add khushal87 unbounded-knapsack-related-codes

Dynamic Programming/coin_change_problem_1.cpp

@@ -0,0 +1,48 @@
+//max number of ways to give a sum
+#include <bits/stdc++.h>
+using namespace std;
+
+int solve(int p[], int n, int cap)
+{
+ int t[n + 1][cap + 1];
+ for (int i = 0; i <= n; i++)
+ {
+ for (int j = 0; j <= cap; j++)
+ {
+ if (j == 0)
+ {
+ t[i][j] = 1;
+ }
+ else if (i == 0 && j > 0)
+ {
+ t[i][j] = 0;
+ }
+ else
+ {
+ if (p[i - 1] <= j)
+ {
+ t[i][j] = t[i][j - p[i - 1]] + t[i - 1][j];
+ }
+ else
+ {
+ t[i][j] = t[i - 1][j];
+ }
+ }
+ }
+ }
+ return t[n][cap];
+}
+
+int main()
+{
+ int n;
+ cin >> n;
+ int p[n];
+ for (int i = 0; i < n; i++)
+ {
+ cin >> p[i];
+ }
+ int cap;
+ cin >> cap;
+ cout << solve(p, n, cap) << endl;
+}

Dynamic Programming/coin_change_problem_2.cpp

@@ -0,0 +1,56 @@
+//minimum number of coin to get a sum
+#include <bits/stdc++.h>
+using namespace std;
+
+int solve(int arr[], int n, int sum)
+{
+ int t[n + 1][sum + 1];
+ for (int i = 0; i <= sum; i++)
+ {
+ t[0][i] = INT_MAX - 1;
+ }
+ for (int i = 1; i <= n; i++)
+ {
+ t[i][0] = 0;
+ }
+ for (int i = 1; i <= sum; i++)
+ {
+ if (i % arr[0] == 0)
+ {
+ t[1][i] = i / arr[0];
+ }
+ else
+ {
+ t[1][i] = INT_MAX - 1;
+ }
+ }
+ for (int i = 2; i <= n; i++)
+ {
+ for (int j = 1; j <= sum; j++)
+ {
+ if (arr[i - 1] <= j)
+ {
+ t[i][j] = min(1 + t[i][j - arr[i - 1]], t[i - 1][j]);
+ }
+ else
+ {
+ t[i][j] = t[i - 1][j];
+ }
+ }
+ }
+ return t[n][sum];
+}
+
+int main()
+{
+ int n;
+ cin >> n;
+ int p[n];
+ for (int i = 0; i < n; i++)
+ {
+ cin >> p[i];
+ }
+ int cap;
+ cin >> cap;
+ cout << solve(p, n, cap) << endl;
+}

Dynamic Programming/count_the_number_of_subset_with_given_sum.cpp

@@ -0,0 +1,53 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+// sum(s1)-sum(s2)=diff
+// sum(s1)+sum(s2)=sumOfArray
+// -> sum(s1)= diff+sumOfArray/2;
+int solve(int p[], int n, int cap)
+{
+ int t[n + 1][cap + 1];
+ for (int i = 0; i <= n; i++)
+ {
+ for (int j = 0; j <= cap; j++)
+ {
+ if (j == 0)
+ {
+ t[i][j] = 1;
+ }
+ else if (i == 0 && j > 0)
+ {
+ t[i][j] = 0;
+ }
+ else
+ {
+ if (p[i - 1] <= j)
+ {
+ t[i][j] = t[i - 1][j - p[i - 1]] + t[i - 1][j];
+ }
+ else
+ {
+ t[i][j] = t[i - 1][j];
+ }
+ }
+ }
+ }
+ return t[n][cap];
+}
+
+int main()
+{
+ int n;
+ cin >> n;
+ int p[n];
+ int sum = 0;
+ for (int i = 0; i < n; i++)
+ {
+ cin >> p[i];
+ sum += p[i];
+ }
+ int diff;
+ cin >> diff;
+ int passedSum = diff + sum / 2;
+ cout << solve(p, n, passedSum) << endl;
+}

