problems(cpp): add “1802. Maximum Value at a Given Index in a Bounded Array”

Signed-off-by: Matej Focko <mfocko@redhat.com>

problems/cpp/maximum-value-at-a-given-index-in-a-bounded-array.cpp

@@ -0,0 +1,54 @@
+#include <cassert>
+
+namespace {
+long sum(long index, long value, long n)
+{
+    long count = 0;
+
+    if (value > index) {
+        count += (2 * value - index) * (index + 1) / 2;
+    } else {
+        count += (value + 1) * value / 2 + index - value + 1;
+    }
+
+    if (value >= n - index) {
+        count += (2 * value - n + 1 + index) * (n - index) / 2;
+    } else {
+        count += (value + 1) * value / 2 + n - index - value;
+    }
+
+    return count - value;
+}
+}
+
+class Solution {
+public:
+    int maxValue(int n, int index, int maxSum)
+    {
+        int left = 1, right = maxSum;
+
+        while (left < right) {
+            int mid = (left + right + 1) / 2;
+            if (sum(index, mid, n) <= maxSum) {
+                left = mid;
+            } else {
+                right = mid - 1;
+            }
+        }
+
+        return left;
+    }
+};
+
+int main()
+{
+    Solution s;
+
+    assert(s.maxValue(4, 2, 6) == 2);
+    assert(s.maxValue(6, 1, 10) == 3);
+
+    // regression
+    assert(s.maxValue(6, 2, 931384943) == 155230825);
+
+    return 0;
+}