Add rust binary search

rust/Cargo.toml

@@ -38,3 +38,7 @@ path = "structures/fenwick_tree.rs"
 [[bin]]
 name = "persistent_tree"
 path = "structures/persistent_tree.rs"
+
+[[bin]]
+name = "binary_search"
+path = "misc/binary_search.rs"

rust/misc/binary_search.rs

@@ -0,0 +1,35 @@
+// invariant: f[lo] == false, f[hi] == true
+pub fn binary_search_first_true<F>(f: F, from_inclusive: i32, to_inclusive: i32) -> i32
+where
+    F: Fn(i32) -> bool,
+{
+    let mut lo = from_inclusive - 1;
+    let mut hi = to_inclusive + 1;
+    while hi - lo > 1 {
+        let mid = (lo + hi) / 2;
+        if !f(mid) {
+            lo = mid;
+        } else {
+            hi = mid;
+        }
+    }
+    hi
+}
+
+#[cfg(test)]
+mod tests {
+    use rstest::rstest;
+    use crate::binary_search_first_true;
+
+    #[rstest]
+    #[case(100, 0)]
+    #[case(100, 1)]
+    #[case(100, 50)]
+    #[case(100, 100)]
+    fn basic_test(
+        #[case] n: i32,
+        #[case] pos: i32,
+    ) {
+        assert_eq!(binary_search_first_true(|i| { i >= pos }, 0, n), pos);
+    }
+}