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feat: update solutions to lc problem: No.0120.Triangle
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7 files changed

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-155
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7 files changed

+109
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‎solution/0000-0099/0072.Edit Distance/README.md‎

Lines changed: 6 additions & 4 deletions
Original file line numberDiff line numberDiff line change
@@ -57,14 +57,16 @@ exection -> execution (插入 'u')
5757

5858
动态规划。
5959

60-
设 `dp[i][j]` 表示将 word1 前 i 个字符组成的字符串 `word1[0...i-1]` 转换成 word2 前 j 个字符组成的字符串 `word2[0...j-1]` 的最小操作次数。
60+
设 `dp[i][j]` 表示将 word1 前 i 个字符组成的字符串 `word1[0...i-1]` 转换成 word2 前 j 个字符组成的字符串 `word2[0...j-1]` 的最小操作次数。m, n 分别表示 word1, word2 的长度。
6161

62-
初始化 `dp[i][0] = i`（`i∈[0, word1.length]`），`dp[0][j] = j` （`j∈[0, word2.length]`）。
62+
初始化 `dp[i][0] = i`（`i∈[0, m]`），`dp[0][j] = j` （`j∈[0, m]`）。
6363

6464
i, j 分别从 1 开始遍历，判断 `word1[i - 1]` 与 `word2[j - 1]` 是否相等：
6565

66-
- 若 `word1[i - 1] == word2[j - 1]`，`dp[i][j] = dp[i - 1][j - 1]`。
67-
- 若 `word1[i - 1] != word2[j - 1]`，`dp[i][j] = min(dp[i - 1][j], dp[i][j - 1], dp[i - 1][j - 1]) + 1`。其中 `dp[i - 1][j] + 1` 对应插入操作，`dp[i][j - 1] + 1` 对应删除操作，`dp[i - 1][j - 1] + 1` 对应替换操作。取三者的最小值即可。
66+
- 若 `word1[i - 1] == word2[j - 1]`，则 `dp[i][j] = dp[i - 1][j - 1]`。
67+
- 若 `word1[i - 1] != word2[j - 1]`，则 `dp[i][j] = min(dp[i - 1][j], dp[i][j - 1], dp[i - 1][j - 1]) + 1`。其中 `dp[i - 1][j] + 1` 对应插入操作，`dp[i][j - 1] + 1` 对应删除操作，`dp[i - 1][j - 1] + 1` 对应替换操作。取三者的最小值即可。
68+
69+
最后返回 `dp[m][n]` 即可。
6870

6971
<!-- tabs:start -->
7072

‎solution/0100-0199/0120.Triangle/README.md‎

Lines changed: 40 additions & 51 deletions
Original file line numberDiff line numberDiff line change
@@ -56,7 +56,7 @@
5656

