Solve some problems.

2024-04-28 14:33:46 -04:00
parent ceca539c70
commit e9873eaa2f
6 changed files with 222 additions and 1 deletions
--- a/python/e141.py
+++ b/python/e141.py
@@ -0,0 +1,81 @@
+from math import isqrt, gcd
+
+
+def issqrt(n):
+    isq = isqrt(n)
+    return isq * isq == n
+
+
+def euler_141_brute_force():
+    import concurrent.futures
+
+    def have_same_ratio(a, b, c, d):
+        if b == 0 or d == 0:
+            raise ValueError("Denominators must be non-zero")
+        return a * d == b * c
+
+    def check_range(start, end):
+        local_sum = 0
+        for i in range(start, end):
+            if i % 10000 == 0:
+                print(i)
+            n = i * i
+            for d in range(1, i):
+                q = n // d
+                r = n % d
+                if r == 0:
+                    continue
+                assert r < d and d < q
+                if have_same_ratio(d, r, q, d):
+                    print(f"{n=} {i=} {r=} {d=} {q=}")
+                    local_sum += n
+                    break
+        return local_sum
+
+    s = 0
+    m = 1_000_000
+    range_size = 10_000
+
+    with concurrent.futures.ProcessPoolExecutor() as executor:
+        futures = []
+        for start in range(1, m, range_size):
+            end = min(start + range_size, m)
+            futures.append(executor.submit(check_range, start, end))
+
+        for future in concurrent.futures.as_completed(futures):
+            s += future.result()
+
+    return s
+
+
+def euler_141():
+    r = 0
+    NMAX = 10**12
+    a = 1
+    while True:
+        if a**3 > NMAX:
+            break
+        for b in range(1, a):
+            if a**3 * b**2 > NMAX:
+                break
+
+            if gcd(a, b) != 1:
+                continue
+
+            c = 1
+            while True:
+                n = a**3 * b * c**2 + c * b**2
+                if n > NMAX:
+                    break
+                if issqrt(n):
+                    # print(n)
+                    r += n
+                c += 1
+        a += 1
+    return r
+
+
+if __name__ == "__main__":
+    solution = euler_141()
+    print("e141.py: " + str(solution))
+    assert solution == 878454337159