feat: add solutions to lc problem: No.3339 (doocs#3698)

No.3339.Find the Number of K-Even Arrays

Author: yanglbme

solution/3300-3399/3339.Find the Number of K-Even Arrays/README.md

@@ -0,0 +1,25 @@
+class Solution {
+public:
+    int countOfArrays(int n, int m, int k) {
+        int f[n][k + 1][2];
+        memset(f, -1, sizeof(f));
+        const int mod = 1e9 + 7;
+        int cnt0 = m / 2;
+        int cnt1 = m - cnt0;
+        auto dfs = [&](auto&& dfs, int i, int j, int k) -> int {
+            if (j < 0) {
+                return 0;
+            }
+            if (i >= n) {
+                return j == 0 ? 1 : 0;
+            }
+            if (f[i][j][k] != -1) {
+                return f[i][j][k];
+            }
+            int a = 1LL * cnt1 * dfs(dfs, i + 1, j, 1) % mod;
+            int b = 1LL * cnt0 * dfs(dfs, i + 1, j - (k & 1 ^ 1), 0) % mod;
+            return f[i][j][k] = (a + b) % mod;
+        };
+        return dfs(dfs, 0, k, 1);
+    }
+};

solution/3300-3399/3339.Find the Number of K-Even Arrays/README_EN.md

@@ -0,0 +1,32 @@
+func countOfArrays(n int, m int, k int) int {
+	f := make([][][2]int, n)
+	for i := range f {
+		f[i] = make([][2]int, k+1)
+		for j := range f[i] {
+			f[i][j] = [2]int{-1, -1}
+		}
+	}
+	const mod int = 1e9 + 7
+	cnt0 := m / 2
+	cnt1 := m - cnt0
+	var dfs func(int, int, int) int
+	dfs = func(i, j, k int) int {
+		if j < 0 {
+			return 0
+		}
+		if i >= n {
+			if j == 0 {
+				return 1
+			}
+			return 0
+		}
+		if f[i][j][k] != -1 {
+			return f[i][j][k]
+		}
+		a := cnt1 * dfs(i+1, j, 1) % mod
+		b := cnt0 * dfs(i+1, j-(k&1^1), 0) % mod
+		f[i][j][k] = (a + b) % mod
+		return f[i][j][k]
+	}
+	return dfs(0, k, 1)
+}

solution/3300-3399/3339.Find the Number of K-Even Arrays/Solution.cpp

@@ -0,0 +1,27 @@
+class Solution {
+    private Integer[][][] f;
+    private long cnt0, cnt1;
+    private final int mod = (int) 1e9 + 7;
+
+    public int countOfArrays(int n, int m, int k) {
+        f = new Integer[n][k + 1][2];
+        cnt0 = m / 2;
+        cnt1 = m - cnt0;
+        return dfs(0, k, 1);
+    }
+
+    private int dfs(int i, int j, int k) {
+        if (j < 0) {
+            return 0;
+        }
+        if (i >= f.length) {
+            return j == 0 ? 1 : 0;
+        }
+        if (f[i][j][k] != null) {
+            return f[i][j][k];
+        }
+        int a = (int) (cnt1 * dfs(i + 1, j, 1) % mod);
+        int b = (int) (cnt0 * dfs(i + 1, j - (k & 1 ^ 1), 0) % mod);
+        return f[i][j][k] = (a + b) % mod;
+    }
+}

solution/3300-3399/3339.Find the Number of K-Even Arrays/Solution.go

@@ -0,0 +1,18 @@
+class Solution:
+    def countOfArrays(self, n: int, m: int, k: int) -> int:
+        @cache
+        def dfs(i: int, j: int, k: int) -> int:
+            if j < 0:
+                return 0
+            if i >= n:
+                return int(j == 0)
+            return (
+                cnt1 * dfs(i + 1, j, 1) + cnt0 * dfs(i + 1, j - (k & 1 ^ 1), 0)
+            ) % mod
+
+        cnt0 = m // 2
+        cnt1 = m - cnt0
+        mod = 10**9 + 7
+        ans = dfs(0, k, 1)
+        dfs.cache_clear()
+        return ans

