Solve problem 100 - this also my 100th problem in total

python/e100.py

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+from fractions import Fraction
+
+
+def euler_100():
+    F_ONE_HALF = Fraction(1, 2)
+    prev_blue_discs, blue_discs = 10, 10
+    while True:
+        # Brute force search blue discs
+        blue_discs += 1
+
+        # Binary search red discs
+        red_upper = blue_discs // 2
+        red_lower = 1
+        while red_upper != red_lower:
+            red_discs = red_lower + (red_upper - red_lower) // 2
+            total_discs = blue_discs + red_discs
+            f1 = Fraction(blue_discs, total_discs)
+            f2 = Fraction(blue_discs - 1, total_discs - 1)
+            f = f1 * f2
+            if f == F_ONE_HALF:
+                # End criterion by Euler Problem
+                if total_discs > 10**12:
+                    return blue_discs
+
+                # The ration between two solutions seems to be constant so we
+                # can get the next larger candidate for blue_discs much
+                # quicker.
+                ratio = blue_discs / prev_blue_discs
+                # print("blue_discs={} ratio={}".format(blue_discs, ratio))
+                prev_blue_discs = blue_discs
+                blue_discs = int(blue_discs * ratio)
+                break
+            elif f < F_ONE_HALF:
+                red_upper = red_discs
+            else:
+                red_lower = red_discs
+
+            # No solution for current number of blue discs
+            if abs(red_upper - red_lower) <= 1:
+                break
+
+
+if __name__ == "__main__":
+    solution = euler_100()
+    print("e100.py: " + str(solution))
+    assert(solution == 756872327473)
+