chore: added comments and changed variable name in hard day 6 solution

hard/day_6/solution.cpp

@@ -1,92 +1,107 @@
-//Write your code here
-// luogu-judger-enable-o2
 #include<bits/stdc++.h>
 using namespace std;
-#define fo(i,a,b) for(int i=a;i<=b;i++)
-char l[1010],r[1010];
-int ct,c[20000][10],fa[20000],s[17000][2010],n,f[2005][17000],ok[2005][17000],l1,l2;
-int nt(int x,int y){
-	return !c[x][y]?c[x][y]=++ct:c[x][y];
+#define fo(i,a,b) for(int i=a;i<=b;i++) // Macro for looping from a to b
+
+char leftString[1010], rightString[1010]; // Arrays for storing left and right strings
+int stateCount, transitions[20000][10], suffixLinks[20000], prefixSums[17000][2010], length, n, dp[2005][17000], reachable[2005][17000], leftLength, rightLength; // Variables for counting, storing transitions, and dynamic programming
+
+int newState(int x, int y){
+    return !transitions[x][y] ? transitions[x][y] = ++stateCount : transitions[x][y]; // Function to get or create a new state
 }
-void ins(){
-	l1=strlen(l+1),l2=strlen(r+1);
-	int x=0,y=0;
-	if(l1==l2){
-		fo(i,1,l1){
-			if(x==y){
-				fo(j,l[i]-'0'+1,r[i]-'0'-1)
-	                s[nt(x,j)][l1-i]++;
-                x=nt(x,l[i]-'0');
-                y=nt(y,r[i]-'0');
-			}
-			else{
-				fo(j,l[i]-'0'+1,9)
-		            s[nt(x,j)][l1-i]++;
-                x=nt(x,l[i]-'0');
-                fo(j,(i==1),r[i]-'0'-1)
-                	s[nt(y,j)][l2-i]++;
-                y=nt(y,r[i]-'0');
-			}
-		}
-		s[x][0]++;
-		if(x!=y)s[y][0]++;
-	}
-	else{
-		fo(i,1,l1){
-			fo(j,l[i]-'0'+1,9)
-				s[nt(x,j)][l1-i]++;
-			x=nt(x,l[i]-'0');
-		}
-		fo(i,1,l2){
-			fo(j,(i==1),r[i]-'0'-1)
-				s[nt(y,j)][l2-i]++;
-			y=nt(y,r[i]-'0');
-		}
-		fo(i,l1+1,l2-1)fo(j,1,9)
-			s[nt(0,j)][i-1]++;
-		s[x][0]++;
-		s[y][0]++;
-	}
+
+void insertStrings(){
+    leftLength = strlen(leftString + 1), rightLength = strlen(rightString + 1); // Get the lengths of left and right strings
+    int x = 0, y = 0; // Initialize states for left and right strings
+    if(leftLength == rightLength){ // If lengths are equal
+        fo(i, 1, leftLength){
+            if(x == y){
+                fo(j, leftString[i] - '0' + 1, rightString[i] - '0' - 1)
+                    prefixSums[newState(x, j)][leftLength - i]++; // Increment count for transitions
+                x = newState(x, leftString[i] - '0'); // Transition to next state
+                y = newState(y, rightString[i] - '0'); // Transition to next state
+            }
+            else{
+                fo(j, leftString[i] - '0' + 1, 9)
+                    prefixSums[newState(x, j)][leftLength - i]++; // Increment count for transitions
+                x = newState(x, leftString[i] - '0'); // Transition to next state
+                fo(j, (i == 1), rightString[i] - '0' - 1)
+                    prefixSums[newState(y, j)][rightLength - i]++; // Increment count for transitions
+                y = newState(y, rightString[i] - '0'); // Transition to next state
+            }
+        }
+        prefixSums[x][0]++; // Increment count for final state
+        if(x != y) prefixSums[y][0]++; // Increment count for final state
+    }
+    else{
+        fo(i, 1, leftLength){
+            fo(j, leftString[i] - '0' + 1, 9)
+                prefixSums[newState(x, j)][leftLength - i]++; // Increment count for transitions
+            x = newState(x, leftString[i] - '0'); // Transition to next state
+        }
+        fo(i, 1, rightLength){
+            fo(j, (i == 1), rightString[i] - '0' - 1)
+                prefixSums[newState(y, j)][rightLength - i]++; // Increment count for transitions
+            y = newState(y, rightString[i] - '0'); // Transition to next state
+        }
+        fo(i, leftLength + 1, rightLength - 1)
