dp

Author: idf

403 Frog Jump.py

@@ -0,0 +1,67 @@
+"""
+A frog is crossing a river. The river is divided into x units and at each unit there may or may not exist a stone. The
+frog can jump on a stone, but it must not jump into the water.
+
+Given a list of stones' positions (in units) in sorted ascending order, determine if the frog is able to cross the river
+by landing on the last stone. Initially, the frog is on the first stone and assume the first jump must be 1 unit.
+
+If the frog's last jump was k units, then its next jump must be either k - 1, k, or k + 1 units. Note that the frog can
+only jump in the forward direction.
+
+Note:
+
+The number of stones is >= 2 and is < 1,100.
+Each stone's position will be a non-negative integer < 231.
+The first stone's position is always 0.
+Example 1:
+
+[0,1,3,5,6,8,12,17]
+
+There are a total of 8 stones.
+The first stone at the 0th unit, second stone at the 1st unit,
+third stone at the 3rd unit, and so on...
+The last stone at the 17th unit.
+
+Return true. The frog can jump to the last stone by jumping
+1 unit to the 2nd stone, then 2 units to the 3rd stone, then
+2 units to the 4th stone, then 3 units to the 6th stone,
+4 units to the 7th stone, and 5 units to the 8th stone.
+Example 2:
+
+[0,1,2,3,4,8,9,11]
+
+Return false. There is no way to jump to the last stone as
+the gap between the 5th and 6th stone is too large.
+"""
+__author__ = 'Daniel'
+
+
+class Solution(object):
+    def canCross(self, stones):
+        """
+        F, step table
+        Let F[i] be stone at position i,
+
+        dp with a set as the table cell.
+        :type stones: List[int]
+        :rtype: bool
+        """
+        F = {}
+        for stone in stones:
+            F[stone] = set()
+
+        F[0].add(0)
+        for stone in stones:
+            for step in F[stone]:
+                for i in (-1, 0, 1):
+                    nxt = stone+step+i
+                    if nxt != stone and nxt in F:
+                        F[nxt].add(step+i)
+
+        return True if F[stones[-1]] else False
+
+
+if __name__ == "__main__":
+    assert Solution().canCross([0, 2]) == False
+    assert Solution().canCross([0, 1, 3, 5, 6, 8, 12, 17]) == True
+    assert Solution().canCross([0, 1, 2, 3, 4, 8, 9, 11]) == False