From e101aa59ec02df13d7d996835d95f5910352b364 Mon Sep 17 00:00:00 2001 From: yanglbme Date: Fri, 25 Aug 2023 09:02:05 +0800 Subject: [PATCH] feat: add solutions to lc problem: No.0964 No.0964.Least Operators to Express Number --- .../images/minesweeper_example_1.png | Bin 73461 -> 0 bytes .../images/minesweeper_example_2.png | Bin 83862 -> 0 bytes .../0529.Minesweeper/images/untitled-2.jpeg | Bin 0 -> 182036 bytes .../0529.Minesweeper/images/untitled.jpeg | Bin 0 -> 166528 bytes .../README.md | 159 +++++++++++++++++- .../README_EN.md | 142 +++++++++++++++- .../Solution.cpp | 27 +++ .../Solution.go | 32 ++++ .../Solution.java | 30 ++++ .../Solution.py | 14 ++ .../Solution.ts | 24 +++ 11 files changed, 426 insertions(+), 2 deletions(-) delete mode 100644 solution/0500-0599/0529.Minesweeper/images/minesweeper_example_1.png delete mode 100644 solution/0500-0599/0529.Minesweeper/images/minesweeper_example_2.png create mode 100644 solution/0500-0599/0529.Minesweeper/images/untitled-2.jpeg create mode 100644 solution/0500-0599/0529.Minesweeper/images/untitled.jpeg create mode 100644 solution/0900-0999/0964.Least Operators to Express Number/Solution.cpp create mode 100644 solution/0900-0999/0964.Least Operators to Express Number/Solution.go create mode 100644 solution/0900-0999/0964.Least Operators to Express Number/Solution.java create mode 100644 solution/0900-0999/0964.Least Operators to Express Number/Solution.py create mode 100644 solution/0900-0999/0964.Least Operators to Express Number/Solution.ts diff --git a/solution/0500-0599/0529.Minesweeper/images/minesweeper_example_1.png b/solution/0500-0599/0529.Minesweeper/images/minesweeper_example_1.png deleted file mode 100644 index 6c0258b1b2831c0229f83b9188f5a1c585af5600..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 73461 zcmdqJbySpZ*FS2ZfPo+&At8teNOwz1OASLKLk}S(4T?pNbb~a=5JL|sAVW&`5K8w* zH=KJwpXYhM?{EFidw%Qua}F$)YmN6k*M044$7k>T*>}JT6}j8^6!@1eUAis*Tw49o 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zx(d0NO_by*VAG#)%KtAtN(tq>38v^|Fz?8``hur|Jrf){2xHd;D-PJ literal 0 HcmV?d00001 diff --git a/solution/0900-0999/0964.Least Operators to Express Number/README.md b/solution/0900-0999/0964.Least Operators to Express Number/README.md index 611e4718a0990..0cf33607a7cb5 100644 --- a/solution/0900-0999/0964.Least Operators to Express Number/README.md +++ b/solution/0900-0999/0964.Least Operators to Express Number/README.md @@ -57,6 +57,23 @@ +**方法一:记忆化搜索** + +我们定义一个函数 $dfs(v)$,表示用 $x$ 凑成数字 $v$ 所需要的最少运算符数量。那么答案就是 $dfs(target)$。 + +函数 $dfs(v)$ 的执行逻辑如下: + +如果 $x \geq v$,那么此时可以用 $v$ 个 $x / x$ 相加来得到 $v$,运算符数量为 $v \times 2 - 1$;也可以用 $x$ 减去 $(x - v)$ 个 $x / x$ 来得到 $v$,运算符数量为 $(x - v) \times 2$。取两者的最小值。 + +否则,我们从 $k=2$ 开始枚举 $x^k$,找到第一个 $x^k \geq v$ 的 $k$: + +- 如果此时 $x^k - v \geq v$,那么只能先得到 $x^{k-1}$,然后再递归计算 $dfs(v - x^{k-1})$,此时运算符数量为 $k - 1 + dfs(v - x^{k-1})$; +- 如果此时 $x^k - v < v$,那么可以按照上面的方式得到 $v$,此时运算符数量为 $k - 1 + dfs(v - x^{k-1})$;也可以先得到 $x^k$,再递归计算 $dfs(x^k - v)$,此时运算符数量为 $k + dfs(x^k - v)$。取两者的最小值。 + +为了避免重复计算,我们使用记忆化搜索的方式实现 $dfs$ 函数。 + +时间复杂度 $O(\log_{x}{target})$,空间复杂度 $O(\log_{x}{target})$。 + ### **Python3** @@ -64,7 +81,20 @@ ```python - +class Solution: + def leastOpsExpressTarget(self, x: int, target: int) -> int: + @cache + def dfs(v: int) -> int: + if x >= v: + return min(v * 2 - 1, 2 * (x - v)) + k = 2 + while x**k < v: + k += 1 + if x**k - v < v: + return min(k + dfs(x**k - v), k - 1 + dfs(v - x ** (k - 1))) + return k - 1 + dfs(v - x ** (k - 1)) + + return dfs(target) ``` ### **Java** @@ -72,7 +102,134 @@ ```java +class Solution { + private int x; + private Map f = new HashMap<>(); + + public int leastOpsExpressTarget(int x, int target) { + this.x = x; + return dfs(target); + } + + private int dfs(int v) { + if (x >= v) { + return Math.min(v * 2 - 1, 2 * (x - v)); + } + if (f.containsKey(v)) { + return f.get(v); + } + int k = 2; + long y = (long) x * x; + while (y < v) { + y *= x; + ++k; + } + int ans = k - 1 + dfs(v - (int) (y / x)); + if (y - v < v) { + ans = Math.min(ans, k + dfs((int) y - v)); + } + f.put(v, ans); + return ans; + } +} +``` + +### **C++** + +```cpp +class Solution { +public: + int leastOpsExpressTarget(int x, int target) { + unordered_map f; + function dfs = [&](int v) -> int { + if (x >= v) { + return min(v * 2 - 1, 2 * (x - v)); + } + if (f.count(v)) { + return f[v]; + } + int k = 2; + long long y = x * x; + while (y < v) { + y *= x; + ++k; + } + int ans = k - 1 + dfs(v - y / x); + if (y - v < v) { + ans = min(ans, k + dfs(y - v)); + } + f[v] = ans; + return ans; + }; + return dfs(target); + } +}; +``` + +### **Go** + +```go +func leastOpsExpressTarget(x int, target int) int { + f := map[int]int{} + var dfs func(int) int + dfs = func(v int) int { + if x > v { + return min(v*2-1, 2*(x-v)) + } + if val, ok := f[v]; ok { + return val + } + k := 2 + y := x * x + for y < v { + y *= x + k++ + } + ans := k - 1 + dfs(v-y/x) + if y-v < v { + ans = min(ans, k+dfs(y-v)) + } + f[v] = ans + return ans + } + return dfs(target) +} + +func min(a, b int) int { + if a < b { + return a + } + return b +} +``` +### **TypeScript** + +```ts +function leastOpsExpressTarget(x: number, target: number): number { + const f: Map = new Map(); + const dfs = (v: number): number => { + if (x > v) { + return Math.min(v * 2 - 1, 2 * (x - v)); + } + if (f.has(v)) { + return f.get(v)!; + } + let k = 2; + let y = x * x; + while (y < v) { + y *= x; + ++k; + } + let ans = k - 1 + dfs(v - Math.floor(y / x)); + if (y - v < v) { + ans = Math.min(ans, k + dfs(y - v)); + } + f.set(v, ans); + return ans; + }; + return dfs(target); +} ``` ### **...** diff --git a/solution/0900-0999/0964.Least Operators to Express Number/README_EN.md b/solution/0900-0999/0964.Least Operators to Express Number/README_EN.md index 0aa99de1b922d..9f789af111673 100644 --- a/solution/0900-0999/0964.Least Operators to Express Number/README_EN.md +++ b/solution/0900-0999/0964.Least Operators to Express Number/README_EN.md @@ -60,13 +60,153 @@ The expression contains 3 operations. ### **Python3** ```python - +class Solution: + def leastOpsExpressTarget(self, x: int, target: int) -> int: + @cache + def dfs(v: int) -> int: + if x >= v: + return min(v * 2 - 1, 2 * (x - v)) + k = 2 + while