DP-evaluateExpressionToTrue.cpp

DP-evaluateExpressionToTrue.cpp

@@ -0,0 +1,99 @@
+#include <bits/stdc++.h>
+using namespace std;
+// for memoization we can use 3D DP
+// but we prefer map
+unordered_map<string, int> mp;
+int solve(string &s, int i, int j, bool isTrue)
+{
+    if (i > j)
+        return 0;
+    if (i == j)
+    {
+        if (isTrue == true)
+        {
+            if (s[i] == 'T')
+            {
+                return 1;
+            }
+            else
+            {
+                return 0;
+            }
+        }
+        else
+        {
+            if (s[i] == 'F')
+            {
+                return 1;
+            }
+            else
+            {
+                return 0;
+            }
+        }
+    }
+    // creating the key for map
+    string temp = to_string(i);
+    temp.push_back('_');
+    temp.append(to_string(j));
+    temp.push_back('_');
+    temp.append(to_string(isTrue));
+    // key creation done
+
+    if (mp.find(temp) != mp.end())
+    {
+        return mp[temp];
+    }
+
+    int ans = 0;
+    for (int k = i + 1; k < j; k += 2)
+    {
+        int leftTrue = solve(s, i, k - 1, true);
+        int leftFalse = solve(s, i, k - 1, false);
+        int rightTrue = solve(s, k + 1, j, true);
+        int rightFalse = solve(s, k + 1, j, false);
+        if (s[k] == '&')
+        {
+            if (isTrue == true)
+            {
+                ans = ans + (leftTrue * rightTrue);
+            }
+            else
+            {
+                ans = ans + (leftTrue * rightFalse) + (leftFalse * rightFalse) + (leftFalse * rightTrue);
+            }
+        }
+        if (s[k] == '|')
+        {
+            if (isTrue == true)
+            {
+                ans = ans + (leftTrue * rightFalse) + (leftTrue * rightTrue) + (leftFalse * rightTrue);
+            }
+            else
+            {
+                ans = ans + (leftFalse * rightFalse);
+            }
+        }
+        if (s[k] == '^')
+        {
+            if (isTrue == true)
+            {
+                ans = ans + (leftTrue * rightFalse) + (leftFalse * rightTrue);
+            }
+            else
+            {
+                ans = ans + (leftFalse * rightFalse) + (leftTrue * rightTrue);
+            }
+        }
+    }
+    return mp[temp] = ans;
+}
+int main()
+{
+    mp.clear();
+    string s = "T^F|F";
+    int n = s.size();
+    bool isTrue = true;
+    cout << solve(s, 0, n - 1, isTrue) << endl;
+    return 0;
+}