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Aug 2, 2024
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feat: add solutions to lc problems: No.3129,3130 #3352

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153 changes: 100 additions & 53 deletions solution/3100-3199/3129.Find All Possible Stable Binary Arrays I/README.md
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Original file line number Diff line number Diff line change
Expand Up @@ -176,41 +176,34 @@ class Solution {
#### C++

```cpp
using ll = long long;

class Solution {
public:
int numberOfStableArrays(int zero, int one, int limit) {
this->limit = limit;
f = vector<vector<array<ll, 2>>>(zero + 1, vector<array<ll, 2>>(one + 1, {-1, -1}));
return (dfs(zero, one, 0) + dfs(zero, one, 1)) % mod;
}

private:
const int mod = 1e9 + 7;
int limit;
vector<vector<array<ll, 2>>> f;

ll dfs(int i, int j, int k) {
if (i < 0 || j < 0) {
return 0;
}
if (i == 0) {
return k == 1 && j <= limit;
}
if (j == 0) {
return k == 0 && i <= limit;
}
ll& res = f[i][j][k];
if (res != -1) {
const int mod = 1e9 + 7;
using ll = long long;
vector<vector<array<ll, 2>>> f = vector<vector<array<ll, 2>>>(zero + 1, vector<array<ll, 2>>(one + 1, {-1, -1}));
auto dfs = [&](auto&& dfs, int i, int j, int k) -> ll {
if (i < 0 || j < 0) {
return 0;
}
if (i == 0) {
return k == 1 && j <= limit;
}
if (j == 0) {
return k == 0 && i <= limit;
}
ll& res = f[i][j][k];
if (res != -1) {
return res;
}
if (k == 0) {
res = (dfs(dfs, i - 1, j, 0) + dfs(dfs, i - 1, j, 1) - dfs(dfs, i - limit - 1, j, 1) + mod) % mod;
} else {
res = (dfs(dfs, i, j - 1, 0) + dfs(dfs, i, j - 1, 1) - dfs(dfs, i, j - limit - 1, 0) + mod) % mod;
}
return res;
}
if (k == 0) {
res = (dfs(i - 1, j, 0) + dfs(i - 1, j, 1) - dfs(i - limit - 1, j, 1) + mod) % mod;
} else {
res = (dfs(i, j - 1, 0) + dfs(i, j - 1, 1) - dfs(i, j - limit - 1, 0) + mod) % mod;
}
return res;
};
return (dfs(dfs, zero, one, 0) + dfs(dfs, zero, one, 1)) % mod;
}
};
```
Expand Down Expand Up @@ -259,6 +252,41 @@ func numberOfStableArrays(zero int, one int, limit int) int {
}
```

#### TypeScript

```ts
function numberOfStableArrays(zero: number, one: number, limit: number): number {
const mod = 1e9 + 7;
const f: number[][][] = Array.from({ length: zero + 1 }, () =>
Array.from({ length: one + 1 }, () => [-1, -1]),
);

const dfs = (i: number, j: number, k: number): number => {
if (i < 0 || j < 0) {
return 0;
}
if (i === 0) {
return k === 1 && j <= limit ? 1 : 0;
}
if (j === 0) {
return k === 0 && i <= limit ? 1 : 0;
}
let res = f[i][j][k];
if (res !== -1) {
return res;
}
if (k === 0) {
res = (dfs(i - 1, j, 0) + dfs(i - 1, j, 1) - dfs(i - limit - 1, j, 1) + mod) % mod;
} else {
res = (dfs(i, j - 1, 0) + dfs(i, j - 1, 1) - dfs(i, j - limit - 1, 0) + mod) % mod;
}
return (f[i][j][k] = res);
};

