How to count occurrence of a character in String - Java programming exercise

Write a program to count number of occurrence of a character in String is one of common programming interview question not just in Java but also in other programming language like C or C++.  As String in a very popular topic on programming interviews and there are lot of good programming exercise on String like "count number of vowels or consonants in String", "count number of characters in String" , How to reverse String in Java using recursion or without using StringBuffer etc, it becomes extremely important to have solid knowledge of String in Java or any other programming language. In Interview, most of the time Interviewer will ask you to write program without using any API method,  as Java is very rich and it always some kind of nice method to do the job, But it also important to know rich Java and open source libraries for writing production quality code. Anyway in this question we will see both API based and non API based(except few) way of to count number of occurrence of a character in String on Java.
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