From e1f1fbc5e16ab432456c484bfd5f587a16c3c745 Mon Sep 17 00:00:00 2001
From: Renkin <906155099@qq.com>
Date: Tue, 21 Nov 2023 11:09:04 +0800
Subject: [PATCH 1/2] fix: fixed i18n for "Code"

---
 src/locales/en.js              | 1 +
 src/locales/zh.js              | 4 ++--
 src/solutionTemplate/index.jsx | 2 +-
 3 files changed, 4 insertions(+), 3 deletions(-)

diff --git a/src/locales/en.js b/src/locales/en.js
index e2f68a2..0abddcf 100644
--- a/src/locales/en.js
+++ b/src/locales/en.js
@@ -295,6 +295,7 @@ const en = {
 
   explanationTemplate: {
     name: "Explanation Template",
+    code: "Code",
     goToTheWebsiteToUse: "Go to the website to use",
     problemAddress: "Problem Address",
     problemDesc: "Problem Description",
diff --git a/src/locales/zh.js b/src/locales/zh.js
index 06d2c66..630a4d8 100644
--- a/src/locales/zh.js
+++ b/src/locales/zh.js
@@ -208,7 +208,6 @@ const zh = {
       item3: "寻找最右边的满足条件的值",
       item4: "寻找最左插入位置",
       item5: "寻找最右插入位置",
-      
     },
     BFS: {
       item1: "带层信息",
@@ -236,7 +235,7 @@ const zh = {
       title: "前缀树",
       item1: "标准前缀树",
     },
-    
+
     uf: {
       title: "并查集",
       item1: "不带权并查集",
@@ -287,6 +286,7 @@ const zh = {
 
   explanationTemplate: {
     name: "题解模板",
+    code: "代码",
     goToTheWebsiteToUse: "去网站使用",
     problemAddress: "题目地址",
     problemDesc: "题目描述",
diff --git a/src/solutionTemplate/index.jsx b/src/solutionTemplate/index.jsx
index 0f5a8dd..accd528 100644
--- a/src/solutionTemplate/index.jsx
+++ b/src/solutionTemplate/index.jsx
@@ -114,7 +114,7 @@ ${desc}
 
 - ${keyword} 
 
-## Code
+## ${t("Locale.explanationTemplate.code")}
 
 - ${t("Locale.explanationTemplate.languageSupport")}：${displayLanguage(
     language

From ada249c5061b35cce80a904982ea29b93876159c Mon Sep 17 00:00:00 2001
From: Renkin <906155099@qq.com>
Date: Tue, 21 Nov 2023 11:48:52 +0800
Subject: [PATCH 2/2] feat: i18n update

---
 src/codeTemplates/grapth.js | 34 ++++++++++++++++++++++++++--------
 src/codeTemplates/preSum.js | 36 +++++++++++++++++++++++++++++-------
 src/locales/en.js           |  2 ++
 src/locales/zh.js           |  2 ++
 4 files changed, 59 insertions(+), 15 deletions(-)

diff --git a/src/codeTemplates/grapth.js b/src/codeTemplates/grapth.js
index 20f39b7..473383f 100644
--- a/src/codeTemplates/grapth.js
+++ b/src/codeTemplates/grapth.js
@@ -15,8 +15,8 @@ module.exports = () => ({
         {
           language: "py",
           desc: `
-          
-比如一个图是这样的：
+${t("Locale.codeTemplate.graph.item1_desc1")}          
+
 
 \`\`\`
 E -- 1 --> B -- 1 --> C -- 1 --> D -- 1 --> F
@@ -25,7 +25,8 @@ E -- 1 --> B -- 1 --> C -- 1 --> D -- 1 --> F
     -------- 2 ---------> G ------- 1 ------
     \`\`\`
 
-我们使用邻接矩阵来构造：
+${t("Locale.codeTemplate.graph.item1_desc2")}          
+
 
 \`\`\`py
 G = {
@@ -47,6 +48,7 @@ import heapq
 
 def dijkstra(graph, start, end):
     # 堆里的数据都是 (cost, i) 的二元祖，其含义是“从 start 走到 i 的距离是 cost”。
+    # The data in the heap consists of tuples (cost, i), where it signifies "the distance from start to i is cost".
     heap = [(0, start)]
     visited = set()
     while heap:
@@ -79,7 +81,10 @@ def dijkstra(graph, start, end):
           language: "py",
           text: `
 # graph 是邻接矩阵，n 是顶点个数
+# The graph is represented as an adjacency matrix, where n represents the number of vertices.
+
 # graph 形如： graph[u][v] = w
+# graph is like: graph[u][v] = w
 def floyd_warshall(graph, n):
     dist = [[float("inf") for _ in range(n)] for _ in range(n)]
 
