From 453f95db9b2e295609fbc1fd5c4b37aad9298c4a Mon Sep 17 00:00:00 2001
From: JatinR05 <71865805+JatinR05@users.noreply.github.com>
Date: Mon, 24 Oct 2022 12:24:31 +0530
Subject: [PATCH] Create minimums_squares_to_represent_a_number.py

added a dynamic programming approach of finding the minimum number of square to represent a number.
eg :
25 = 5*5
37 = 6*6 + 1*1
21 = 4*4 + 2*2 + 1*1
---
 .../minimums_squares_to_represent_a_number.py | 35 +++++++++++++++++++
 1 file changed, 35 insertions(+)
 create mode 100644 dynamic_programming/minimums_squares_to_represent_a_number.py

diff --git a/dynamic_programming/minimums_squares_to_represent_a_number.py b/dynamic_programming/minimums_squares_to_represent_a_number.py
new file mode 100644
index 000000000000..71ef804eac31
--- /dev/null
+++ b/dynamic_programming/minimums_squares_to_represent_a_number.py
@@ -0,0 +1,35 @@
+import math,sys
+
+def minimum_squares_to_represent_a_number(number: int) -> int:
+    """
+    Count the number of minimum squares to represent a number
+    >>> minimum_squares_to_represent_a_number(25)
+    1
+    >>> minimum_squares_to_represent_a_number(37)
+    2
+    >>> minimum_squares_to_represent_a_number(21)
+    3
+    >>> minimum_squares_to_represent_a_number(58)
+    2
+    >>> minimum_squares_to_represent_a_number(-1)
+    Traceback (most recent call last):
+        ...
+    ValueError: the value of input must be positive
+    """
+    if number < 0:
+        raise ValueError("the value of input must be positive")
+    dp = [-1 for x in range(number+1)]
+    dp[0] = 0
+    for i in range(1,number+1):
+        ans = sys.maxsize
+        root = int(math.sqrt(i))
+        for j in range(1,root+1):
+            currAns = 1 + dp[i-(j**2)]
+            ans = min(ans,currAns)
+        dp[i] = ans
+    return dp[number]
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()