seg_tree: max_right/min_left return the boundary index

Author: Cameron Custer

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

@@ -6,14 +6,16 @@
 //!     return vl + vr;
 //!   });
 //!   tree st(n, LLONG_MAX, ranges::min);
-//!   st.max_right(l, r, [&](int m, ll value) -> bool {
-//!     // l < m <= r
-//!     // value = op(a[l], a[l+1], ..., a[m-1])
-//!   });
-//!   st.min_left(l, r, [&](int m, ll value) -> bool {
-//!     // l <= m < r
-//!     // value = op(a[m], ..., a[r-2], a[r-1])
-//!   });
+//!   int m1 = st.max_right(l, r,
+//!     [&](int m, ll value) -> bool {
+//!       // l < m <= r
+//!       // value = op(a[l], a[l+1], ..., a[m-1])
+//!     }); // max m such that f holds; l if none
+//!   int m2 = st.min_left(l, r,
+//!     [&](int m, ll value) -> bool {
+//!       // l <= m < r
+//!       // value = op(a[m], ..., a[r-2], a[r-1])
+//!     }); // min m such that f holds; r if none
 //! @endcode
 //! @time O(n + q log n)
 //! @space O(n)

library/data_structures_[l,r)/seg_tree_uncommon/max_right.hpp

@@ -1,9 +1,10 @@
-void max_right(int l, int r, auto f) {
+int max_right(int l, int r, auto f) {
   for (T x = unit; l < r;) {
     int u = l + n,
         v = bit_width(min(u & -u, r - l) + 0u) - 1,
         m = l + (1 << v);
     if (T y = op(x, s[u >> v]); f(m, y)) l = m, x = y;
     else r = m - 1;
   }
+  return l;
 }

library/data_structures_[l,r)/seg_tree_uncommon/min_left.hpp

@@ -1,4 +1,4 @@
-void min_left(int l, int r, auto f) {
+int min_left(int l, int r, auto f) {
   for (T x = unit; l < r;) {
     int u = r + n,
         v = bit_width(min(u & -u, r - l) + 0u) - 1,
@@ -7,4 +7,5 @@ void min_left(int l, int r, auto f) {
       r = m, x = y;
     else l = m + 1;
   }
+  return r;
 }

library/data_structures_[l,r]/seg_tree.hpp

@@ -5,14 +5,16 @@
 //!     return vl + vr;
 //!   });
 //!   tree st(n, LLONG_MAX, ranges::min);
-//!   st.max_right(l, r, [&](int m, ll value) -> bool {
-//!     // l <= m <= r
-//!     // value = op(a[l], a[l+1], ..., a[m])
-//!   });
-//!   st.min_left(l, r, [&](int m, ll value) -> bool {
-//!     // l <= m <= r
-//!     // value = op(a[m], ..., a[r-1], a[r])
-//!   });
+//!   int m1 = st.max_right(l, r,
+//!     [&](int m, ll value) -> bool {
+//!       // l <= m <= r
+//!       // value = op(a[l], a[l+1], ..., a[m])
+//!     }); // min m such that f fails; r+1 if none
+//!   int m2 = st.min_left(l, r,
+//!     [&](int m, ll value) -> bool {
+//!       // l <= m <= r
+//!       // value = op(a[m], ..., a[r-1], a[r])
+//!     }); // max m such that f fails; l-1 if none
 //! @endcode
 //! @time O(n + q log n)
 //! @space O(n)

library/data_structures_[l,r]/seg_tree_uncommon/max_right.hpp

@@ -1,4 +1,4 @@
-void max_right(int l, int r, auto f) {
+int max_right(int l, int r, auto f) {
   if (T x = s[l + n]; f(l, x))
     for (l++; l <= r;) {
       int u = l + n,
@@ -8,4 +8,5 @@ void max_right(int l, int r, auto f) {
         l = m + 1, x = y;
       else r = m - 1;
     }
+  return l;
 }

tests/library_checker_aizu_tests/data_structures/simple_tree_inc_walk.test.cpp

@@ -21,21 +21,15 @@ int main() {
     } else if (type == 2) {
       cout << st.query(k, k) << '\n';
     } else if (type == 3) {
-      // returns first element in [k,n-1] such that mx > 0
-      int idx = -1;
-      st.max_right(k, n - 1, [&](int m, int mx) {
-        if (mx == 0) return 1;
-        idx = m;
-        return 0;
-      });
-      cout << idx << '\n';
+      // index of first element in [k,n-1] such that mx > 0
+      int idx = st.max_right(k, n - 1,
+        [&](int, int mx) { return mx == 0; });
+      cout << (idx == n ? -1 : idx) << '\n';
     } else {
       assert(type == 4);
-      int idx = -1;
-      cout << st.min_left(0, k, [&](int m, int mx) {
-        if (mx == 0) return 1;
-        idx = m;
-        return 0;
+      // index of last element in [0,k] such that mx > 0
+      cout << st.min_left(0, k, [&](int, int mx) {
+        return mx == 0;
       }) << '\n';
     }
   }

tests/library_checker_aizu_tests/data_structures/simple_tree_walk.test.cpp

@@ -20,23 +20,16 @@ int main() {
     } else if (type == 2) {
       cout << st.query(k, k + 1) << '\n';
     } else if (type == 3) {
-      // returns first element in [k,n) such that mx > 0
-      int idx = -1;
-      st.max_right(k, n, [&](int m, int mx) {
-        if (mx == 0) return 1;
-        idx = m - 1;
-        return 0;
-      });
-      cout << idx << '\n';
+      // index of first element in [k,n) such that mx > 0
+      int idx = st.max_right(k, n,
+        [&](int, int mx) { return mx == 0; });
+      cout << (idx == n ? -1 : idx) << '\n';
     } else {
       assert(type == 4);
-      int idx = -1;
-      st.min_left(0, k + 1, [&](int m, int mx) {
-        if (mx == 0) return 1;
-        idx = m;
-        return 0;
-      });
-      cout << idx << '\n';
+      // index of last element in [0,k] such that mx > 0
+      int idx = st.min_left(0, k + 1,
+        [&](int, int mx) { return mx == 0; });
+      cout << idx - 1 << '\n';
     }
   }
   return 0;