Add: Add 2025/1/20

Author: whats2000

2661-First Completely Painted Row or Column/Note.md

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+# 916. 2661. First Completely Painted Row or Column
+
+You are given a 0-indexed integer array `arr`, and an `m x n` integer matrix `mat`. 
+`arr` and `mat` both contain all the integers in the range `[1, m * n]`.
+
+Go through each index `i` in `arr` starting from index `0` and 
+paint the cell in `mat` containing the integer `arr[i]`.
+
+Return the smallest index `i` at which either a row or a column will be completely painted in `mat`.
+
+## 基礎思路
+這題很重要的是建立索引列表，即數字對應到的行列，這樣可以快速找到對應的行列，然後進行計數，當計數等於m或n時，即找到答案。
+對應表比較有效率的是構建兩個陣列，一個是行對應表，一個是列對應表，這樣可以快速找到對應的行列。
+當然字典也是一個不錯的選擇，但是字典的查找效率比較低。
+
+## 解題步驟
+
+### Step 1: 取得行列數
+
+```typescript
+const n = mat.length;    // 行數
+const m = mat[0].length; // 列數
+```
+
+### Step 2: 建立行列對應表
+
+```typescript
+// 用來建立數字對應到行列的索引表
+const numberToRow: number[] = new Array(n * m);
+const numberToCol: number[] = new Array(n * m);
+
+// 遍歷矩陣，建立數字對應到行列的索引表
+for (let row = 0; row < n; row++) {
+  for (let col = 0; col < m; col++) {
+    const value = mat[row][col];
+    numberToRow[value] = row;
+    numberToCol[value] = col;
+  }
+}
+```
+
+### Step 3: 利用行列對應表進行計數，並找到答案
+
+```typescript
+// 用建立行列計數表
+const rowCounts: number[] = new Array(n).fill(0);
+const colCounts: number[] = new Array(m).fill(0);
+
+// 遍歷arr，進行計數
+for (let i = 0; i < arr.length; i++) {
+  const current = arr[i];
+  const row = numberToRow[current];
+  const col = numberToCol[current];
+
+  // 更新行列計數
+  rowCounts[row]++;
+  colCounts[col]++;
+
+  // 判斷是否找到答案，即行計數等於m或列計數等於n
+  if (rowCounts[row] === m || colCounts[col] === n) {
+    return i;
+  }
+}
+```
+
+## Step 4: 返回-1
+
+```typescript
+// 如果沒有找到答案，返回-1
+return -1;
+```
+雖然本題不會出現找不到答案的情況，但是實際應用中，這個是個好習慣。
+
+## 時間複雜度
+- 建立索引表的時間複雜度為$O(n \times m)$
+- 遍歷arr的時間複雜度為$O(n \times m)$
+- 總的時間複雜度為$O(n \times m)$
+
+> $O(n \times m)$
+
+## 空間複雜度
+
+- 兩個索引表的空間複雜度為$O(n \times m)$
+- 兩個計數表的空間複雜度為$O(n + m)$
+- 總的空間複雜度為$O(n \times m)$
+
+> $O(n \times m)$

2661-First Completely Painted Row or Column/answer.ts

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+function firstCompleteIndex(arr: number[], mat: number[][]): number {
+  const n = mat.length;    // Number of rows
+  const m = mat[0].length; // Number of columns
+
+  // Arrays to map each number in the matrix to its row and column indices
+  const numberToRow: number[] = new Array(n * m);
+  const numberToCol: number[] = new Array(n * m);
+
+  // Preprocess the matrix to create a direct mapping of numbers to their row and column
+  for (let row = 0; row < n; row++) {
+    for (let col = 0; col < m; col++) {
+      const value = mat[row][col];
+      numberToRow[value] = row;
+      numberToCol[value] = col;
+    }
+  }
+
+  // Arrays to track how many elements have been filled in each row and column
+  const rowCounts: number[] = new Array(n).fill(0);
+  const colCounts: number[] = new Array(m).fill(0);
+
+  // Process the `arr` to find the first completed row or column
+  for (let i = 0; i < arr.length; i++) {
+    const current = arr[i];
+    const row = numberToRow[current];
+    const col = numberToCol[current];
+
+    // Update row and column counts
+    rowCounts[row]++;
+    colCounts[col]++;
+
+    // Check if the current row or column is completed, we will return the index if it is
+    if (rowCounts[row] === m || colCounts[col] === n) {
+      return i;
+    }
+  }
+
+  // Return -1 if no row or column is completed
+  return -1;
+}