feat: add solutions to lc problem: No.3747

Author: yanglbme

solution/3700-3799/3747.Count Distinct Integers After Removing Zeros/README.md

@@ -61,32 +61,217 @@ edit_url: https://github.com/doocs/leetcode/edit/main/solution/3700-3799/3747.Co
 
 <!-- solution:start -->
 
-### 方法一
+### 方法一：数位 DP
+
+题目实际上是要我们统计区间 $[1, n]$ 之间，数字中不含 0 的整数个数。我们可以使用数位 DP 来解决这个问题。
+
+我们设计一个函数 $\text{dfs}(i, \text{zero}, \text{lead}, \text{limit})$，表示当前处理到数字的第 $i$ 位，用 $\text{zero}$ 表示当前数字中是否已经出现过非零数字，用 $\text{lead}$ 表示当前是否还在处理前导零，而 $\text{limit}$ 表示当前数字是否受上界限制的方案数。答案为 $\text{dfs}(0, 0, 1, 1)$。
+
+函数 $\text{dfs}(i, \text{zero}, \text{lead}, \text{limit})$ 中，如果 $i$ 大于等于数字的长度，那么我们就可以判断 $\text{zero}$ 和 $\text{lead}$，如果 $\text{zero}$ 为假且 $\text{lead}$ 为假，说明当前数字中不含 0，我们就返回 $1$，否则返回 $0$。
+
+对于 $\text{dfs}(i, \text{zero}, \text{lead}, \text{limit})$，我们可以枚举当前数位 $d$ 的值，然后递归计算 $\text{dfs}(i+1, \text{nxt\_zero}, \text{nxt\_lead}, \text{nxt\_limit})$，其中 $\text{nxt\_zero}$ 表示当前数字中是否已经出现过非零数字，$\text{nxt\_lead}$ 表示当前是否还在处理前导零，而 $\text{nxt\_limit}$ 表示当前数字是否受上界限制。如果 $\text{limit}$ 为真，那么 $up$ 就是当前数位的上界，否则 $up$ 为 $9$。
+
+时间复杂度 $O(\log_{10} n \times D)$，空间复杂度 $O(\log_{10} n)$。其中 $D$ 表示数字 0 到 9 的个数。
 
 <!-- tabs:start -->
 
 #### Python3
 
 ```python
-
+class Solution:
+    def countDistinct(self, n: int) -> int:
+        @cache
+        def dfs(i: int, zero: bool, lead: bool, lim: bool) -> int:
+            if i >= len(s):
+                return 1 if (not zero and not lead) else 0
+            up = int(s[i]) if lim else 9
+            ans = 0
+            for j in range(up + 1):
+                nxt_zero = zero or (j == 0 and not lead)
+                nxt_lead = lead and j == 0
+                nxt_lim = lim and j == up
+                ans += dfs(i + 1, nxt_zero, nxt_lead, nxt_lim)
+            return ans
+
+        s = str(n)
+        return dfs(0, False, True, True)
 ```
 
 #### Java
 
 ```java
-
+class Solution {
+    private char[] s;
+    private Long[][][][] f;
+
+    public long countDistinct(long n) {
+        s = String.valueOf(n).toCharArray();
+        f = new Long[s.length][2][2][2];
+        return dfs(0, 0, 1, 1);
+    }
+
+    private long dfs(int i, int zero, int lead, int limit) {
+        if (i == s.length) {
+            return (zero == 0 && lead == 0) ? 1 : 0;
+        }
+
+        if (limit == 0 && f[i][zero][lead][limit] != null) {
+            return f[i][zero][lead][limit];
+        }
+
+        int up = limit == 1 ? s[i] - '0' : 9;
+        long ans = 0;
+        for (int d = 0; d <= up; d++) {
+            int nxtZero = zero == 1 || (d == 0 && lead == 0) ? 1 : 0;
+            int nxtLead = (lead == 1 && d == 0) ? 1 : 0;
+            int nxtLimit = (limit == 1 && d == up) ? 1 : 0;
+            ans += dfs(i + 1, nxtZero, nxtLead, nxtLimit);
+        }
+
+        if (limit == 0) {
+            f[i][zero][lead][limit] = ans;
+        }
+        return ans;
+    }
+}
 ```
 
