Added code for palindrome partitioning problem under dynamic programming

Author: agnivg

dynamic_programming/palindrome_partitioning.py

@@ -0,0 +1,39 @@
+"""
+Given a string s, partition s such that every substring of the
+partition is a palindrome.
+Find the minimum cuts needed for a palindrome partitioning of s.
+
+Time Complexity: O(n^2)
+Space Complexity: O(n^2)
+For other explanations refer to: https://www.youtube.com/watch?v=_H8V5hJUGd0
+"""
+
+
+def find_minimum_partitions(s):
+    """
+    Returns the minimum cuts needed for a palindrome partitioning of s
+
+    >>> find_minimum_partitions("aab")
+    1
+    >>> find_minimum_partitions("aaa")
+    0
+    >>> find_minimum_partitions("ababbbabbababa")
+    3
+    """
+    n = len(s)
+    cut = [0 for i in range(n)]
+    ispalindrome = [[False for i in range(n)] for j in range(n)]
+    for i in range(n):
+        mincut = i
+        for j in range(i + 1):
+            if s[i] == s[j] and (i - j < 2 or ispalindrome[j + 1][i - 1]):
+                ispalindrome[j][i] = True
+                mincut = min(mincut, 0 if j == 0 else (cut[j - 1] + 1))
+        cut[i] = mincut
+    return cut[n - 1]
+
+
+if __name__ == "__main__":
+    s = input("Enter the string: ").strip()
+    ans = find_minimum_partitions(s)
+    print(f"Minimum number of partitions required for the string is {ans}")