Dynamic Programming/minimum_subset_sum_difference.cpp

@@ -0,0 +1,61 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+int solve(int arr[], int n)
+{
+ int sum = 0;
+ for (int i = 0; i < n; i++)
+ sum += arr[i];
+ bool t[n + 1][sum + 1];
+ for (int i = 0; i <= n; i++)
+ {
+ for (int j = 0; j <= sum; j++)
+ {
+ if (j == 0)
+ {
+ t[i][j] = true;
+ }
+ else if (i == 0 && j > 0)
+ {
+ t[i][j] = false;
+ }
+ else
+ {
+ if (arr[i - 1] <= j)
+ {
+ t[i][j] = t[i - 1][j - arr[i - 1]] || t[i - 1][j];
+ }
+ else
+ {
+ t[i][j] = t[i - 1][j];
+ }
+ }
+ }
+ }
+ vector<int> temp;
+ for (int i = 0; i <= sum / 2; i++)
+ {
+ if (t[n][i])
+ {
+ temp.push_back(i);
+ }
+ }
+ int minm = INT_MAX;
+ for (auto j : temp)
+ {
+ minm = min(minm, sum - 2 * j);
+ }
+ return minm;
+}
+
+int main()
+{
+ int n;
+ cin >> n;
+ int arr[n];
+ for (int i = 0; i < n; i++)
+ {
+ cin >> arr[i];
+ }
+ cout << solve(arr, n) << endl;
+}

Dynamic Programming/rod_cutting.cpp

@@ -0,0 +1,41 @@
+//same as unbounded cpp
+#include <bits/stdc++.h>
+using namespace std;
+
+int solve(int p[], int len[], int n, int lenRod)
+{
+ int t[n + 1][lenRod + 1];
+ for (int i = 0; i <= n; i++)
+ {
+ for (int j = 0; j <= lenRod; j++)
+ {
+ if (i == 0 || j == 0)
+ {
+ t[i][j] = 0;
+ }
+ else if (len[i - 1] <= j)
+ {
+ t[i][j] = max(p[i - 1] + t[i][j - len[i - 1]], t[i - 1][j]);
+ }
+ else
+ {
+ t[i][j] = t[i - 1][j];
+ }
+ }
+ }
+ return t[n][lenRod];
+}
+
+int main()
+{
+ int n;
+ cin >> n;
+ int p[n], len[n];
+ for (int i = 0; i < n; i++)
+ {
+ cin >> p[i] >> len[i];
+ }
+ int lenRod;
+ cin >> lenRod;
+ cout << solve(p, len, n, lenRod) << endl;
+}

Dynamic Programming/target_sum.cpp

@@ -0,0 +1,53 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+// sum(s1)-sum(s2)=diff
+// sum(s1)+sum(s2)=sumOfArray
+// -> sum(s1)= diff+sumOfArray/2;
+int solve(int p[], int n, int cap)
+{
+ int t[n + 1][cap + 1];
+ for (int i = 0; i <= n; i++)
+ {
+ for (int j = 0; j <= cap; j++)
+ {
+ if (j == 0)
+ {
+ t[i][j] = 1;
+ }
+ else if (i == 0 && j > 0)
+ {
+ t[i][j] = 0;
+ }
+ else
+ {
+ if (p[i - 1] <= j)
+ {
+ t[i][j] = t[i - 1][j - p[i - 1]] + t[i - 1][j];
+ }
+ else
+ {
+ t[i][j] = t[i - 1][j];
+ }
+ }
+ }
+ }
+ return t[n][cap];
+}
+
+int main()
+{
+ int n;
+ cin >> n;
+ int p[n];
+ int sum = 0;
+ for (int i = 0; i < n; i++)
+ {
+ cin >> p[i];
+ sum += p[i];
+ }
+ int diff;
+ cin >> diff;
+ int passedSum = diff + sum / 2;
+ cout << solve(p, n, passedSum) << endl;
+}

Dynamic Programming/unbounded_knapsack.cpp

@@ -0,0 +1,40 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+int solve(int p[], int w[], int n, int cap)
+{
+ int t[n + 1][cap + 1];
+ for (int i = 0; i <= n; i++)
+ {
+ for (int j = 0; j <= cap; j++)
+ {
+ if (i == 0 || j == 0)
+ {
+ t[i][j] = 0;
+ }
+ else if (w[i - 1] <= j)
+ {
+ t[i][j] = max(p[i - 1] + t[i][j - w[i - 1]], t[i - 1][j]);
+ }
+ else
+ {
+ t[i][j] = t[i - 1][j];
+ }
+ }
+ }
+ return t[n][cap];
+}
+
+int main()
+{
+ int n;
+ cin >> n;
+ int p[n], w[n];
+ for (int i = 0; i < n; i++)
+ {
+ cin >> p[i] >> w[i];
+ }
+ int cap;
+ cin >> cap;
+ cout << solve(p, w, n, cap) << endl;
+}