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    <p>There are many ways to do this, but the simplest algorithm is to simply process forward left to right, passing the stack as a parameter</p> <pre><code>FUNCTION isBalanced(String input, String stack) : boolean IF isEmpty(input) RETURN isEmpty(stack) ELSE IF isOpen(firstChar(input)) RETURN isBalanced(allButFirst(input), stack + firstChar(input)) ELSE IF isClose(firstChar(input)) RETURN NOT isEmpty(stack) AND isMatching(firstChar(input), lastChar(stack)) AND isBalanced(allButFirst(input), allButLast(stack)) ELSE ERROR "Invalid character" </code></pre> <hr> <p>Here it is implemented in Java. Note that I've switched it now so that the stack pushes in <em>front</em> instead of at the <em>back</em> of the string, for convenience. I've also modified it so that it just skips non-parenthesis symbols instead of reporting it as an error.</p> <pre><code>static String open = "([&lt;{"; static String close = ")]&gt;}"; static boolean isOpen(char ch) { return open.indexOf(ch) != -1; } static boolean isClose(char ch) { return close.indexOf(ch) != -1; } static boolean isMatching(char chOpen, char chClose) { return open.indexOf(chOpen) == close.indexOf(chClose); } static boolean isBalanced(String input, String stack) { return input.isEmpty() ? stack.isEmpty() : isOpen(input.charAt(0)) ? isBalanced(input.substring(1), input.charAt(0) + stack) : isClose(input.charAt(0)) ? !stack.isEmpty() &amp;&amp; isMatching(stack.charAt(0), input.charAt(0)) &amp;&amp; isBalanced(input.substring(1), stack.substring(1)) : isBalanced(input.substring(1), stack); } </code></pre> <p>Test harness:</p> <pre><code> String[] tests = { "()[]&lt;&gt;{}", "(&lt;", "]}", "()&lt;", "(][)", "{(X)[XY]}", }; for (String s : tests) { System.out.println(s + " = " + isBalanced(s, "")); } </code></pre> <p>Output:</p> <pre><code>()[]&lt;&gt;{} = true (&lt; = false ]} = false ()&lt; = false (][) = false {(X)[XY]} = true </code></pre>
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