+            fo(j, 1, 9)
+                prefixSums[newState(0, j)][i - 1]++; // Increment count for transitions
+        prefixSums[x][0]++; // Increment count for final state
+        prefixSums[y][0]++; // Increment count for final state
+    }
 }
-queue<int>q;
-void bd(){
-    fo(i,0,9)if(c[0][i])
-	    q.push(c[0][i]);
-    while(!q.empty()){
-    	int x=q.front();
-    	q.pop();
-    	fo(i,0,l2-1)s[x][i]+=s[fa[x]][i];
-        fo(i,0,9){
-        	if(c[x][i]){
-        		q.push(c[x][i]);
-        		fa[c[x][i]]=c[fa[x]][i];
-			}
-			else c[x][i]=c[fa[x]][i];
-		}
-	}
-	fo(i,0,ct)fo(j,1,n)
-        s[i][j]+=s[i][j-1];
+
+queue<int> bfsQueue; // Queue for BFS
+
+void buildAutomaton(){
+    fo(i, 0, 9) if(transitions[0][i])
+        bfsQueue.push(transitions[0][i]); // Push initial states to the queue
+    while(!bfsQueue.empty()){
+        int currentState = bfsQueue.front();
+        bfsQueue.pop();
+        fo(i, 0, rightLength - 1)
+            prefixSums[currentState][i] += prefixSums[suffixLinks[currentState]][i]; // Update counts using suffix link
+        fo(i, 0, 9){
+            if(transitions[currentState][i]){
+                bfsQueue.push(transitions[currentState][i]);
+                suffixLinks[transitions[currentState][i]] = transitions[suffixLinks[currentState]][i]; // Set suffix link
+            }
+            else transitions[currentState][i] = transitions[suffixLinks[currentState]][i]; // Set transition
+        }
+    }
+    fo(i, 0, stateCount)
+        fo(j, 1, n)
+            prefixSums[i][j] += prefixSums[i][j - 1]; // Compute prefix sums
 }
+
 int main(){
-	scanf("%s%s%d",l+1,r+1,&n);
-	ins();
-	bd();
-	memset(f,-32,sizeof(f));
-	f[0][0]=0;
-	fo(i,0,n-1)fo(j,0,ct)if(f[i][j]>=0)
-		fo(k,0,9)f[i+1][c[j][k]]=max(f[i+1][c[j][k]],f[i][j]+s[c[j][k]][n-i-1]);
-	int r=-1e9;
-	fo(i,0,ct)r=max(r,f[n][i]);
-	printf("%d\n",r);
-	fo(i,0,ct)ok[n][i]=(r==f[n][i]);
-	for(int i=n-1;i;i--)
-		fo(j,0,ct)fo(k,0,9)
-			ok[i][j]|=ok[i+1][c[j][k]]&&(f[i+1][c[j][k]]==f[i][j]+s[c[j][k]][n-i-1]);
-	int x=0;
-	fo(i,1,n)fo(k,0,9)
-		if(ok[i][c[x][k]]&&f[i][c[x][k]]==f[i-1][x]+s[c[x][k]][n-i]){
-			printf("%d",k);
-			x=c[x][k];
-			break;
-		}
+    scanf("%s%s%d", leftString + 1, rightString + 1, &n); // Input left, right strings, and n
+    insertStrings(); // Construct automaton
+    buildAutomaton(); // Build automaton
+    memset(dp, -32, sizeof(dp)); // Initialize DP table
+    dp[0][0] = 0; // Base case
+    fo(i, 0, n - 1)
+        fo(j, 0, stateCount)
+            if(dp[i][j] >= 0)
+                fo(k, 0, 9)
+                    dp[i + 1][transitions[j][k]] = max(dp[i + 1][transitions[j][k]], dp[i][j] + prefixSums[transitions[j][k]][n - i - 1]); // DP transition
+    int result = -1e9; // Initialize result
+    fo(i, 0, stateCount)
+        result = max(result, dp[n][i]); // Update result
+    printf("%d\n", result); // Output result
+
+    fo(i, 0, stateCount)
+        reachable[n][i] = (result == dp[n][i]); // Mark states achieving the result
+    for(int i = n - 1; i; i--)
+        fo(j, 0, stateCount)
+            fo(k, 0, 9)
+                reachable[i][j] |= reachable[i + 1][transitions[j][k]] && (dp[i + 1][transitions[j][k]] == dp[i][j] + prefixSums[transitions[j][k]][n - i - 1]); // Mark states for next iteration
+    int currentState = 0; // Initialize state
+    fo(i, 1, n)
+        fo(k, 0, 9)
+            if(reachable[i][transitions[currentState][k]] && dp[i][transitions[currentState][k]] == dp[i - 1][currentState] + prefixSums[transitions[currentState][k]][n - i]){
+                printf("%d", k); // Output character
+                currentState = transitions[currentState][k]; // Transition to next state
+                break;
+            }
 }