Symbol(clack:cancel)

solutions/0000_0029/0018.MaxPathSum1/eular_18_1.py

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+"""
+By starting at the top of the triangle below and moving to adjacent numbers on the row below,
+the maximum total from top to bottom is 23.
+
+3
+7 4
+2 4 6
+8 5 9 3
+
+That is, 3 + 7 + 4 + 9 = 23 .
+
+Find the maximum total from top to bottom of the triangle below:
+
+75
+95 64
+17 47 82
+18 35 87 10
+20 04 82 47 65
+19 01 23 75 03 34
+88 02 77 73 07 63 67
+99 65 04 28 06 16 70 92
+41 41 26 56 83 40 80 70 33
+41 48 72 33 47 32 37 16 94 29
+53 71 44 65 25 43 91 52 97 51 14
+70 11 33 28 77 73 17 78 39 68 17 57
+91 71 52 38 17 14 91 43 58 50 27 29 48
+63 66 04 68 89 53 67 30 73 16 69 87 40 31
+04 62 98 27 23 09 70 98 73 93 38 53 60 04 23
+"""
+
+TXT = """75
+95 64
+17 47 82
+18 35 87 10
+20 04 82 47 65
+19 01 23 75 03 34
+88 02 77 73 07 63 67
+99 65 04 28 06 16 70 92
+41 41 26 56 83 40 80 70 33
+41 48 72 33 47 32 37 16 94 29
+53 71 44 65 25 43 91 52 97 51 14
+70 11 33 28 77 73 17 78 39 68 17 57
+91 71 52 38 17 14 91 43 58 50 27 29 48
+63 66 04 68 89 53 67 30 73 16 69 87 40 31
+04 62 98 27 23 09 70 98 73 93 38 53 60 04 23"""
+
+
+def triangle_best_choice(triangle: list[list[int]]) -> tuple[int, int]:
+    if len(triangle) == 2:
+        res = max(triangle[1][0], triangle[1][1])
+        index = triangle[1].index(res)
+        return res, index
+    else:
+        one = max(triangle[1][0] + triangle[2][0], triangle[1][0] + triangle[2][1])
+        two = max(triangle[1][1] + triangle[2][1], triangle[1][1] + triangle[2][2])
+        if one >= two:
+            return triangle[1][0], 0
+        else:
+            return triangle[1][1], 1
+
+
+def triangle_best_path(triangle: list[list[int]]) -> list[int]:
+    max_len = len(triangle)
+    if max_len == 1:
+        return triangle[0]
+    coln = 0
+    res = triangle[0]
+    for i in range(max_len - 1):
+        if i + 2 < max_len:
+            keypart = [
+                triangle[i][coln : coln + 1],
+                triangle[i + 1][coln : coln + 2],
+                triangle[i + 2][coln : coln + 3],
+            ]
+        else:
+            keypart = [triangle[i][coln : coln + 1], triangle[i + 1][coln : coln + 2]]
+        tres, delta = triangle_best_choice(keypart)
+        res.append(tres)
+        coln += delta
+    return res
+
+
+def main() -> None:
+    data = TXT.split("\n")
+    triangle = [list(map(int, row.split())) for row in data]
+    res = triangle_best_path(triangle)
+    print(f"{sum(res)} = {' + '.join(map(str, res))}")
+
+
+if __name__ == "__main__":
+    main()