Sparse Table

CSES/1647v2.cc

@@ -0,0 +1,36 @@
+#include <iostream>
+#include <vector>
+#include <algorithm>
+using namespace std;
+typedef vector<int> vi;
+
+class SparseTable {
+private:
+    vector<vi> SpT;
+    int N, LOG;
+public:
+    SparseTable(const vi& A) {
+        N = A.size();
+        LOG = 31 - __builtin_clz(N)+1;
+        SpT.resize(N, vi(LOG));
+        for(int i = 0; i < N; ++i) SpT[i][0] = A[i];
+        for(int j = 1; j < LOG; ++j) for(int i = 0; i + (1<<j) - 1 < N; ++i) {
+            SpT[i][j] = min(SpT[i][j-1], SpT[i+(1<<(j-1))][j-1]);
+        }
+    }
+
+    int RMQ(int L, int R) {
+        int k = 31 - __builtin_clz(R-L+1);
+        return min(SpT[L][k], SpT[R-(1<<k)+1][k]);
+    }
+};
+
+int main() {
+    int n, q; cin >> n >> q;
+    vi v(n); for(auto& e : v) cin >> e;
+    SparseTable table(v);
+    for(int i = 0; i < q; ++i) {
+        int L, R; cin >> L >> R;
+        cout << table.RMQ(L-1, R-1) << endl;
+    }
+}

Study/sparse_table.cc

@@ -1,36 +1,28 @@
 #include <iostream>
 #include <vector>
-#define FOR(i,a,b) for(int i = a; i <= b; ++i)
 using namespace std;
 typedef vector<int> vi;
 
-classSparseTable {
+class SparseTable {
 private:
-    vi A, L2, P2;,
-    vector<vi> SpT;
+    vi A;
+    vector<vector<int>> SpT;
+    int LOG, N;
 public:
     SparseTable(vi& initialA) {
         A = initialA;
-        int n = A.size();
-        int L2_n = log2(n)+1;
-        L2.assign((1<<L2_n)+1,0);
-        P2.assign(L2_n+1,0);
-        FOR(i,0,L2_n) L2[(1<<i)] = i, P2[i] = (1<<i);
-        FOR(i,2,P2[L2_n]) if(L2[i] == 0) L2[i] = L2[i-1];
-        SpT = vector<vi>(L2_n, vi(n));
-        FOR(i,0,n-1) SpT[0][i] = i;
-        for(int i = 1; P2[i] <= n; ++i)
-            for(int j = 0; j+P2[i]-1 < n; ++j) {
-                int x = SpT[i-1][j];
-                int y = SpT[i-1][j+P2[i-1]];
-                SpT[i][j] = A[x] <= A[y] ? x : y;
-            }
+        N = A.size();
+        LOG = 31-__builtin_clz(N)+1;
+        SpT.resize(N, vector<int>(LOG, 0));
+        for(int i = 0; i < N; ++i) SpT[i][0] = A[i];
+        for(int j = 1; j < LOG; ++j) for(int i = 0; i + (1<<j) - 1 < N; ++i) {
+            SpT[i][j] = min(SpT[i][j-1], SpT[i+(1<<(j-1))][j-1]);
+        }
     }
 
-    int RMQ(int i, int j) {
-        int k = L2[j-i+1];
-        int x = SpT[k][i];
-        int y = SpT[k][j-P2[k]+1];
-        return A[x] <= A[y] ? x : y;
+    int RMQ(int L, int R) {
+        int len = R-L+1;
+        int k = 31 - __builtin_clz(len);
+        return min(SpT[L][k], SpT[R-(1<<k)+1][k]);
     }
 };