sms

Author: dolphingarlic

infoarena/infoarena sms.cpp

@@ -0,0 +1,30 @@
+/*
+Infoarena sms
+- dp[i] = The EV of the time it takes to type character i after having typed i - 1 characters
+        = pC[s[i] - 'a'] * 1 + pI[s[i] - 'a'] * (dp[i] + 2) + pB[s[i] - 'a'] * (dp[i - 1] + dp[i] + 1)
+        = (1 + pI[s[i] - 'a'] + pB[s[i] - 'a'] * dp[i - 1]) / pC[s[i] - 'a']
+- By linearity of expectation, the answer = sum(dp[i])
+- Complexity: O(N)
+*/
+
+#include <bits/stdc++.h>
+using namespace std;
+
+double pC[26], pI[26], pB[26];
+
+int main() {
+    ifstream cin("sms.in");
+    ofstream cout("sms.out");
+    int n, k;
+    string s;
+    cin >> n >> k >> s;
+    for (int i = 0; i < k; i++) cin >> pC[i] >> pI[i] >> pB[i];
+    double ans = 0, prv = 0;
+    for (int i = 0; i < n; i++) {
+        double nxt = (1 + pI[s[i] - 'a'] + pB[s[i] - 'a'] * prv) / pC[s[i] - 'a'];
+        ans += nxt;
+        prv = nxt;
+    }
+    cout << fixed << setprecision(6) << ans;
+    return 0;
+}