399. 除法求值
給出方程式A / B = k, 其中A 和B 均為用字串表示的變數,k 是一個浮點型數字。根據已知方程式求解問題,並返回計算結果。如果結果不存在,則返回-1.0。
輸入總是有效的。你可以假設除法運算中不會出現除數為 0 的情況,且不存在任何矛盾的結果。
示例 1:
輸入:equations = [["a","b"],["b","c"]], values = [2.0,3.0], queries = [["a","c"],["b","a"],["a","e"],["a","a"],["x","x"]]
輸出:[6.00000,0.50000,-1.00000,1.00000,-1.00000]
解釋:
給定:a / b = 2.0, b / c = 3.0
問題:a / c = ?, b / a = ?, a / e = ?, a / a = ?, x / x = ?
返回:[6.0, 0.5, -1.0, 1.0, -1.0 ]
示例 2:
輸入:equations = [["a","b"],["b","c"],["bc","cd"]], values = [1.5,2.5,5.0], queries = [["a","c"],["c","b"],["bc","cd"],["cd","bc"]]
輸出:[3.75000,0.40000,5.00000,0.20000]
示例 3:
輸入:equations = [["a","b"]], values = [0.5], queries = [["a","b"],["b","a"],["a","c"],["x","y"]]
輸出:[0.50000,2.00000,-1.00000,-1.00000]
提示:
1 <= equations.length <= 20
equations[i].length == 2
1 <= equations[i][0].length, equations[i][1].length <= 5
values.length ==equations.length
0.0 <values[i] <= 20.0
1 <= queries.length <= 20
queries[i].length == 2
1 <= queries[i][0].length, queries[i][1].length <= 5
equations[i][0], equations[i][1],queries[i][0], queries[i][1] 由小寫英文字母與數字組成
Floyd
from collections import defaultdict class Solution: def calcEquation(self, equations: List[List[str]], values: List[float], queries: List[List[str]]) -> List[float]: edges=defaultdict(dict) verts=set() for (a,b),c in zip(equations,values): verts.add(a) verts.add(b) edges[a][b]=c edges[b][a]=1/c for k in verts: ek=edges[k] for i in verts: if i==k: continue ei=edges[i] for j in verts: if k==j or i==j or j in ei: continue if k in ei and j in ek: ei[j]=ei[k]*ek[j] res=[] for a,b in queries: if a in edges and b in edges[a]: res.append(edges[a][b]) elif a==b and a in verts and b in verts: res.append(1) else: res.append(-1) return res