 #### C++
 
 ```cpp
-
+class Solution {
+public:
+    long long countDistinct(long long n) {
+        string s = to_string(n);
+        int m = s.size();
+        static long long f[20][2][2][2];
+        memset(f, -1, sizeof(f));
+
+        auto dfs = [&](this auto&& dfs, int i, int zero, int lead, int limit) -> long long {
+            if (i == m) {
+                return (zero == 0 && lead == 0) ? 1 : 0;
+            }
+            if (!limit && f[i][zero][lead][limit] != -1) {
+                return f[i][zero][lead][limit];
+            }
+
+            int up = limit ? (s[i] - '0') : 9;
+            long long ans = 0;
+            for (int d = 0; d <= up; d++) {
+                int nxtZero = zero || (d == 0 && !lead);
+                int nxtLead = lead && d == 0;
+                int nxtLimit = limit && d == up;
+                ans += dfs(i + 1, nxtZero, nxtLead, nxtLimit);
+            }
+
+            if (!limit) f[i][zero][lead][limit] = ans;
+            return ans;
+        };
+
+        return dfs(0, 0, 1, 1);
+    }
+};
 ```
 
 #### Go
 
 ```go
+func countDistinct(n int64) int64 {
+	s := []byte(fmt.Sprint(n))
+	m := len(s)
+	var f [20][2][2][2]int64
+	for i := range f {
+		for j := range f[i] {
+			for k := range f[i][j] {
+				for t := range f[i][j][k] {
+					f[i][j][k][t] = -1
+				}
+			}
+		}
+	}
+
+	var dfs func(i, zero, lead, limit int) int64
+	dfs = func(i, zero, lead, limit int) int64 {
+		if i == m {
+			if zero == 0 && lead == 0 {
+				return 1
+			}
+			return 0
+		}
+
+		if limit == 0 && f[i][zero][lead][limit] != -1 {
+			return f[i][zero][lead][limit]
+		}
+
+		up := 9
+		if limit == 1 {
+			up = int(s[i] - '0')
+		}
+
+		var ans int64 = 0
+		for d := 0; d <= up; d++ {
+			nxtZero := zero
+			if d == 0 && lead == 0 {
+				nxtZero = 1
+			}
+			nxtLead := 0
+			if lead == 1 && d == 0 {
+				nxtLead = 1
+			}
+			nxtLimit := 0
+			if limit == 1 && d == up {
+				nxtLimit = 1
+			}
+			ans += dfs(i+1, nxtZero, nxtLead, nxtLimit)
+		}
+
+		if limit == 0 {
+			f[i][zero][lead][limit] = ans
+		}
+		return ans
+	}
+
+	return dfs(0, 0, 1, 1)
+}
+```
 
+#### TypeScript
+
+```ts
+function countDistinct(n: number): number {
+    const s = n.toString();
+    const m = s.length;
+
+    const f: number[][][][] = Array.from({ length: m }, () =>
+        Array.from({ length: 2 }, () => Array.from({ length: 2 }, () => Array(2).fill(-1))),
+    );
+
+    const dfs = (i: number, zero: number, lead: number, limit: number): number => {
+        if (i === m) {
+            return zero === 0 && lead === 0 ? 1 : 0;
+        }
+
+        if (limit === 0 && f[i][zero][lead][limit] !== -1) {
+            return f[i][zero][lead][limit];
+        }
+
+        const up = limit === 1 ? parseInt(s[i]) : 9;
+        let ans = 0;
+        for (let d = 0; d <= up; d++) {
+            const nxtZero = zero === 1 || (d === 0 && lead === 0) ? 1 : 0;
+            const nxtLead = lead === 1 && d === 0 ? 1 : 0;
+            const nxtLimit = limit === 1 && d === up ? 1 : 0;
+            ans += dfs(i + 1, nxtZero, nxtLead, nxtLimit);
+        }
+
+        if (limit === 0) {
+            f[i][zero][lead][limit] = ans;
+        }
+        return ans;
+    };
+
+    return dfs(0, 0, 1, 1);
+}
 ```
 
 <!-- tabs:end -->