bulves

Author: thecodingwizard

LMIO/LMIO 19-bulves.cpp

@@ -0,0 +1,74 @@
+/*
+ * slope trick!
+ *
+ * https://usaco.guide/adv/slope
+ */
+
+#include <bits/stdc++.h>
+
+using namespace std;
+
+using ll = long long;
+#define ii pair<int, int>
+#define f first
+#define s second
+#define pb push_back
+#define mp make_pair
+#define all(x) x.begin(), x.end()
+#define sz(x) (int)x.size()
+#define F0R(i, n) for (int i = 0; i < n; i++)
+#define FOR(i, a, b) for (int i = a; i < b; i++)
+#define inf 1000000010
+
+int main() {
+    cin.tie(0)->sync_with_stdio(0);
+
+    int n; cin >> n;
+
+    ll dp0 = 0; // y-intercept
+
+    // slope increases by one at each of these points
+    priority_queue<ll> slopeChanges;
+
+    ll initialSlope = 0;
+
+    ll totA = 0, totB = 0;
+    ll diff;
+    F0R(i, n) {
+        int a, b; cin >> a >> b; totA += a; totB += b;
+
+        diff = totA - totB;
+
+        dp0 += abs(diff);
+        initialSlope--;
+
+        // at x = diff, the function slope changes by two
+        slopeChanges.push(diff);
+        slopeChanges.push(diff);
+
+        // remove the final slope change that will cause the slope to become positive
+        slopeChanges.pop();
+    }
+
+    // Want to calculate dp value where x = diff (the final difference)
+    vector<ll> changes;
+    while (!slopeChanges.empty()) { changes.pb(slopeChanges.top()); slopeChanges.pop(); }
+    reverse(all(changes));
+    ll curX = 0, slope = initialSlope;
+    for (ll x : changes) {
+        ll dist = x - curX;
+        if (x >= diff) {
+            dp0 += slope*dist;
+            break;
+        }
+        if (x >= 0) {
+            dp0 += slope*dist;
+            curX = x;
+        }
+        slope++;
+    }
+
+    cout << dp0 << endl;
+
+    return 0;
+}

input.txt

@@ -1,3 +1,7 @@
-20
-3 1 4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4
-
+6
+1 2
+0 0
+2 0
+0 0
+0 0
+0 1