20250513

159-7.py

@@ -0,0 +1,36 @@
+def FindRootZone(fx,start,stop,step):
+    x = start
+    while x < stop:
+        if fx(x) * fx(x+step) < 0:
+            return x
+        x += step
+    return None
+
+# 求n次方根迭代过程如下
+def GetNthRoot(a,n):
+    if a < 0 and n % 2 == 0:
+        print("Cannot compute even root of negative number")
+        return None
+    fx = lambda x: x**n - a
+    dfx = lambda x: n * x**(n-1)
+    err = 1e-10
+    N0 = 100
+    x0 = 0
+    if a > 0:
+        x0 = FindRootZone(fx, 0, a, 0.01)
+    else:
+        x0 = FindRootZone(fx, a, 0, 0.01)
+
+    count = 0
+    x1 = x0 + 1 + err
+    while abs(x1 - x0) > err or abs(fx(x1)) > err: # 添加条件修正根误差太大的问题
+        x1 = x0 - fx(x0) / dfx(x0)
+        count += 1
+        if count > N0:
+            return None
+        x0 = x1
+    return x1
+
+if __name__ == "__main__":
+    re = GetNthRoot(30, 5)
+    print(re)