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feat: update solutions to lc problem: No.0799
No.0799.Champagne Tower
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‎solution/0700-0799/0799.Champagne Tower/README.md

+116-38
Original file line numberDiff line numberDiff line change
@@ -54,11 +54,17 @@
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**方法一：模拟**
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直接模拟倒香槟的过程，定义二维数组 $g$，初始时 `g[0][j]=poured`。
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我们直接模拟倒香槟的过程。
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对于每一层，如果当前杯子的香槟量 $g[i][j]$ 大于 $1$，香槟会向下一层的两个杯子倒入，倒入的量为 $\frac{g[i][j]-1}{2}$，即当前杯子的香槟量减去 $1$ 后除以 $2$，然后当前杯子的香槟量更新为 $1$。
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定义一个二维数组 $f$，其中 $f[i][j]$ 表示第 $i$ 层第 $j$ 个玻璃杯中的香槟量。初始时 $f[0][0] = poured$。
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最后返回 `g[query_row][query_glass]` 即可。
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对于每一层，如果当前杯子的香槟量 $f[i][j]$ 大于 $1$，香槟会流向下一层的两个杯子，流入的量为 $\frac{f[i][j]-1}{2}$，即当前杯子的香槟量减去 $1$ 后除以 $2$，然后当前杯子的香槟量更新为 $1$。
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模拟结束，返回 $f[query\_row][query\_glass]$ 即可。
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由于每一层的香槟量只与上一层的香槟量有关，因此我们可以用滚动数组的方式优化空间复杂度，将二维数组优化为一维数组。
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时间复杂度 $O(n^2)$，空间复杂度 $O(n)$。其中 $n$ 为层数，即 $query\_row$。
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<!-- tabs:start -->
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@@ -69,16 +75,31 @@
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```python
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class Solution:
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def champagneTower(self, poured: int, query_row: int, query_glass: int) -> float:
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g = [[0] * 110 for _ in range(110)]
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g[0][0] = poured
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f = [[0] * 101 for _ in range(101)]
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f[0][0] = poured
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for i in range(query_row + 1):
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for j in range(i + 1):
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if g[i][j] > 1:
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half = (g[i][j] - 1) / 2
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g[i][j] = 1
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g[i + 1][j] += half
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g[i + 1][j + 1] += half
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return g[query_row][query_glass]
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if f[i][j] > 1:
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half = (f[i][j] - 1) / 2
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f[i][j] = 1
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f[i + 1][j] += half
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f[i + 1][j + 1] += half
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return f[query_row][query_glass]
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```
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```python
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class Solution:
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def champagneTower(self, poured: int, query_row: int, query_glass: int) -> float:
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f = [poured]
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for i in range(1, query_row + 1):
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g = [0] * (i + 1)
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for j, v in enumerate(f):
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if v > 1:
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half = (v - 1) / 2
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g[j] += half
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g[j + 1] += half
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f = g
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return min(1, f[query_glass])
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```
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### **Java**
@@ -88,19 +109,39 @@ class Solution:
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```java
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class Solution {
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public double champagneTower(int poured, int query_row, int query_glass) {
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double[][] g = new double[110][110];
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g[0][0] = poured;
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double[][] f = new double[101][101];
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f[0][0] = poured;
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for (int i = 0; i <= query_row; ++i) {
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for (int j = 0; j <= i; ++j) {
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if (g[i][j] > 1) {
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double half = (g[i][j] - 1) / 2.0;
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g[i][j] = 1;
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g[i + 1][j] += half;
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g[i + 1][j + 1] += half;
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if (f[i][j] > 1) {
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double half = (f[i][j] - 1) / 2.0;
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f[i][j] = 1;
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f[i + 1][j] += half;
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f[i + 1][j + 1] += half;
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}
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}
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}
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return g[query_row][query_glass];
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return f[query_row][query_glass];
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}
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}
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```
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```java
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class Solution {
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public double champagneTower(int poured, int query_row, int query_glass) {
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double[] f = {poured};
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for (int i = 1; i <= query_row; ++i) {
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double[] g = new double[i + 1];
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for (int j = 0; j < i; ++j) {
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if (f[j] > 1) {
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double half = (f[j] - 1) / 2.0;
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g[j] += half;
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g[j + 1] += half;
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}
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}
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f = g;
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}
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return Math.min(1, f[query_glass]);
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}
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}
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```
@@ -111,19 +152,41 @@ class Solution {
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class Solution {
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public:
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double champagneTower(int poured, int query_row, int query_glass) {
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double g[110][110] = {0.0};
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g[0][0] = poured;
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double f[101][101] = {0.0};
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f[0][0] = poured;
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for (int i = 0; i <= query_row; ++i) {
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for (int j = 0; j <= i; ++j) {
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if (g[i][j] > 1) {
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double half = (g[i][j] - 1) / 2.0;
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g[i][j] = 1;
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g[i + 1][j] += half;
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g[i + 1][j + 1] += half;
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if (f[i][j] > 1) {
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double half = (f[i][j] - 1) / 2.0;
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f[i][j] = 1;
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f[i + 1][j] += half;
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f[i + 1][j + 1] += half;
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}
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}
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}
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return f[query_row][query_glass];
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}
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};
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```
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```cpp
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class Solution {
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public:
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double champagneTower(int poured, int query_row, int query_glass) {
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double f[101] = {(double) poured};
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double g[101];
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for (int i = 1; i <= query_row; ++i) {
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memset(g, 0, sizeof g);
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for (int j = 0; j < i; ++j) {
181+
if (f[j] > 1) {
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double half = (f[j] - 1) / 2.0;
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g[j] += half;
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g[j + 1] += half;
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}
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}
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memcpy(f, g, sizeof g);
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}
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return g[query_row][query_glass];
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return min(1.0, f[query_glass]);
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}
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};
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```
@@ -132,22 +195,37 @@ public:
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```go
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func champagneTower(poured int, query_row int, query_glass int) float64 {
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g := make([][]float64, 110)
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for i := range g {
137-
g[i] = make([]float64, 110)
138-
}
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g[0][0] = float64(poured)
198+
f := [101][101]float64{}
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f[0][0] = float64(poured)
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for i := 0; i <= query_row; i++ {
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for j := 0; j <= i; j++ {
142-
if g[i][j] > 1 {
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half := (g[i][j] - 1) / 2.0
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g[i][j] = 1
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g[i+1][j] += half
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g[i+1][j+1] += half
202+
if f[i][j] > 1 {
203+
half := (f[i][j] - 1) / 2.0
204+
f[i][j] = 1
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f[i+1][j] += half
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f[i+1][j+1] += half
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}
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}
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}
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return f[query_row][query_glass]
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}
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```
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```go
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func champagneTower(poured int, query_row int, query_glass int) float64 {
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f := []float64{float64(poured)}
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for i := 1; i <= query_row; i++ {
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g := make([]float64, i+1)
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for j, v := range f {
220+
if v > 1 {
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half := (v - 1) / 2.0
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g[j] += half
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g[j+1] += half
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}
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}
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f = g
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}
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return g[query_row][query_glass]
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return math.Min(1, f[query_glass])
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}
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```
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