x**k < v: + k += 1 + if x**k - v < v: + return min(k + dfs(x**k - v), k - 1 + dfs(v - x ** (k - 1))) + return k - 1 + dfs(v - x ** (k - 1)) + + return dfs(target) ``` ### **Java** ```java +class Solution { + private int x; + private Map f = new HashMap<>(); + + public int leastOpsExpressTarget(int x, int target) { + this.x = x; + return dfs(target); + } + + private int dfs(int v) { + if (x >= v) { + return Math.min(v * 2 - 1, 2 * (x - v)); + } + if (f.containsKey(v)) { + return f.get(v); + } + int k = 2; + long y = (long) x * x; + while (y < v) { + y *= x; + ++k; + } + int ans = k - 1 + dfs(v - (int) (y / x)); + if (y - v < v) { + ans = Math.min(ans, k + dfs((int) y - v)); + } + f.put(v, ans); + return ans; + } +} +``` + +### **C++** + +```cpp +class Solution { +public: + int leastOpsExpressTarget(int x, int target) { + unordered_map f; + function dfs = [&](int v) -> int { + if (x >= v) { + return min(v * 2 - 1, 2 * (x - v)); + } + if (f.count(v)) { + return f[v]; + } + int k = 2; + long long y = x * x; + while (y < v) { + y *= x; + ++k; + } + int ans = k - 1 + dfs(v - y / x); + if (y - v < v) { + ans = min(ans, k + dfs(y - v)); + } + f[v] = ans; + return ans; + }; + return dfs(target); + } +}; +``` + +### **Go** + +```go +func leastOpsExpressTarget(x int, target int) int { + f := map[int]int{} + var dfs func(int) int + dfs = func(v int) int { + if x > v { + return min(v*2-1, 2*(x-v)) + } + if val, ok := f[v]; ok { + return val + } + k := 2 + y := x * x + for y < v { + y *= x + k++ + } + ans := k - 1 + dfs(v-y/x) + if y-v < v { + ans = min(ans, k+dfs(y-v)) + } + f[v] = ans + return ans + } + return dfs(target) +} + +func min(a, b int) int { + if a < b { + return a + } + return b +} +``` +### **TypeScript** + +```ts +function leastOpsExpressTarget(x: number, target: number): number { + const f: Map = new Map(); + const dfs = (v: number): number => { + if (x > v) { + return Math.min(v * 2 - 1, 2 * (x - v)); + } + if (f.has(v)) { + return f.get(v)!; + } + let k = 2; + let y = x * x; + while (y < v) { + y *= x; + ++k; + } + let ans = k - 1 + dfs(v - Math.floor(y / x)); + if (y - v < v) { + ans = Math.min(ans, k + dfs(y - v)); + } + f.set(v, ans); + return ans; + }; + return dfs(target); +} ``` ### **...** diff --git a/solution/0900-0999/0964.Least Operators to Express Number/Solution.cpp b/solution/0900-0999/0964.Least Operators to Express Number/Solution.cpp new file mode 100644 index 0000000000000..7659d5f29ae8b --- /dev/null +++ b/solution/0900-0999/0964.Least Operators to Express Number/Solution.cpp @@ -0,0 +1,27 @@ +class Solution { +public: + int leastOpsExpressTarget(int x, int target) { + unordered_map f; + function dfs = [&](int v) -> int { + if (x >= v) { + return min(v * 2 - 1, 2 * (x - v)); + } + if (f.count(v)) { + return f[v]; + } + int k = 2; + long long y = x * x; + while (y < v) { + y *= x; + ++k; + } + int ans = k - 1 + dfs(v - y / x); + if (y - v < v) { + ans = min(ans, k + dfs(y - v)); + } + f[v] = ans; + return ans; + }; + return dfs(target); + } +}; \ No newline at end of file diff --git a/solution/0900-0999/0964.Least Operators to