Modulo multiplicative Inverse

mathematic/Problems/ModuloMultiplictiveInverse.java

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+
+/*Given two integers ‘a’ and ‘m’. The task is to find the smallest modular multiplicative inverse of ‘a’ under modulo ‘m’.
+
+ 
+
+Example 1:
+
+Input:
+a = 3
+m = 11
+Output: 4
+Explanation: Since (4*3) mod 11 = 1, 4 
+is modulo inverse of 3. One might think,
+15 also as a valid output as "(15*3)
+mod 11"  is also 1, but 15 is not in 
+ring {0, 1, 2, ... 10}, so not valid.
+ 
+
+Example 2:
+
+Input:
+a = 10
+m = 17
+Output: 12
+Explanation: Since (12*10) mod 17 = 1,
+12 is the modulo inverse of 10.
+ 
+
+Your Task:
+You don't need to read input or print anything. Your task is to complete the function function modInverse() that takes a and m as input parameters and returns modular multiplicative inverse of ‘a’ under modulo ‘m’. If the modular multiplicative inverse doesn't exist return -1.
+
+ 
+
+Expected Time Complexity : O(m)
+Expected Auxilliary Space : O(1)
+
+ 
+
+Constraints:
+1 <= a <= 104
+1 <= m <= 104 */
+
+
+package mathematic.Problems;
+
+public class ModuloMultiplictiveInverse {
+    public int modInverse(int a, int m)
+    {
+      //Your code here
+       for (int x = 1; x < m; x++)
+            if (((a%m) * (x%m)) % m == 1)
+                return x;
+        return -1;
+    }
+}