Bisection Method for Exponential Root

Time Limit: 2sMemory: 256MB

Problem

Implement the bisection method to find the root of $f(x) = e^x - b$ on the interval $[\text{lo}, \text{hi}]$ .

The root is $x = \ln(b)$ , but you must find it using bisection — not the closed-form formula.

Algorithm: Repeat $n$ times:

Compute $\text{mid} = (\text{lo} + \text{hi}) / 2$
If $f(\text{mid}) > 0$ , set $\text{hi} = \text{mid}$ ; otherwise set $\text{lo} = \text{mid}$

After $n$ iterations, output $(\text{lo} + \text{hi}) / 2$ .

Four space-separated values: b lo hi n

The midpoint approximation of $\ln(b)$ , to 4 decimal places.

Example 1

Input(Four space-separated values: b lo hi n)

1.0 -1.0 1.0 20

Output

0.0000

ln(1) = 0. Bisection on [-1, 1] converges to 0.0000.

Example 2

Input(Four space-separated values: b lo hi n)

2.0 0.0 1.0 25

Output

0.6931

ln(2) = 0.6931. Bisection on [0, 1] converges accurately.

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