Express Number/Solution.go b/solution/0900-0999/0964.Least Operators to Express Number/Solution.go new file mode 100644 index 0000000000000..21294f12aa66a --- /dev/null +++ b/solution/0900-0999/0964.Least Operators to Express Number/Solution.go @@ -0,0 +1,32 @@ +func leastOpsExpressTarget(x int, target int) int { + f := map[int]int{} + var dfs func(int) int + dfs = func(v int) int { + if x > v { + return min(v*2-1, 2*(x-v)) + } + if val, ok := f[v]; ok { + return val + } + k := 2 + y := x * x + for y < v { + y *= x + k++ + } + ans := k - 1 + dfs(v-y/x) + if y-v < v { + ans = min(ans, k+dfs(y-v)) + } + f[v] = ans + return ans + } + return dfs(target) +} + +func min(a, b int) int { + if a < b { + return a + } + return b +} \ No newline at end of file diff --git a/solution/0900-0999/0964.Least Operators to Express Number/Solution.java b/solution/0900-0999/0964.Least Operators to Express Number/Solution.java new file mode 100644 index 0000000000000..a427eef6933b2 --- /dev/null +++ b/solution/0900-0999/0964.Least Operators to Express Number/Solution.java @@ -0,0 +1,30 @@ +class Solution { + private int x; + private Map f = new HashMap<>(); + + public int leastOpsExpressTarget(int x, int target) { + this.x = x; + return dfs(target); + } + + private int dfs(int v) { + if (x >= v) { + return Math.min(v * 2 - 1, 2 * (x - v)); + } + if (f.containsKey(v)) { + return f.get(v); + } + int k = 2; + long y = (long) x * x; + while (y < v) { + y *= x; + ++k; + } + int ans = k - 1 + dfs(v - (int) (y / x)); + if (y - v < v) { + ans = Math.min(ans, k + dfs((int) y - v)); + } + f.put(v, ans); + return ans; + } +} \ No newline at end of file diff --git a/solution/0900-0999/0964.Least Operators to Express Number/Solution.py b/solution/0900-0999/0964.Least Operators to Express Number/Solution.py new file mode 100644 index 0000000000000..9fde3d4861333 --- /dev/null +++ b/solution/0900-0999/0964.Least Operators to Express Number/Solution.py @@ -0,0 +1,14 @@ +class Solution: + def leastOpsExpressTarget(self, x: int, target: int) -> int: + @cache + def dfs(v: int) -> int: + if x >= v: + return min(v * 2 - 1, 2 * (x - v)) + k = 2 + while x**k < v: + k += 1 + if x**k - v < v: + return min(k + dfs(x**k - v), k - 1 + dfs(v - x ** (k - 1))) + return k - 1 + dfs(v - x ** (k - 1)) + + return dfs(target) diff --git a/solution/0900-0999/0964.Least Operators to Express Number/Solution.ts b/solution/0900-0999/0964.Least Operators to Express Number/Solution.ts new file mode 100644 index 0000000000000..6c24330f70cc4 --- /dev/null +++ b/solution/0900-0999/0964.Least Operators to Express Number/Solution.ts @@ -0,0 +1,24 @@ +function leastOpsExpressTarget(x: number, target: number): number { + const f: Map = new Map(); + const dfs = (v: number): number => { + if (x > v) { + return Math.min(v * 2 - 1, 2 * (x - v)); + } + if (f.has(v)) { + return f.get(v)!; + } + let k = 2; + let y = x * x; + while (y < v) { + y *= x; + ++k; + } + let ans = k - 1 + dfs(v - Math.floor(y / x)); + if (y - v < v) { + ans = Math.min(ans, k + dfs(y - v)); + } + f.set(v, ans); + return ans; + }; + return dfs(target); +}