py sol for ac-nuske

solutions/silver/ac-nuske.mdx

@@ -283,4 +283,76 @@ public class Main {
 ```
 
 </JavaSection>
+
+<PySection>
+
+```py
+MAX_SIZE = 2000
+
+n, m, q = map(int, input().split())
+
+grid = [[False] * (MAX_SIZE + 1) for _ in range(MAX_SIZE + 1)]
+
+# Read the grid
+for i in range(1, n + 1):
+    row = input()
+    for j in range(1, m + 1):
+        grid[i][j] = row[j - 1] == '1'
+
+# Overall prefix sums array. pref[x][y] is how many components
+# we have in the 2D array from (1, 1) to (x, y), inclusive.
+pref = [[0] * (MAX_SIZE + 1) for _ in range(MAX_SIZE + 1)]
+
+for i in range(1, n + 1):
+    for j in range(1, m + 1):
+        pref[i][j] = pref[i - 1][j] + pref[i][j - 1] - pref[i - 1][j - 1]
+        if grid[i][j]:
+            """
+              0
+            0 1
+            A new connected component forms!
+            """
+            if not grid[i - 1][j] and not grid[i][j - 1]:
+                pref[i][j] += 1
+
+            """
+              1
+            1 1
+            Two connected componets merge!
+            """
+            if grid[i - 1][j] and grid[i][j - 1]:
+                pref[i][j] -= 1
+
+# horpref[x][y]: number of connected components in the row from (x, 1) to (x, y)
+horpref = [[0] * (MAX_SIZE + 1) for _ in range(MAX_SIZE + 1)]
+
+# verpref[x][y]: number of connected components in the column from (1, y) to (x, y)
+verpref = [[0] * (MAX_SIZE + 1) for _ in range(MAX_SIZE + 1)]
+
+for i in range(1, n + 1):
+    for j in range(1, m + 1):
+        horpref[i][j] = horpref[i][j - 1]
+        verpref[i][j] = verpref[i - 1][j]
+        if grid[i][j]:
+            horpref[i][j] += not grid[i][j - 1]
+            verpref[i][j] += not grid[i - 1][j]
+
+for _ in range(q):
+    a, b, c, d = map(int, input().split())
+
+    # Whether we start with a connected component
+    ans = grid[a][b]
+
+    # How many new components appear in the top row and leftmost column
+    ans += horpref[a][d] - horpref[a][b]
+    ans += verpref[c][b] - verpref[a][b]
+
+    # Change in the number of connected components in the rest of the grid
+    ans += pref[c][d] - pref[a][d] - pref[c][b] + pref[a][b]
+
+    print(ans)
+```
+
+</PySection>
+
 </LanguageSection>