@@ -87,10 +92,13 @@ def floyd_warshall(graph, n):
         for j in range(n):
             dist[i][j] = graph[i][j]
 
+    # 将顶点k与所有其他顶点(i, j)进行比较
     # check vertex k against all other vertices (i, j)
     for k in range(n):
+        # 循环遍历图数组的行
         # looping through rows of graph array
         for i in range(n):
+            # 循环遍历图数组的列
             # looping through columns of graph array
             for j in range(n):
                 if (
@@ -116,7 +124,9 @@ def floyd_warshall(graph, n):
         {
           language: "py",
           text: `
+# 如果不存在，返回-1
 # return -1 for not exsit
+# 如果存在，返回 dis map，dis[v]表示从点s到点v的最小花费
 # else return dis map where dis[v] means for point s the least cost to point v
 def bell_man(edges, s):
     dis = defaultdict(lambda: math.inf)
@@ -245,7 +255,8 @@ def PrimsAlgorithm(l):  # noqa: E741
                 set_position(positions[start], temp)
 
                 top_to_bottom(heap, m, size, positions)
-
+    
+    # 如果最小堆中任意节点的值减小，则更新函数
     # Update function if value of any node in min-heap decreases
     def bottom_to_top(val, index, heap, position):
         temp = position[index]
@@ -283,10 +294,16 @@ def PrimsAlgorithm(l):  # noqa: E741
         return temp
 
     visited = [0 for i in range(len(l))]
-    Nbr_TV = [-1 for i in range(len(l))]  # Neighboring Tree Vertex of selected vertex
+    # 所选顶点的邻近树顶点
+    # Neighboring Tree Vertex of selected vertex
+    Nbr_TV = [-1 for i in range(len(l))]  
+    # 部分树的探索顶点到邻近顶点的最小距离
     # Minimum Distance of explored vertex with neighboring vertex of partial tree
+    # 以图表形式呈现
     # formed in graph
-    Distance_TV = []  # Heap of Distance of vertices from their neighboring vertex
+    # 堆顶点到相邻顶点的距离
+    # Heap of Distance of vertices from their neighboring vertex
+    Distance_TV = []  
     Positions = []
 
     for x in range(len(l)):
@@ -339,8 +356,9 @@ if __name__ == "__main__":  # pragma: no cover
           text: `
 def topologicalSort(graph):
     """
+    Kahn算法是使用广度优先搜索（BFS）来找到有向无环图（Directed Acyclic Graph）的拓扑排序的算法。
     Kahn's Algorithm is used to find Topological ordering of Directed Acyclic Graph
-    using BFS
+    using BFS.
     """
     indegree = [0] * len(graph)
     queue = collections.deque([])
@@ -369,7 +387,7 @@ def topologicalSort(graph):
     else:
         print(topo)
 
-
+# 图的邻接表
 # Adjacency List of Graph
 graph = {0: [1, 2], 1: [3], 2: [3], 3: [4, 5], 4: [], 5: []}
 topologicalSort(graph)
diff --git a/src/codeTemplates/preSum.js b/src/codeTemplates/preSum.js
index b4a6042..fe7ed57 100644
--- a/src/codeTemplates/preSum.js
+++ b/src/codeTemplates/preSum.js
@@ -2,53 +2,75 @@
 const { t } = require("../locales");
 const pre1dJSCode = `
   // 建立
+  // build
   const pre = [0]
   for(const num of nums) {
       pre.push(pre[pre.length-1] + num)
   }
   // 使用，等价于 nums[i] + nums[i + 1] + ... + nums[j]
+  // Use, equivalent to nums[i] + nums[i + 1] + ... + nums[j]
   pre[j+1] - pre[i]
 `;
 
 const pre1dPythonCode = `
   # 建立
+  # build
   pre = []
   for num in nums:
       pre.append(pre[-1] + num)
   #  使用，等价于 nums[i] + nums[i + 1] + ... + nums[j]
+  # Use, equivalent to nums[i] + nums[i + 1] + ... + nums[j]
   pre[j+1] - pre[i] 
 `;
 
 const pre2dPythonCode = `
   m,n = len(matrix), len(matrix[0])
   # 建立
+  # build
   pre = [[0 for _ in range(n + 1)] for _ in range(m + 1)]
   for i in range(1, m+1):
       for j in range(1, n +1):
           pre[i][j] = pre[i-1][j]+ pre[i][j-1] - pre[i-1][j-1] + matrix[i-1][j-1]
 
