From a97af5143e1f904001811722f72e64dcb11a4105 Mon Sep 17 00:00:00 2001
From: Matt Chang <tingyugenius@gmail.com>
Date: Fri, 31 Mar 2023 10:46:35 +0800
Subject: [PATCH] ADD # 1444. Number of Ways of Cutting a Pizza

---
 DP/cutPizza.go  | 66 +++++++++++++++++++++++++++++++++++++++++++++++++
 DP/readme.md    | 38 ++++++++++++++++++++++++++++
 test/dp_test.go | 17 +++++++++++++
 3 files changed, 121 insertions(+)
 create mode 100644 DP/cutPizza.go

diff --git a/DP/cutPizza.go b/DP/cutPizza.go
new file mode 100644
index 0000000..d22b0e2
--- /dev/null
+++ b/DP/cutPizza.go
@@ -0,0 +1,66 @@
+package DP
+
+func CurPizza(pizza []string, k int) int {
+	return ways(pizza, k)
+}
+
+func ways(pizza []string, k int) int {
+	s := make([][]int, 51)
+	for i := 0; i < len(s); i++ {
+		s[i] = make([]int, 51)
+	}
+	count := func(r1, c1, r2, c2 int) int {
+		var sum int
+		for i := r1; i <= r2; i++ {
+			sum += s[i][c2+1] - s[i][c1]
+		}
+		return sum
+	}
+	f := make([][][]int, 51)
+	for i := 0; i < len(f); i++ {
+		f[i] = make([][]int, 51)
+		for j := 0; j < len(f[i]); j++ {
+			f[i][j] = make([]int, 11)
+		}
+	}
+
+	mod := int(1e9 + 7)
+	rows, cols := len(pizza), len(pizza[0])
+	for i := 0; i < rows; i++ {
+		s[i][0] = 0
+		for j := 0; j < cols; j++ {
+			var tmp int
+			if pizza[i][j] == 'A' {
+				tmp = 1
+			}
+			s[i][j+1] = s[i][j] + tmp
+		}
+	}
+	for i := 0; i < rows; i++ {
+		for j := 0; j < cols; j++ {
+			if count(i, j, rows-1, cols-1) > 0 {
+				f[i][j][0] = 1
+			}
+		}
+	}
+
+	for p := 1; p < k; p++ {
+		for i := 0; i < rows; i++ {
+			for j := 0; j < cols; j++ {
+				f[i][j][p] = 0
+				for q := j; q < cols; q++ {
+					if count(i, j, rows-1, q) > 0 {
+						f[i][j][p] = (f[i][j][p] + f[i][q+1][p-1]) % mod
+					}
+				}
+				for q := i; q < rows; q++ {
+					if count(i, j, q, cols-1) > 0 {
+						f[i][j][p] = (f[i][j][p] + f[q+1][j][p-1]) % mod
+					}
+				}
+			}
+		}
+	}
+	return f[0][0][k-1]
+
+}
diff --git a/DP/readme.md b/DP/readme.md
index 8bd4dac..4888059 100644
--- a/DP/readme.md
+++ b/DP/readme.md
@@ -1,3 +1,41 @@
+# 1444. Number of Ways of Cutting a Pizza
+
+Given a rectangular pizza represented as a rows x cols matrix containing the following characters: 'A' (an apple) and '.' (empty cell) and given the integer k. You have to cut the pizza into k pieces using k-1 cuts.
+
+For each cut you choose the direction: vertical or horizontal, then you choose a cut position at the cell boundary and cut the pizza into two pieces. If you cut the pizza vertically, give the left part of the pizza to a person. If you cut the pizza horizontally, give the upper part of the pizza to a person. Give the last piece of pizza to the last person.
+
+Return the number of ways of cutting the pizza such that each piece contains at least one apple. Since the answer can be a huge number, return this modulo 10^9 + 7.
+
+
+Example 1:
+
+![](https://assets.leetcode.com/uploads/2020/04/23/ways_to_cut_apple_1.png)
+```
+Input: pizza = ["A..","AAA","..."], k = 3
+Output: 3
+Explanation: The figure above shows the three ways to cut the pizza. Note that pieces must contain at least one apple.
+```
+Example 2:
+
+```
+Input: pizza = ["A..","AA.","..."], k = 3
+Output: 1
+```
+Example 3:
+
+```
+Input: pizza = ["A..","A..","..."], k = 1
+Output: 1
+```
+
+Constraints:
+
+* 1 <= rows, cols <= 50
+* rows == pizza.length
+* cols == pizza[i].length
+* 1 <= k <= 10
+* pizza consists of characters 'A' and '.' only.
+
 # 87. Scramble String
 
 We can scramble a string s to get a string t using the following algorithm:
diff --git a/test/dp_test.go b/test/dp_test.go
index b8a9c6d..82f10b8 100644
--- a/test/dp_test.go
+++ b/test/dp_test.go
@@ -6,6 +6,23 @@ import (
 	"testing"
 )
 
+func TestCutPizza(t *testing.T) {
+	testData := []struct {
+		pizza    []string
+		k        int
+		expected int
+	}{
+		{[]string{"A..", "AAA", "..."}, 3, 3},
+		{[]string{"A..", "AA.", "..."}, 3, 1},
+		{[]string{"A..", "A..", "..."}, 1, 1},
+	}
+
+	for _, td := range testData {
+		result := DP.CurPizza(td.pizza, td.k)
+		assert.Equal(t, result, td.expected)
+	}
+}
+
 func TestIsScramble(t *testing.T) {
 	testData := []struct {
 		s1       string