Merge pull request #94 from Amank2005/patch-5

Create Book Allocation

cpp/Book Allocation

@@ -0,0 +1,100 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+// Utility function to check if current minimum value
+// is feasible or not.
+bool isPossible(int arr[], int n, int m, int curr_min)
+{
+    int studentsRequired = 1;
+    int curr_sum = 0;
+
+    // iterate over all books
+    for (int i = 0; i < n; i++) {
+        // check if current number of pages are greater
+        // than curr_min that means we will get the result
+        // after mid no. of pages
+        if (arr[i] > curr_min)
+            return false;
+
+        // count how many students are required
+        // to distribute curr_min pages
+        if (curr_sum + arr[i] > curr_min) {
+            // increment student count
+            studentsRequired++;
+
+            // update curr_sum
+            curr_sum = arr[i];
+
+            // if students required becomes greater
+            // than given no. of students,return false
+            if (studentsRequired > m)
+                return false;
+        }
+
+        // else update curr_sum
+        else
+            curr_sum += arr[i];
+    }
+    return true;
+}
+
+// function to find minimum pages
+int findPages(int arr[], int n, int m)
+{
+    long long sum = 0;
+
+    // return -1 if no. of books is less than
+    // no. of students
+    if (n < m)
+        return -1;
+    int mx = INT_MIN;
+
+    // Count total number of pages
+    for (int i = 0; i < n; i++) {
+        sum += arr[i];
+        mx = max(mx, arr[i]);
+    }
+
+    // initialize start as 0 pages and end as
+    // total pages
+    int start = mx, end = sum;
+    int result = INT_MAX;
+
+    // traverse until start <= end
+    while (start <= end) {
+        // check if it is possible to distribute
+        // books by using mid as current minimum
+        int mid = (start + end) / 2;
+        if (isPossible(arr, n, m, mid)) {
+            // update result to current distribution
+            // as it's the best we have found till now.
+            result = mid;
+
+            // as we are finding minimum and books
+            // are sorted so reduce end = mid -1
+            // that means
+            end = mid - 1;
+        }
+
+        else
+            // if not possible means pages should be
+            // increased so update start = mid + 1
+            start = mid + 1;
+    }
+
+    // at-last return minimum no. of  pages
+    return result;
+}
+
+// Driver code
+int main()
+{
+    // Number of pages in books
+    int arr[] = { 12, 34, 67, 90 };
+    int n = sizeof arr / sizeof arr[0];
+    int m = 2; // No. of students
+
+    cout << "Minimum number of pages = "
+         << findPages(arr, n, m) << endl;
+    return 0;
+}