solution/3300-3399/3339.Find the Number of K-Even Arrays/Solution.java

@@ -0,0 +1,23 @@
+function countOfArrays(n: number, m: number, k: number): number {
+    const f = Array.from({ length: n }, () =>
+        Array.from({ length: k + 1 }, () => Array(2).fill(-1)),
+    );
+    const mod = 1e9 + 7;
+    const cnt0 = Math.floor(m / 2);
+    const cnt1 = m - cnt0;
+    const dfs = (i: number, j: number, k: number): number => {
+        if (j < 0) {
+            return 0;
+        }
+        if (i >= n) {
+            return j === 0 ? 1 : 0;
+        }
+        if (f[i][j][k] !== -1) {
+            return f[i][j][k];
+        }
+        const a = (cnt1 * dfs(i + 1, j, 1)) % mod;
+        const b = (cnt0 * dfs(i + 1, j - ((k & 1) ^ 1), 0)) % mod;
+        return (f[i][j][k] = (a + b) % mod);
+    };
+    return dfs(0, k, 1);
+}

solution/3300-3399/3339.Find the Number of K-Even Arrays/Solution.py

@@ -0,0 +1,18 @@
+class Solution {
+public:
+    int countOfArrays(int n, int m, int k) {
+        int f[n + 1][k + 1][2];
+        memset(f, 0, sizeof(f));
+        f[0][0][1] = 1;
+        const int mod = 1e9 + 7;
+        int cnt0 = m / 2;
+        int cnt1 = m - cnt0;
+        for (int i = 1; i <= n; ++i) {
+            for (int j = 0; j <= k; ++j) {
+                f[i][j][0] = 1LL * (f[i - 1][j][1] + (j ? f[i - 1][j - 1][0] : 0)) * cnt0 % mod;
+                f[i][j][1] = 1LL * (f[i - 1][j][0] + f[i - 1][j][1]) * cnt1 % mod;
+            }
+        }
+        return (f[n][k][0] + f[n][k][1]) % mod;
+    }
+};

solution/3300-3399/3339.Find the Number of K-Even Arrays/Solution.ts

@@ -0,0 +1,20 @@
+func countOfArrays(n int, m int, k int) int {
+	f := make([][][2]int, n+1)
+	for i := range f {
+		f[i] = make([][2]int, k+1)
+	}
+	f[0][0][1] = 1
+	cnt0 := m / 2
+	cnt1 := m - cnt0
+	const mod int = 1e9 + 7
+	for i := 1; i <= n; i++ {
+		for j := 0; j <= k; j++ {
+			f[i][j][0] = cnt0 * f[i-1][j][1] % mod
+			if j > 0 {
+				f[i][j][0] = (f[i][j][0] + cnt0*f[i-1][j-1][0]%mod) % mod
+			}
+			f[i][j][1] = cnt1 * (f[i-1][j][0] + f[i-1][j][1]) % mod
+		}
+	}
+	return (f[n][k][0] + f[n][k][1]) % mod
+}

solution/3300-3399/3339.Find the Number of K-Even Arrays/Solution2.cpp

@@ -0,0 +1,17 @@
+class Solution {
+    public int countOfArrays(int n, int m, int k) {
+        int[][][] f = new int[n + 1][k + 1][2];
+        int cnt0 = m / 2;
+        int cnt1 = m - cnt0;
+        final int mod = (int) 1e9 + 7;
+        f[0][0][1] = 1;
+        for (int i = 1; i <= n; ++i) {
+            for (int j = 0; j <= k; ++j) {
+                f[i][j][0]
+                    = (int) (1L * cnt0 * (f[i - 1][j][1] + (j > 0 ? f[i - 1][j - 1][0] : 0)) % mod);
+                f[i][j][1] = (int) (1L * cnt1 * (f[i - 1][j][0] + f[i - 1][j][1]) % mod);
+            }
+        }
+        return (f[n][k][0] + f[n][k][1]) % mod;
+    }
+}

solution/3300-3399/3339.Find the Number of K-Even Arrays/Solution2.go

@@ -0,0 +1,14 @@
+class Solution:
+    def countOfArrays(self, n: int, m: int, k: int) -> int:
+        f = [[[0] * 2 for _ in range(k + 1)] for _ in range(n + 1)]
+        cnt0 = m // 2
+        cnt1 = m - cnt0
+        mod = 10**9 + 7
+        f[0][0][1] = 1
+        for i in range(1, n + 1):
+            for j in range(k + 1):
+                f[i][j][0] = (
+                    (f[i - 1][j][1] + (f[i - 1][j - 1][0] if j else 0)) * cnt0 % mod
+                )
+                f[i][j][1] = (f[i - 1][j][0] + f[i - 1][j][1]) * cnt1 % mod
+        return sum(f[n][k]) % mod