return (dfs(zero, one, 0) + dfs(zero, one, 1)) % mod;
}
```

<!-- tabs:end -->

<!-- solution:end -->
Expand Down Expand Up @@ -295,16 +323,10 @@ class Solution:
f[0][j][1] = 1
for i in range(1, zero + 1):
for j in range(1, one + 1):
f[i][j][0] = (
f[i - 1][j][0]
+ f[i - 1][j][1]
- (0 if i - limit - 1 < 0 else f[i - limit - 1][j][1])
) % mod
f[i][j][1] = (
f[i][j - 1][0]
+ f[i][j - 1][1]
- (0 if j - limit - 1 < 0 else f[i][j - limit - 1][0])
) % mod
x = 0 if i - limit - 1 < 0 else f[i - limit - 1][j][1]
y = 0 if j - limit - 1 < 0 else f[i][j - limit - 1][0]
f[i][j][0] = (f[i - 1][j][0] + f[i - 1][j][1] - x) % mod
f[i][j][1] = (f[i][j - 1][0] + f[i][j - 1][1] - y) % mod
return sum(f[zero][one]) % mod
```

Expand All @@ -323,12 +345,10 @@ class Solution {
}
for (int i = 1; i <= zero; ++i) {
for (int j = 1; j <= one; ++j) {
f[i][j][0] = (f[i - 1][j][0] + f[i - 1][j][1]
- (i - limit - 1 < 0 ? 0 : f[i - limit - 1][j][1]) + mod)
% mod;
f[i][j][1] = (f[i][j - 1][0] + f[i][j - 1][1]
- (j - limit - 1 < 0 ? 0 : f[i][j - limit - 1][0]) + mod)
% mod;
long x = i - limit - 1 < 0 ? 0 : f[i - limit - 1][j][1];
long y = j - limit - 1 < 0 ? 0 : f[i][j - limit - 1][0];
f[i][j][0] = (f[i - 1][j][0] + f[i - 1][j][1] - x + mod) % mod;
f[i][j][1] = (f[i][j - 1][0] + f[i][j - 1][1] - y + mod) % mod;
}
}
return (int) ((f[zero][one][0] + f[zero][one][1]) % mod);
Expand All @@ -354,12 +374,10 @@ public:
}
for (int i = 1; i <= zero; ++i) {
for (int j = 1; j <= one; ++j) {
f[i][j][0] = (f[i - 1][j][0] + f[i - 1][j][1]
- (i - limit - 1 < 0 ? 0 : f[i - limit - 1][j][1]) + mod)
% mod;
f[i][j][1] = (f[i][j - 1][0] + f[i][j - 1][1]
- (j - limit - 1 < 0 ? 0 : f[i][j - limit - 1][0]) + mod)
% mod;
ll x = i - limit - 1 < 0 ? 0 : f[i - limit - 1][j][1];
ll y = j - limit - 1 < 0 ? 0 : f[i][j - limit - 1][0];
f[i][j][0] = (f[i - 1][j][0] + f[i - 1][j][1] - x + mod) % mod;
f[i][j][1] = (f[i][j - 1][0] + f[i][j - 1][1] - y + mod) % mod;
}
}
return (f[zero][one][0] + f[zero][one][1]) % mod;
Expand Down Expand Up @@ -398,6 +416,35 @@ func numberOfStableArrays(zero int, one int, limit int) int {
}
```

#### TypeScript

```ts
function numberOfStableArrays(zero: number, one: number, limit: number): number {
const mod = 1e9 + 7;
const f: number[][][] = Array.from({ length: zero + 1 }, () =>
Array.from({ length: one + 1 }, () => [0, 0]),
);

for (let i = 1; i <= Math.min(limit, zero); i++) {
f[i][0][0] = 1;
}
for (let j = 1; j <= Math.min(limit, one); j++) {
f[0][j][1] = 1;
}

for (let i = 1; i <= zero; i++) {
for (let j = 1; j <= one; j++) {
const x = i - limit - 1 < 0 ? 0 : f[i - limit - 1][j][1];
const y = j - limit - 1 < 0 ? 0 : f[i][j - limit - 1][0];
f[i][j][0] = (f[i - 1][j][0] + f[i - 1][j][1] - x + mod) % mod;
f[i][j][1] = (f[i][j - 1][0] + f[i][j - 1][1] - y + mod) % mod;
}
}

return (f[zero][one][0] + f[zero][one][1]) % mod;
}
```

<!-- tabs:end -->

<!-- solution:end -->
Expand Down
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