1][0][0];
dp[i][0][2] = dp[i - 1][0][1];
dp[i][1][1] = dp[i - 1][1][0];
dp[i][1][2] = dp[i - 1][1][1];
// P
dp[i][0][0] = (dp[i - 1][0][0] + dp[i - 1][0][1] + dp[i - 1][0][2]) % MOD;
dp[i][1][0] = (dp[i][1][0] + dp[i - 1][1][0] + dp[i - 1][1][1] + dp[i - 1][1][2]) % MOD;
}
long ans = 0;
for (int j = 0; j < 2; j++) {
for (int k = 0; k < 3; k++) {
ans = (ans + dp[n - 1][j][k]) % MOD;
}
}
return (int) ans;
}
}
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| constexpr int MOD = 1e9 + 7;
class Solution {
public:
int checkRecord(int n) {
using ll = long long;
vector<vector<vector<ll>>> dp(n, vector<vector<ll>>(2, vector<ll>(3)));
// base case
dp[0][0][0] = dp[0][0][1] = dp[0][1][0] = 1;
for (int i = 1; i < n; ++i) {
// A
dp[i][1][0] = (dp[i - 1][0][0] + dp[i - 1][0][1] + dp[i - 1][0][2]) % MOD;
// L
dp[i][0][1] = dp[i - 1][0][0];
dp[i][0][2] = dp[i - 1][0][1];
dp[i][1][1] = dp[i - 1][1][0];
dp[i][1][2] = dp[i - 1][1][1];
// P
dp[i][0][0] = (dp[i - 1][0][0] + dp[i - 1][0][1] + dp[i - 1][0][2]) % MOD;
dp[i][1][0] = (dp[i][1][0] + dp[i - 1][1][0] + dp[i - 1][1][1] + dp[i - 1][1][2]) % MOD;
}
ll ans = 0;
for (int j = 0; j < 2; ++j) {
for (int k = 0; k < 3; ++k) {
ans = (ans + dp[n - 1][j][k]) % MOD;
}
}
return ans;
}
};
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| const _mod int = 1e9 + 7
func checkRecord(n int) int {
dp := make([][][]int, n)
for i := 0; i < n; i++ {
dp[i] = make([][]int, 2)
for j := 0; j < 2; j++ {
dp[i][j] = make([]int, 3)
}
}
// base case
dp[0][0][0] = 1
dp[0][0][1] = 1
dp[0][1][0] = 1
for i := 1; i < n; i++ {
// A
dp[i][1][0] = (dp[i-1][0][0] + dp[i-1][0][1] + dp[i-1][0][2]) % _mod
// L
dp[i][0][1] = dp[i-1][0][0]
dp[i][0][2] = dp[i-1][0][1]
dp[i][1][1] = dp[i-1][1][0]
dp[i][1][2] = dp[i-1][1][1]
// P
dp[i][0][0] = (dp[i-1][0][0] + dp[i-1][0][1] + dp[i-1][0][2]) % _mod
dp[i][1][0] = (dp[i][1][0] + dp[i-1][1][0] + dp[i-1][1][1] + dp[i-1][1][2]) % _mod
}
var ans int
for j := 0; j < 2; j++ {
for k := 0; k < 3; k++ {
ans = (ans + dp[n-1][j][k]) % _mod
}
}
return ans
}
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