docs: fix wrong examples and time/space claims

Author: Cameron Custer

library/convolution/min_plus_convolution_convex_and_arbitrary.hpp

@@ -2,7 +2,7 @@
 //! @param convex,arbitrary arrays where convex satisfies
 //!   convex[i+1]-convex[i] <= convex[i+2]-convex[i+1]
 //! @returns array `res` where `res[k]` = the min of
-//!   (a[i]+b[j]) for all pairs (i,j) where i+j==k
+//!   (convex[j]+arbitrary[i]) over pairs with i+j==k
 //! @time O((n + m) log (n + m))
 //! @space O(n + m)
 vi min_plus(const vi& convex, const vi& arbitrary) {

library/data_structures_[l,r)/bit.hpp

@@ -5,8 +5,8 @@
 //!     // sum = a[0] + a[1] + ... + a[r - 1]
 //!   });
 //!   int r = bit.walk2(sum);
-//!   // Returns min r s.t. sum of [0,r] >= sum
-//!   // Returns n if sum of [0,n-1] < sum
+//!   // Returns min r s.t. sum of [0,r+1) >= sum
+//!   // Returns n if sum of [0,n) < sum
 //!   // Returns -1 if sum <= 0
 //! @endcode
 //! @time O(n + q log n)

library/graphs/min_vertex_cover.hpp

@@ -9,8 +9,8 @@
 //!   auto [mvc_l, mvc_r] = cover(g, r);
 //!   // mvc_l[u] == 1 iff u in mvc
 //! @endcode
-//! @time O(n + q * log n)
-//! @space O(n * \alpha(n))
+//! @time O(n + m)
+//! @space O(n)
 pair<vi, vi> cover(const vector<vi>& g, vi& r) {
   int n = sz(g), t = 0;
   vi cl(n), cr(sz(r)), q(n);

library/math/num_distinct_subsequences.hpp

@@ -1,6 +1,6 @@
 #pragma once
 //! returns the number of distinct subsequences
-//!   of a, including the empty subsquence
+//!   of a, including the empty subsequence
 //! @time O(n log n)
 //! @space O(n)
 int num_subsequences(const vi& a, int mod) {

library/math/partitions.hpp

@@ -4,7 +4,7 @@ const int mod = 998'244'353;
 //! @code
 //!   auto p = partitions(n);
 //! @endcode
-//! p[i] = number of partitions of i numbers
+//! p[i] = number of partitions of i
 //! @time O(n sqrt n)
 //! @space O(n)
 vector<ll> partitions(int n) {

library/strings/suffix_array/compare/compare_substrings.hpp

@@ -7,9 +7,9 @@
 //!   int cmp = saq.cmp_substrs(l1,r1,l2,r2);
 //! @endcode
 //! requires l1,l2 < n
-//! if cmp1<0 then s[l1,r1) < s[l2,r2)
-//! if cmp1=0 then s[l1,r1) = s[l2,r2)
-//! if cmp1>0 then s[l1,r1) > s[l2,r2)
+//! if cmp<0 then s[l1,r1) < s[l2,r2)
+//! if cmp=0 then s[l1,r1) = s[l2,r2)
+//! if cmp>0 then s[l1,r1) > s[l2,r2)
 //! @time O(1)
 //! @space O(1)
 int cmp_substrs(int l1, int r1, int l2, int r2) {