solution/3300-3399/3339.Find the Number of K-Even Arrays/Solution2.java

@@ -0,0 +1,16 @@
+function countOfArrays(n: number, m: number, k: number): number {
+    const f: number[][][] = Array.from({ length: n + 1 }, () =>
+        Array.from({ length: k + 1 }, () => Array(2).fill(0)),
+    );
+    f[0][0][1] = 1;
+    const mod = 1e9 + 7;
+    const cnt0 = Math.floor(m / 2);
+    const cnt1 = m - cnt0;
+    for (let i = 1; i <= n; ++i) {
+        for (let j = 0; j <= k; ++j) {
+            f[i][j][0] = (cnt0 * (f[i - 1][j][1] + (j ? f[i - 1][j - 1][0] : 0))) % mod;
+            f[i][j][1] = (cnt1 * (f[i - 1][j][0] + f[i - 1][j][1])) % mod;
+        }
+    }
+    return (f[n][k][0] + f[n][k][1]) % mod;
+}

solution/3300-3399/3339.Find the Number of K-Even Arrays/Solution2.py

@@ -0,0 +1,20 @@
+class Solution {
+public:
+    int countOfArrays(int n, int m, int k) {
+        vector<vector<int>> f(k + 1, vector<int>(2));
+        int cnt0 = m / 2;
+        int cnt1 = m - cnt0;
+        const int mod = 1e9 + 7;
+        f[0][1] = 1;
+
+        for (int i = 0; i < n; ++i) {
+            vector<vector<int>> g(k + 1, vector<int>(2));
+            for (int j = 0; j <= k; ++j) {
+                g[j][0] = (1LL * cnt0 * (f[j][1] + (j > 0 ? f[j - 1][0] : 0)) % mod) % mod;
+                g[j][1] = (1LL * cnt1 * (f[j][0] + f[j][1]) % mod) % mod;
+            }
+            f = g;
+        }
+        return (f[k][0] + f[k][1]) % mod;
+    }
+};

solution/3300-3399/3339.Find the Number of K-Even Arrays/Solution2.ts

@@ -0,0 +1,23 @@
+func countOfArrays(n int, m int, k int) int {
+	const mod = 1e9 + 7
+	cnt0 := m / 2
+	cnt1 := m - cnt0
+	f := make([][2]int, k+1)
+	f[0][1] = 1
+
+	for i := 0; i < n; i++ {
+		g := make([][2]int, k+1)
+		for j := 0; j <= k; j++ {
+			g[j][0] = (cnt0 * (f[j][1] + func() int {
+				if j > 0 {
+					return f[j-1][0]
+				}
+				return 0
+			}()) % mod) % mod
+			g[j][1] = (cnt1 * (f[j][0] + f[j][1]) % mod) % mod
+		}
+		f = g
+	}
+
+	return (f[k][0] + f[k][1]) % mod
+}

solution/3300-3399/3339.Find the Number of K-Even Arrays/Solution3.cpp

@@ -0,0 +1,18 @@
+class Solution {
+    public int countOfArrays(int n, int m, int k) {
+        int[][] f = new int[k + 1][2];
+        int cnt0 = m / 2;
+        int cnt1 = m - cnt0;
+        final int mod = (int) 1e9 + 7;
+        f[0][1] = 1;
+        for (int i = 0; i < n; ++i) {
+            int[][] g = new int[k + 1][2];
+            for (int j = 0; j <= k; ++j) {
+                g[j][0] = (int) (1L * cnt0 * (f[j][1] + (j > 0 ? f[j - 1][0] : 0)) % mod);
+                g[j][1] = (int) (1L * cnt1 * (f[j][0] + f[j][1]) % mod);
+            }
+            f = g;
+        }
+        return (f[k][0] + f[k][1]) % mod;
+    }
+}

solution/3300-3399/3339.Find the Number of K-Even Arrays/Solution3.go

@@ -0,0 +1,14 @@
+class Solution:
+    def countOfArrays(self, n: int, m: int, k: int) -> int:
+        f = [[0] * 2 for _ in range(k + 1)]
+        cnt0 = m // 2
+        cnt1 = m - cnt0
+        mod = 10**9 + 7
+        f[0][1] = 1
+        for _ in range(n):
+            g = [[0] * 2 for _ in range(k + 1)]
+            for j in range(k + 1):
+                g[j][0] = (f[j][1] + (f[j - 1][0] if j else 0)) * cnt0 % mod
+                g[j][1] = (f[j][0] + f[j][1]) * cnt1 % mod
+            f = g
+        return sum(f[k]) % mod

