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Nov 27, 2024
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feat: add solutions to lc problem: No.0935 #3819

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551 changes: 431 additions & 120 deletions solution/0900-0999/0935.Knight Dialer/README.md
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608 changes: 492 additions & 116 deletions solution/0900-0999/0935.Knight Dialer/README_EN.md
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34 changes: 15 additions & 19 deletions solution/0900-0999/0935.Knight Dialer/Solution.cpp
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Original file line number Diff line number Diff line change
@@ -1,25 +1,21 @@
using ll = long long;

class Solution {
public:
int knightDialer(int n) {
if (n == 1) return 10;
int mod = 1e9 + 7;
vector<ll> f(10, 1ll);
const int mod = 1e9 + 7;
vector<long long> f(10, 1);
while (--n) {
vector<ll> t(10);
t[0] = f[4] + f[6];
t[1] = f[6] + f[8];
t[2] = f[7] + f[9];
t[3] = f[4] + f[8];
t[4] = f[0] + f[3] + f[9];
t[6] = f[0] + f[1] + f[7];
t[7] = f[2] + f[6];
t[8] = f[1] + f[3];
t[9] = f[2] + f[4];
for (int i = 0; i < 10; ++i) f[i] = t[i] % mod;
vector<long long> g(10);
g[0] = (f[4] + f[6]) % mod;
g[1] = (f[6] + f[8]) % mod;
g[2] = (f[7] + f[9]) % mod;
g[3] = (f[4] + f[8]) % mod;
g[4] = (f[0] + f[3] + f[9]) % mod;
g[6] = (f[0] + f[1] + f[7]) % mod;
g[7] = (f[2] + f[6]) % mod;
g[8] = (f[1] + f[3]) % mod;
g[9] = (f[2] + f[4]) % mod;
f = g;
}
ll ans = accumulate(f.begin(), f.end(), 0ll);
return (int) (ans % mod);
return accumulate(f.begin(), f.end(), 0LL) % mod;
}
};
};
37 changes: 19 additions & 18 deletions solution/0900-0999/0935.Knight Dialer/Solution.cs
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@@ -1,24 +1,25 @@
public class Solution {
public int KnightDialer(int n) {
if (n == 1) return 10;
int A = 4;
int B = 2;
int C = 2;
int D = 1;
int MOD = (int)1e9 + 7;
for (int i = 0; i < n - 1; i++) {
int tempA = A;
int tempB = B;
int tempC = C;
int tempD = D;
A = ((2 * tempB) % MOD + (2 * tempC) % MOD) % MOD;
B = tempA;
C = (tempA + (2 * tempD) % MOD) % MOD;
D = tempC;
const int mod = 1000000007;
long[] f = new long[10];
for (int i = 0; i < 10; i++) {
f[i] = 1;
}

int ans = (A + B) % MOD;
ans = (ans + C) % MOD;
return (ans + D) % MOD;
while (--n > 0) {
long[] g = new long[10];
g[0] = (f[4] + f[6]) % mod;
g[1] = (f[6] + f[8]) % mod;
g[2] = (f[7] + f[9]) % mod;
g[3] = (f[4] + f[8]) % mod;
g[4] = (f[0] + f[3] + f[9]) % mod;
g[6] = (f[0] + f[1] + f[7]) % mod;
g[7] = (f[2] + f[6]) % mod;
g[8] = (f[1] + f[3]) % mod;
g[9] = (f[2] + f[4]) % mod;
f = g;
}

return (int)(f.Sum() % mod);
}
}
40 changes: 17 additions & 23 deletions solution/0900-0999/0935.Knight Dialer/Solution.go
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Original file line number Diff line number Diff line change
@@ -1,30 +1,24 @@
func knightDialer(n int) int {
if n == 1 {
return 10
}
func knightDialer(n int) (ans int) {
f := make([]int, 10)
for i := range f {
f[i] = 1
}
mod := int(1e9) + 7
const mod int = 1e9 + 7
for i := 1; i < n; i++ {
t := make([]int, 10)
t[0] = f[4] + f[6]
t[1] = f[6] + f[8]
t[2] = f[7] + f[9]
t[3] = f[4] + f[8]
t[4] = f[0] + f[3] + f[9]
t[6] = f[0] + f[1] + f[7]
t[7] = f[2] + f[6]
t[8] = f[1] + f[3]
t[9] = f[2] + f[4]
for j, v := range t {
f[j] = v % mod
}
g := make([]int, 10)
g[0] = (f[4] + f[6]) % mod
g[1] = (f[6] + f[8]) % mod
g[2] = (f[7] + f[9]) % mod
g[3] = (f[4] + f[8]) % mod
g[4] = (f[0] + f[3] + f[9]) % mod
g[6] = (f[0] + f[1] + f[7]) % mod
g[7] = (f[2] + f[6]) % mod
g[8] = (f[1] + f[3]) % mod
g[9] = (f[2] + f[4]) % mod
f = g
}
ans := 0
for _, v := range f {
ans = (ans + v) % mod
for _, x := range f {
ans = (ans + x) % mod
}
return ans
}
return
}
38 changes: 14 additions & 24 deletions solution/0900-0999/0935.Knight Dialer/Solution.java
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@@ -1,31 +1,21 @@
class Solution {
private static final int MOD = (int) 1e9 + 7;

