Added Maths problems

Author: Prashant Jain

src/in/knowledgegate/dsa/math/AddStrings.java

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+package in.knowledgegate.dsa.math;
+
+/**
+ * Given two non-negative integers, num1 and num2
+ * represented as string, return the sum of num1
+ * and num2 as a string.
+ *
+ * You must solve the problem without using any
+ * built-in library for handling large integers
+ * (such as BigInteger). You must also not convert
+ * the inputs to integers directly.
+ *
+ * Example 1:
+ *
+ * Input: num1 = "11", num2 = "123"
+ * Output: "134"
+ * Example 2:
+ *
+ * Input: num1 = "456", num2 = "77"
+ * Output: "533"
+ * Example 3:
+ *
+ * Input: num1 = "0", num2 = "0"
+ * Output: "0"
+ *
+ *
+ * Constraints:
+ *
+ * 1 <= num1.length, num2.length <= 104
+ * num1 and num2 consist of only digits.
+ * num1 and num2 don't have any leading zeros except for the zero itself.
+ */
+public class AddStrings {
+    public static void main(String[] args) {
+        AddStrings addStrings = new AddStrings();
+        System.out.println("Sum is: "
+            + addStrings.addStrings("456765765",
+            "777868"));
+    }
+    public String addStrings(String num1, String num2) {
+        int carry = 0;
+        StringBuilder result = new StringBuilder();
+        int i = num1.length() - 1;
+        int j = num2.length() - 1;
+        while (i >= 0 || j >= 0 || carry > 0) {
+            int x = i >= 0 ? num1.charAt(i--) - '0': 0;
+            int y = j >= 0 ? num2.charAt(j--) - '0': 0;
+            int rem = (x + y + carry) % 10;
+            result.insert(0, rem);
+            carry = (x + y + carry) / 10;
+        }
+        return result.toString();
+    }
+}

src/in/knowledgegate/dsa/math/ConvertNumberToHexadecimal.java

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+package in.knowledgegate.dsa.math;
+
+/**
+ * Given an integer num, return a string representing
+ * its hexadecimal representation. For negative
+ * integers, two’s complement method is used.
+ *
+ * All the letters in the answer string should be
+ * lowercase characters, and there should not be
+ * any leading zeros in the answer except for the
+ * zero itself.
+ *
+ * Note: You are not allowed to use any built-in
+ * library method to directly solve this problem.
+ *
+ * Example 1:
+ * Input: num = 26
+ * Output: "1a"
+ *
+ * Example 2:
+ * Input: num = -1
+ * Output: "ffffffff"
+ *
+ * Constraints:
+ * -231 <= num <= 231 - 1
+ */
+public class ConvertNumberToHexadecimal {
+    public static void main(String[] args) {
+        ConvertNumberToHexadecimal converter =
+            new ConvertNumberToHexadecimal();
+        System.out.println("Output is: "
+            + converter.toHex(156));
+    }
+
+    public String toHex(int num) {
+        char[] hex = new char[]{'0', '1', '2',
+            '3', '4', '5', '6', '7', '8', '9', 'a'
+            , 'b', 'c', 'd', 'e', 'f'};
+        StringBuilder sb = new StringBuilder();
+        while (num > 0) {
+            int rem = num % 16;
+            sb.insert(0, hex[rem]);
+            num /= 16;
+        }
+        return sb.toString();
+    }
+}

src/in/knowledgegate/dsa/math/CountPrimes.java

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+package in.knowledgegate.dsa.math;
+
+/**
+ * Given an integer n, return the number of prime
+ * numbers that are strictly less than n.
+ *
+ * Example 1:
+ * Input: n = 10
+ * Output: 4
+ * Explanation: There are 4 prime numbers less
+ * than 10, they are 2, 3, 5, 7
+ *
+ * Example 2:
+ * Input: n = 0
+ * Output: 0
+ *
+ * Example 3:
+ * Input: n = 1
+ * Output: 0
+ *
+ * Constraints:
+ * 0 <= n <= 5 * 106
+ */
+public class CountPrimes {
+    public static void main(String[] args) {
+        CountPrimes counter = new CountPrimes();
+        System.out.println("No of prime are:"
+            + counter.countPrimes(100));
+    }
+
+    public int countPrimes(int n) {
+        boolean[] notPrime = new boolean[n];
+        int countPrime = 0;
+        for (int i = 2; i < n; i++) {
+            if (!notPrime[i]) {
+                countPrime++;
+                for (int j = 2; i*j < n; j++) {
+                    notPrime[i*j] = true;
+                }
+            }
+        }
+        return countPrime;
+    }
+}

src/in/knowledgegate/dsa/math/ExcelSheetColumnNumber.java

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+package in.knowledgegate.dsa.math;
+
+/**
+ * Given a string columnTitle that represents the
+ * column title as appears in an Excel sheet,
+ * return its corresponding column number.
+ *
+ * For example:
+ * A -> 1
+ * B -> 2
+ * C -> 3
+ * ...
+ * Z -> 26
+ * AA -> 27
+ * AB -> 28
+ * ...
+ *
+ *
+ * Example 1:
+ * Input: columnTitle = "A"
+ * Output: 1
+ *
+ * Example 2:
+ * Input: columnTitle = "AB"
+ * Output: 28
+ *
+ * Example 3:
+ * Input: columnTitle = "ZY"
+ * Output: 701
+ *
+ * Constraints:
+ * 1 <= columnTitle.length <= 7
+ * columnTitle consists only of uppercase English letters.
+ * columnTitle is in the range ["A", "FXSHRXW"].
+ */
+public class ExcelSheetColumnNumber {
+
+    public static void main(String[] args) {
+        ExcelSheetColumnNumber baseConversion =
+            new ExcelSheetColumnNumber();
+        System.out.println("Output is:" +
+            baseConversion.titleToNumber("AB"));
+    }
+
+    public int titleToNumber(String columnTitle) {
+        int result = 0, pow = 0;
+        for (int i = columnTitle.length() - 1; i >= 0; i--, pow++) {
+            char c = columnTitle.charAt(i);
+            int val = c - 'A' + 1;
+            result += val * (int)Math.pow(26, pow);
+        }
+        return result;
+    }
+}