5757
<!-- 这里可写通用的实现逻辑 -->
5858

59-
动态规划。
59+
动态规划。自底向上。
6060

6161
<!-- tabs:start -->
6262

@@ -68,15 +68,24 @@
6868
class Solution:
6969
def minimumTotal(self, triangle: List[List[int]]) -> int:
7070
n = len(triangle)
71-
for i in range(1, n):
71+
dp = [[0] * (n + 1) for _ in range(n + 1)]
72+
for i in range(n - 1, -1, -1):
7273
for j in range(i + 1):
73-
mi = float('inf')
74-
if j > 0:
75-
mi = min(mi, triangle[i - 1][j - 1])
76-
if j < i:
77-
mi = min(mi, triangle[i - 1][j])
78-
triangle[i][j] += mi
79-
return min(triangle[n - 1])
74+
dp[i][j] = min(dp[i + 1][j], dp[i + 1][j + 1]) + triangle[i][j]
75+
return dp[0][0]
76+
```
77+
78+
空间优化：
79+
80+
```python
81+
class Solution:
82+
def minimumTotal(self, triangle: List[List[int]]) -> int:
83+
n = len(triangle)
84+
dp = [0] * (n + 1)
85+
for i in range(n - 1, -1, -1):
86+
for j in range(i + 1):
87+
dp[j] = min(dp[j], dp[j + 1]) + triangle[i][j]
88+
return dp[0]
8089
```
8190

8291
### **Java**
@@ -87,23 +96,13 @@ class Solution:
8796
class Solution {
8897
public int minimumTotal(List<List<Integer>> triangle) {
8998
int n = triangle.size();
90-
for (int i = 1; i < n; ++i) {
91-
for (int j = 0; j < i + 1; ++j) {
92-
int mi = Integer.MAX_VALUE;
93-
if (j > 0) {
94-
mi = Math.min(mi, triangle.get(i - 1).get(j - 1));
95-
}
96-
if (j < i) {
97-
mi = Math.min(mi, triangle.get(i - 1).get(j));
98-
}
99-
triangle.get(i).set(j, triangle.get(i).get(j) + mi);
99+
int[] dp = new int[n + 1];
100+
for (int i = n - 1; i >= 0; --i) {
101+
for (int j = 0; j <= i; ++j) {
102+
dp[j] = Math.min(dp[j], dp[j + 1]) + triangle.get(i).get(j);
100103
}
101104
}
102-
int res = Integer.MAX_VALUE;
103-
for (int val : triangle.get(n - 1)) {
104-
res = Math.min(res, val);
105-
}
106-
return res;
105+
return dp[0];
107106
}
108107
}
109108
```
@@ -115,19 +114,15 @@ class Solution {
115114
public:
116115
int minimumTotal(vector<vector<int>>& triangle) {
117116
int n = triangle.size();
118-
for (int i = 1; i < n; ++i) {
119-
for (int j = 0; j < i + 1; ++j) {
120-
int mi = INT_MAX;
121-
if (j > 0) mi = min(mi, triangle[i - 1][j - 1]);
122-
if (j < i) mi = min(mi, triangle[i - 1][j]);
123-
triangle[i][j] += mi;
117+
vector<int> dp(n + 1);
118+
for (int i = n - 1; i >= 0; --i)
119+
{
120+
for (int j = 0; j <= i; ++j)
121+
{
122+
dp[j] = min(dp[j], dp[j + 1]) + triangle[i][j];
124123
}
125124
}
126-
int res = INT_MAX;
127-
for (int& val : triangle[n - 1]) {
128-
res = min(res, val);
129-
}
130-
return res;
125+
return dp[0];
131126
}
132127
};
133128
```
@@ -137,26 +132,20 @@ public:
137132
```go
138133
func minimumTotal(triangle [][]int) int {
139134
n := len(triangle)
140-
for i := 1; i < n; i++ {
141-
for j := 0; j < i+1; j++ {
142-
mi := 2000000
143-
if j > 0 && mi > triangle[i-1][j-1] {
144-
mi = triangle[i-1][j-1]
145-
}
146-
if j < i && mi > triangle[i-1][j] {
147-
mi = triangle[i-1][j]
148-
}
149-
triangle[i][j] += mi
135+
dp := make([]int, n+1)
136+
for i := n - 1; i >= 0; i-- {
137+
for j := 0; j <= i; j++ {
138+
dp[j] = min(dp[j], dp[j+1]) + triangle[i][j]
150139
}
151140
}
141+
return dp[0]
142+
}
152143
153-
res := 2000000
154-
for j := 0; j < n; j++ {
155-
if res > triangle[n-1][j] {
156-
res = triangle[n-1][j]
157-
}
144+
func min(a, b int) int {
145+
if a < b {
146+
return a
158147
}
159-
return res
148+
return b
160149
}
161150
```
162151

‎solution/0100-0199/0120.Triangle/README_EN.md‎

Lines changed: 37 additions & 50 deletions
Original file line numberDiff line numberDiff line change
@@ -54,15 +54,22 @@ Dynamic programming.
5454
class Solution:
5555
def minimumTotal(self, triangle: List[List[int]]) -> int:
5656
n = len(triangle)
57-
for i in range(1, n):
57+
dp = [[0] * (n + 1) for _ in range(n + 1)]
58+
for i in range(n - 1, -1, -1):
5859
for j in range(i + 1):
59-
mi = float('inf')
60-
if j > 0:
61-
mi = min(mi, triangle[i - 1][j - 1])
62-
if j < i:
63-
mi = min(mi, triangle[i - 1][j])
64-
triangle[i][j] += mi
65-
return min(triangle[n - 1])
60+
dp[i][j] = min(dp[i + 1][j], dp[i + 1][j + 1]) + triangle[i][j]
61+
return dp[0][0]
62+
```
63+
64+
```python
65+
class Solution:
66+
def minimumTotal(self, triangle: List[List[int]]) -> int:
67+
n = len(triangle)
68+
dp = [0] * (n + 1)
69+
for i in range(n - 1, -1, -1):
70+
for j in range(i + 1):
71+
dp[j] = min(dp[j], dp[j + 1]) + triangle[i][j]
72+
return dp[0]
6673
```
6774