public int knightDialer(int n) {
if (n == 1) {
return 10;
}
final int mod = (int) 1e9 + 7;
long[] f = new long[10];
Arrays.fill(f, 1);
while (--n > 0) {
long[] t = new long[10];
t[0] = f[4] + f[6];
t[1] = f[6] + f[8];
t[2] = f[7] + f[9];
t[3] = f[4] + f[8];
t[4] = f[0] + f[3] + f[9];
t[6] = f[0] + f[1] + f[7];
t[7] = f[2] + f[6];
t[8] = f[1] + f[3];
t[9] = f[2] + f[4];
for (int i = 0; i < 10; ++i) {
f[i] = t[i] % MOD;
}
}
long ans = 0;
for (long v : f) {
ans = (ans + v) % MOD;
long[] g = new long[10];
g[0] = (f[4] + f[6]) % mod;
g[1] = (f[6] + f[8]) % mod;
g[2] = (f[7] + f[9]) % mod;
g[3] = (f[4] + f[8]) % mod;
g[4] = (f[0] + f[3] + f[9]) % mod;
g[6] = (f[0] + f[1] + f[7]) % mod;
g[7] = (f[2] + f[6]) % mod;
g[8] = (f[1] + f[3]) % mod;
g[9] = (f[2] + f[4]) % mod;
f = g;
}
return (int) ans;
return (int) (Arrays.stream(f).sum() % mod);
}
}
}
26 changes: 12 additions & 14 deletions solution/0900-0999/0935.Knight Dialer/Solution.py
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@@ -1,18 +1,16 @@
class Solution:
def knightDialer(self, n: int) -> int:
if n == 1:
return 10
f = [1] * 10
for _ in range(n - 1):
t = [0] * 10
t[0] = f[4] + f[6]
t[1] = f[6] + f[8]
t[2] = f[7] + f[9]
t[3] = f[4] + f[8]
t[4] = f[0] + f[3] + f[9]
t[6] = f[0] + f[1] + f[7]
t[7] = f[2] + f[6]
t[8] = f[1] + f[3]
t[9] = f[2] + f[4]
f = t
return sum(t) % (10**9 + 7)
g = [0] * 10
g[0] = f[4] + f[6]
g[1] = f[6] + f[8]
g[2] = f[7] + f[9]
g[3] = f[4] + f[8]
g[4] = f[0] + f[3] + f[9]
g[6] = f[0] + f[1] + f[7]
g[7] = f[2] + f[6]
g[8] = f[1] + f[3]
g[9] = f[2] + f[4]
f = g
return sum(f) % (10**9 + 7)
46 changes: 46 additions & 0 deletions solution/0900-0999/0935.Knight Dialer/Solution2.cpp
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class Solution {
public:
int knightDialer(int n) {
const int mod = 1e9 + 7;
vector<vector<int>> base = {
{0, 0, 0, 0, 1, 0, 1, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 1, 0, 1, 0},
{0, 0, 0, 0, 0, 0, 0, 1, 0, 1},
{0, 0, 0, 0, 1, 0, 0, 0, 1, 0},
{1, 0, 0, 1, 0, 0, 0, 0, 0, 1},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{1, 1, 0, 0, 0, 0, 0, 1, 0, 0},
{0, 0, 1, 0, 0, 0, 1, 0, 0, 0},
{0, 1, 0, 1, 0, 0, 0, 0, 0, 0},
{0, 0, 1, 0, 1, 0, 0, 0, 0, 0}};
vector<vector<int>> res = pow(base, n - 1, mod);
return accumulate(res[0].begin(), res[0].end(), 0LL) % mod;
}

