feat: add Project Euler problem 114 solution 1 (#6300)

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>

DIRECTORY.md

@@ -854,6 +854,8 @@
     * [Sol1](project_euler/problem_112/sol1.py)
   * Problem 113
     * [Sol1](project_euler/problem_113/sol1.py)
+  * Problem 114
+    * [Sol1](project_euler/problem_114/sol1.py)
   * Problem 119
     * [Sol1](project_euler/problem_119/sol1.py)
   * Problem 120

project_euler/problem_114/sol1.py

@@ -0,0 +1,58 @@
+"""
+Project Euler Problem 114: https://projecteuler.net/problem=114
+
+A row measuring seven units in length has red blocks with a minimum length
+of three units placed on it, such that any two red blocks
+(which are allowed to be different lengths) are separated by at least one grey square.
+There are exactly seventeen ways of doing this.
+
+    |g|g|g|g|g|g|g|    |r,r,r|g|g|g|g|
+
+    |g|r,r,r|g|g|g|    |g|g|r,r,r|g|g|
+
+    |g|g|g|r,r,r|g|    |g|g|g|g|r,r,r|
+
+    |r,r,r|g|r,r,r|    |r,r,r,r|g|g|g|
+
+    |g|r,r,r,r|g|g|    |g|g|r,r,r,r|g|
+
+    |g|g|g|r,r,r,r|    |r,r,r,r,r|g|g|
+
+    |g|r,r,r,r,r|g|    |g|g|r,r,r,r,r|
+
+    |r,r,r,r,r,r|g|    |g|r,r,r,r,r,r|
+
+    |r,r,r,r,r,r,r|
+
+How many ways can a row measuring fifty units in length be filled?
+
+NOTE: Although the example above does not lend itself to the possibility,
+in general it is permitted to mix block sizes. For example,
+on a row measuring eight units in length you could use red (3), grey (1), and red (4).
+"""
+
+
+def solution(length: int = 50) -> int:
+    """
+    Returns the number of ways a row of the given length can be filled
+
+    >>> solution(7)
+    17
+    """
+
+    ways_number = [1] * (length + 1)
+
+    for row_length in range(3, length + 1):
+        for block_length in range(3, row_length + 1):
+            for block_start in range(row_length - block_length):
+                ways_number[row_length] += ways_number[
+                    row_length - block_start - block_length - 1
+                ]
+
+            ways_number[row_length] += 1
+
+    return ways_number[length]
+
+
+if __name__ == "__main__":
+    print(f"{solution() = }")