6875
### **Java**
@@ -71,23 +78,13 @@ class Solution:
7178
class Solution {
7279
public int minimumTotal(List<List<Integer>> triangle) {
7380
int n = triangle.size();
74-
for (int i = 1; i < n; ++i) {
75-
for (int j = 0; j < i + 1; ++j) {
76-
int mi = Integer.MAX_VALUE;
77-
if (j > 0) {
78-
mi = Math.min(mi, triangle.get(i - 1).get(j - 1));
79-
}
80-
if (j < i) {
81-
mi = Math.min(mi, triangle.get(i - 1).get(j));
82-
}
83-
triangle.get(i).set(j, triangle.get(i).get(j) + mi);
81+
int[] dp = new int[n + 1];
82+
for (int i = n - 1; i >= 0; --i) {
83+
for (int j = 0; j <= i; ++j) {
84+
dp[j] = Math.min(dp[j], dp[j + 1]) + triangle.get(i).get(j);
8485
}
8586
}
86-
int res = Integer.MAX_VALUE;
87-
for (int val : triangle.get(n - 1)) {
88-
res = Math.min(res, val);
89-
}
90-
return res;
87+
return dp[0];
9188
}
9289
}
9390
```
@@ -99,19 +96,15 @@ class Solution {
9996
public:
10097
int minimumTotal(vector<vector<int>>& triangle) {
10198
int n = triangle.size();
102-
for (int i = 1; i < n; ++i) {
103-
for (int j = 0; j < i + 1; ++j) {
104-
int mi = INT_MAX;
105-
if (j > 0) mi = min(mi, triangle[i - 1][j - 1]);
106-
if (j < i) mi = min(mi, triangle[i - 1][j]);
107-
triangle[i][j] += mi;
99+
vector<int> dp(n + 1);
100+
for (int i = n - 1; i >= 0; --i)
101+
{
102+
for (int j = 0; j <= i; ++j)
103+
{
104+
dp[j] = min(dp[j], dp[j + 1]) + triangle[i][j];
108105
}
109106
}
110-
int res = INT_MAX;
111-
for (int& val : triangle[n - 1]) {
112-
res = min(res, val);
113-
}
114-
return res;
107+
return dp[0];
115108
}
116109
};
117110
```
@@ -121,26 +114,20 @@ public:
121114
```go
122115
func minimumTotal(triangle [][]int) int {
123116
n := len(triangle)
124-
for i := 1; i < n; i++ {
125-
for j := 0; j < i+1; j++ {
126-
mi := 2000000
127-
if j > 0 && mi > triangle[i-1][j-1] {
128-
mi = triangle[i-1][j-1]
129-
}
130-
if j < i && mi > triangle[i-1][j] {
131-
mi = triangle[i-1][j]
132-
}
133-
triangle[i][j] += mi
117+
dp := make([]int, n+1)
118+
for i := n - 1; i >= 0; i-- {
119+
for j := 0; j <= i; j++ {
120+
dp[j] = min(dp[j], dp[j+1]) + triangle[i][j]
134121
}
135122
}
123+
return dp[0]
124+
}
136125
137-
res := 2000000
138-
for j := 0; j < n; j++ {
139-
if res > triangle[n-1][j] {
140-
res = triangle[n-1][j]
141-
}
126+
func min(a, b int) int {
127+
if a < b {
128+
return a
142129
}
143-
return res
130+
return b
144131
}
145132
```
146133