private:
vector<vector<int>> mul(const vector<vector<int>>& a, const vector<vector<int>>& b, int mod) {
int m = a.size(), n = b[0].size();
vector<vector<int>> c(m, vector<int>(n, 0));
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j) {
for (int k = 0; k < b.size(); ++k) {
c[i][j] = (c[i][j] + (1LL * a[i][k] * b[k][j]) % mod) % mod;
}
}
}
return c;
}

vector<vector<int>> pow(vector<vector<int>>& a, int n, int mod) {
int size = a.size();
vector<vector<int>> res(1, vector<int>(size, 1));
while (n > 0) {
if (n % 2 == 1) {
res = mul(res, a, mod);
}
a = mul(a, a, mod);
n /= 2;
}
return res;
}
};
60 changes: 60 additions & 0 deletions solution/0900-0999/0935.Knight Dialer/Solution2.cs
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public class Solution {
private const int mod = 1000000007;
private readonly int[][] baseMatrix = {
new int[] {0, 0, 0, 0, 1, 0, 1, 0, 0, 0},
new int[] {0, 0, 0, 0, 0, 0, 1, 0, 1, 0},
new int[] {0, 0, 0, 0, 0, 0, 0, 1, 0, 1},
new int[] {0, 0, 0, 0, 1, 0, 0, 0, 1, 0},
new int[] {1, 0, 0, 1, 0, 0, 0, 0, 0, 1},
new int[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
new int[] {1, 1, 0, 0, 0, 0, 0, 1, 0, 0},
new int[] {0, 0, 1, 0, 0, 0, 1, 0, 0, 0},
new int[] {0, 1, 0, 1, 0, 0, 0, 0, 0, 0},
new int[] {0, 0, 1, 0, 1, 0, 0, 0, 0, 0}
};

public int KnightDialer(int n) {
int[][] res = Pow(baseMatrix, n - 1);
int ans = 0;
foreach (var x in res[0]) {
ans = (ans + x) % mod;
}
return ans;
}

private int[][] Mul(int[][] a, int[][] b) {
int m = a.Length, n = b[0].Length;
int[][] c = new int[m][];
for (int i = 0; i < m; i++) {
c[i] = new int[n];
}

for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
for (int k = 0; k < b.Length; k++) {
c[i][j] = (int)((c[i][j] + (long)a[i][k] * b[k][j]) % mod);
}
}
}
return c;
}

private int[][] Pow(int[][] a, int n) {
int size = a.Length;
int[][] res = new int[1][];
res[0] = new int[size];
for (int i = 0; i < size; i++) {
res[0][i] = 1;
}

while (n > 0) {
if (n % 2 == 1) {
res = Mul(res, a);
}
a = Mul(a, a);
n /= 2;
}

return res;
}
}
59 changes: 59 additions & 0 deletions solution/0900-0999/0935.Knight Dialer/Solution2.go
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const mod = 1e9 + 7

func knightDialer(n int) int {
base := [][]int{
{0, 0, 0, 0, 1, 0, 1, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 1, 0, 1, 0},
{0, 0, 0, 0, 0, 0, 0, 1, 0, 1},
{0, 0, 0, 0, 1, 0, 0, 0, 1, 0},
{1, 0, 0, 1, 0, 0, 0, 0, 0, 1},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{1, 1, 0, 0, 0, 0, 0, 1, 0, 0},
{0, 0, 1, 0, 0, 0, 1, 0, 0, 0},
{0, 1, 0, 1, 0, 0, 0, 0, 0, 0},
{0, 0, 1, 0, 1, 0, 0, 0, 0, 0},
}

res := pow(base, n-1)
ans := 0
for _, x := range res[0] {
ans = (ans + x) % mod
}
return ans
}

func mul(a, b [][]int) [][]int {
m := len(a)
n := len(b[0])
c := make([][]int, m)
for i := range c {
c[i] = make([]int, n)
}
for i := 0; i < m; i++ {
for j := 0; j < n; j++ {
for k := 0; k < len(b); k++ {
c[i][j] = (c[i][j] + a[i][k]*b[k][j]) % mod
}
}
}
return c
}

func pow(a [][]int, n int) [][]int {
size := len(a)
res := make([][]int, 1)
res[0] = make([]int, size)
for i := 0; i < size; i++ {
res[0][i] = 1
}

for n > 0 {
if n%2 == 1 {
res = mul(res, a)
}
a = mul(a, a)
n /= 2
}

return res
}
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