   # 使用，等价于以(x1,y1)为矩阵左上角以(x2,y2)为矩阵右下角的所有格子的和
+  # Use, equivalent to the sum of all cells with (x1, y1) as the upper left corner and (x2, y2) as the lower right corner
   pre[x2+1][y2+1] + pre[x1][y1] - pre[x1][y2+1] - pre[x2+1][y1]
 `;
 
 const diff1dPythonCode = `
         # 差分数组一般是对一个数组的若干区间进行若干次加减操作，求最终更新后的数组。
-        d = [0] * n # 差分数组
-        ans = [0] * n # 经过若干次操作后的最终数组
-        for start, end, inc in updates: # updates 就是一系列操作，start 是开始坐标，end 是结束坐标，inc 是增加的值（可为负数）。
+        # The difference array is generally to perform several addition and subtraction operations on several intervals of an array to obtain the finally updated array.
+        
+        # 差分数组
+        # difference array
+        d = [0] * n
+        # 经过若干次操作后的最终数组
+        # the final array after several operations
+        ans = [0] * n 
+        # updates 就是一系列操作，start 是开始坐标，end 是结束坐标，inc 是增加的值（可为负数）。
+        # updates is a series of operations, start is the starting coordinate, end is the ending coordinate, and inc is the added value (can be negative).
+        for start, end, inc in updates: 
             d[start] += seats
             if end+1 < n: d[end+1] -= inc
         return list(accumulate(d))
 `;
 
 const diff2dPythonCode = `
-        matrix = [[0] * n for _ in range(n)] # 经过若干次操作后的最终数组
-        diff = [[0] * (n+1) for _ in range(n+1)] # 差分数组
-        for r1, c1, r2, c2, inc in updates: # updates r1,c1 是左上角坐标，r2, c2 是右下角坐标，inc 是增加的值（可为负数）。
+        # 经过若干次操作后的最终数组
+        # the final array after several operations
+        matrix = [[0] * n for _ in range(n)]
+        # 差分数组
+        # difference array
+        diff = [[0] * (n+1) for _ in range(n+1)] 
+        # updates r1,c1 是左上角坐标，r2, c2 是右下角坐标，inc 是增加的值（可为负数）。
+        # updates r1,c1 is the upper left corner coordinate, r2, c2 is the lower right corner coordinate, and inc is the added value (can be negative).
+        for r1, c1, r2, c2, inc in updates: 
             diff[r1][c1] += inc
             diff[r1][c2+1] -= inc
             diff[r2+1][c1] -= inc
-            diff[r2+1][c2+1] += inc # 别忘记了，由于我们在两个地方对减去 1， 因此在右下角会多减去一个，加上去即可。
+            # 别忘记了，由于我们在两个地方对减去 1， 因此在右下角会多减去一个，加上去即可。
+            # Don't forget, because we subtract 1 in two places, one more will be subtracted in the lower right corner, so add it back.
+            diff[r2+1][c2+1] += inc 
         for i in range(n):
             for j in range(n):
                 matrix[i][j] = diff[i][j]
diff --git a/src/locales/en.js b/src/locales/en.js
index 0abddcf..f9f8a4a 100644
--- a/src/locales/en.js
+++ b/src/locales/en.js
@@ -200,6 +200,8 @@ const en = {
     graph: {
       title: "Graph",
       item1: "dijkstra(single-source greedy shortest path)",
+      item1_desc1: "For example, consider a graph like this:",
+      item1_desc2: "We construct it using an adjacency matrix:",
       item2: "floyd_warshall(multi-source dynamic programming shortest path)",
       item3: "Bellman–Ford(single-source dynamic programming shortest path)",
       item4:
diff --git a/src/locales/zh.js b/src/locales/zh.js
index 630a4d8..72aa22a 100644
--- a/src/locales/zh.js
+++ b/src/locales/zh.js
@@ -195,6 +195,8 @@ const zh = {
     graph: {
       title: "图",
       item1: "dijkstra(单源贪心最短路径)",
+      item1_desc1: "比如一个图是这样的：",
+      item1_desc2: "我们使用邻接矩阵来构造：",
       item2: "floyd_warshall(多源动态规划最短路径)",
       item3: "Bellman–Ford（单源动态规划最短路径）",
       item4: "Kruskal（又称加边法，是一种最小生成树算法）",