‎solution/0100-0199/0120.Triangle/Solution.cpp‎

Lines changed: 7 additions & 11 deletions
Original file line numberDiff line numberDiff line change
@@ -2,18 +2,14 @@ class Solution {
22
public:
33
int minimumTotal(vector<vector<int>>& triangle) {
44
int n = triangle.size();
5-
for (int i = 1; i < n; ++i) {
6-
for (int j = 0; j < i + 1; ++j) {
7-
int mi = INT_MAX;
8-
if (j > 0) mi = min(mi, triangle[i - 1][j - 1]);
9-
if (j < i) mi = min(mi, triangle[i - 1][j]);
10-
triangle[i][j] += mi;
5+
vector<int> dp(n + 1);
6+
for (int i = n - 1; i >= 0; --i)
7+
{
8+
for (int j = 0; j <= i; ++j)
9+
{
10+
dp[j] = min(dp[j], dp[j + 1]) + triangle[i][j];
1111
}
1212
}
13-
int res = INT_MAX;
14-
for (int& val : triangle[n - 1]) {
15-
res = min(res, val);
16-
}
17-
return res;
13+
return dp[0];
1814
}
1915
};

‎solution/0100-0199/0120.Triangle/Solution.go‎

Lines changed: 10 additions & 16 deletions
Original file line numberDiff line numberDiff line change
@@ -1,23 +1,17 @@
11
func minimumTotal(triangle [][]int) int {
22
n := len(triangle)
3-
for i := 1; i < n; i++ {
4-
for j := 0; j < i+1; j++ {
5-
mi := 2000000
6-
if j > 0 && mi > triangle[i-1][j-1] {
7-
mi = triangle[i-1][j-1]
8-
}
9-
if j < i && mi > triangle[i-1][j] {
10-
mi = triangle[i-1][j]
11-
}
12-
triangle[i][j] += mi
3+
dp := make([]int, n+1)
4+
for i := n - 1; i >= 0; i-- {
5+
for j := 0; j <= i; j++ {
6+
dp[j] = min(dp[j], dp[j+1]) + triangle[i][j]
137
}
148
}
9+
return dp[0]
10+
}
1511

16-
res := 2000000
17-
for j := 0; j < n; j++ {
18-
if res > triangle[n-1][j] {
19-
res = triangle[n-1][j]
20-
}
12+
func min(a, b int) int {
13+
if a < b {
14+
return a
2115
}
22-
return res
16+
return b
2317
}

‎solution/0100-0199/0120.Triangle/Solution.java‎

Lines changed: 5 additions & 15 deletions
Original file line numberDiff line numberDiff line change
@@ -1,22 +1,12 @@
11
class Solution {
22
public int minimumTotal(List<List<Integer>> triangle) {
33
int n = triangle.size();
4-
for (int i = 1; i < n; ++i) {
5-
for (int j = 0; j < i + 1; ++j) {
6-
int mi = Integer.MAX_VALUE;
7-
if (j > 0) {
8-
mi = Math.min(mi, triangle.get(i - 1).get(j - 1));
9-
}
10-
if (j < i) {
11-
mi = Math.min(mi, triangle.get(i - 1).get(j));
12-
}
13-
triangle.get(i).set(j, triangle.get(i).get(j) + mi);
4+
int[] dp = new int[n + 1];
5+
for (int i = n - 1; i >= 0; --i) {
6+
for (int j = 0; j <= i; ++j) {
7+
dp[j] = Math.min(dp[j], dp[j + 1]) + triangle.get(i).get(j);
148
}
159
}
16-
int res = Integer.MAX_VALUE;
17-
for (int val : triangle.get(n - 1)) {
18-
res = Math.min(res, val);
19-
}
20-
return res;
10+
return dp[0];
2111
}
2212
}

‎solution/0100-0199/0120.Triangle/Solution.py‎

Lines changed: 4 additions & 8 deletions
Original file line numberDiff line numberDiff line change
@@ -1,12 +1,8 @@
11
class Solution:
22
def minimumTotal(self, triangle: List[List[int]]) -> int:
33
n = len(triangle)
4-
for i in range(1, n):
4+
dp = [0] * (n + 1)
5+
for i in range(n - 1, -1, -1):
56
for j in range(i + 1):
6-
mi = float('inf')
7-
if j > 0:
8-
mi = min(mi, triangle[i - 1][j - 1])
9-
if j < i:
10-
mi = min(mi, triangle[i - 1][j])
11-
triangle[i][j] += mi
12-
return min(triangle[n - 1])
7+
dp[j] = min(dp[j], dp[j + 1]) + triangle[i][j]
8+
return dp[0]

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