solution/3300-3399/3339.Find the Number of K-Even Arrays/Solution3.java

@@ -0,0 +1,16 @@
+function countOfArrays(n: number, m: number, k: number): number {
+    const mod = 1e9 + 7;
+    const cnt0 = Math.floor(m / 2);
+    const cnt1 = m - cnt0;
+    const f: number[][] = Array.from({ length: k + 1 }, () => [0, 0]);
+    f[0][1] = 1;
+    for (let i = 0; i < n; i++) {
+        const g: number[][] = Array.from({ length: k + 1 }, () => [0, 0]);
+        for (let j = 0; j <= k; j++) {
+            g[j][0] = ((cnt0 * (f[j][1] + (j > 0 ? f[j - 1][0] : 0))) % mod) % mod;
+            g[j][1] = ((cnt1 * (f[j][0] + f[j][1])) % mod) % mod;
+        }
+        f.splice(0, f.length, ...g);
+    }
+    return (f[k][0] + f[k][1]) % mod;
+}

solution/3300-3399/3339.Find the Number of K-Even Arrays/Solution3.py

@@ -3349,6 +3349,7 @@
 |  3336  |  [最大公约数相等的子序列数量](/solution/3300-3399/3336.Find%20the%20Number%20of%20Subsequences%20With%20Equal%20GCD/README.md)  |  `数组`,`数学`,`动态规划`,`数论`  |  困难  |  第 421 场周赛  |
 |  3337  |  [字符串转换后的长度 II](/solution/3300-3399/3337.Total%20Characters%20in%20String%20After%20Transformations%20II/README.md)  |  `哈希表`,`数学`,`字符串`,`动态规划`,`计数`  |  困难  |  第 421 场周赛  |
 |  3338  |  [第二高的薪水 II](/solution/3300-3399/3338.Second%20Highest%20Salary%20II/README.md)  |  `数据库`  |  中等  |  🔒  |
+|  3339  |  [查找 K 偶数数组的数量](/solution/3300-3399/3339.Find%20the%20Number%20of%20K-Even%20Arrays/README.md)  |  `动态规划`  |  中等  |  🔒  |
 
 ## 版权
 
@@ -3359,4 +3360,4 @@
 欢迎各位小伙伴们添加 @yanglbme 的个人微信（微信号：YLB0109），备注 「**leetcode**」。后续我们会创建算法、技术相关的交流群，大家一起交流学习，分享经验，共同进步。
 
 | <img src="https://cdn-doocs.oss-cn-shenzhen.aliyuncs.com/gh/doocs/images/qrcode-for-yanglbme.png" width="260px" align="left"/> |
-| ------------------------------------------------------------------------------------------------------------------------------ |
+| ------------------------------------------------------------------------------------------------------------------------------ |

solution/3300-3399/3339.Find the Number of K-Even Arrays/Solution3.ts

@@ -3347,6 +3347,7 @@ Press <kbd>Control</kbd> + <kbd>F</kbd>(or <kbd>Command</kbd> + <kbd>F</kbd> on
 |  3336  |  [Find the Number of Subsequences With Equal GCD](/solution/3300-3399/3336.Find%20the%20Number%20of%20Subsequences%20With%20Equal%20GCD/README_EN.md)  |  `Array`,`Math`,`Dynamic Programming`,`Number Theory`  |  Hard  |  Weekly Contest 421  |
 |  3337  |  [Total Characters in String After Transformations II](/solution/3300-3399/3337.Total%20Characters%20in%20String%20After%20Transformations%20II/README_EN.md)  |  `Hash Table`,`Math`,`String`,`Dynamic Programming`,`Counting`  |  Hard  |  Weekly Contest 421  |
 |  3338  |  [Second Highest Salary II](/solution/3300-3399/3338.Second%20Highest%20Salary%20II/README_EN.md)  |  `Database`  |  Medium  |  🔒  |
+|  3339  |  [Find the Number of K-Even Arrays](/solution/3300-3399/3339.Find%20the%20Number%20of%20K-Even%20Arrays/README_EN.md)  |  `Dynamic Programming`  |  Medium  |  🔒  |
 
 ## Copyright