067.Add Binary

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Test cases

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"1"
"1"
"0"
"0"
"0"
"1010101"
"1100011"
"10101101010"
"10011"
"11011"

Solution 1: accepted 3ms 81%

The performance is good, but the style is a diseaster man.

Time: O(n)
Space: O(n) 

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public String addBinary(String a, String b) {
    int la = a.length();
    int lb = b.length();
    int common = la < lb? la : lb;
    boolean carry = false;
    StringBuilder sb = new StringBuilder();
    for (int i = 0; i < common; i++ ) {
        char ca = a.charAt(la - i - 1);
        char cb = b.charAt(lb - i - 1);
        if (ca != cb) {  // 1 and 0
            if(carry) {
                sb.insert(0, "0"); // keep carrying on
            } else {
                sb.insert(0, "1");   
            }
        } else if (ca == '1') { // 1 and 1
            if(carry) {
                sb.insert(0, "1"); // keep carrying on
            } else {
                sb.insert(0, "0");
                carry = true;
            }
        } else { // 0 and 0
            if(carry) {
                sb.insert(0, "1");
                carry = false;
            } else {
                sb.insert(0, "0");   
            }
        }
    }
    String longer = la < lb? b : a;
    for (int j = longer.length() - common - 1; j >= 0; j--) {
        if (longer.charAt(j) == '1') {
            if (carry) {
                sb.insert(0, "0"); // keep carrying on
            } else {
                sb.insert(0, "1");
            }
        } else {
            if (carry) {
                sb.insert(0, "1");
                carry = false;
            } else {
                sb.insert(0, "0");
            }
        }
    }
    if (carry) {
        sb.insert(0, "1");
    }
    return sb.toString();
}

Solution 2: accepted 6ms

Looks better, but worse performance than solution 1. 

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public String addBinary(String a, String b) {       
    int i = a.length() - 1;
    int j = b.length() - 1;
    int carry = 0;
    StringBuilder sb = new StringBuilder();
    while (i >= 0 || j >= 0) {
        int sum = carry;
        if (i >= 0) 
            sum += Character.getNumericValue(a.charAt(i--));
        if (j >= 0) 
            sum += Character.getNumericValue(b.charAt(j--));
        sb.insert(0, Integer.toString(sum % 2));
        carry = sum >= 2? 1 : 0;
    }
    if (carry > 0)
        sb.insert(0, "1");
    return sb.toString();
}

Further improvement: 4ms

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public String addBinary(String a, String b) {       
    int i = a.length() - 1;
    int j = b.length() - 1;
    int carry = 0;
    StringBuilder sb = new StringBuilder();
    while (i >= 0 || j >= 0) {
        int sum = carry;
        if (i >= 0) 
            sum += a.charAt(i--) - '0'; // get numeric value: ('9' = 57)-('0' = 48) = 9, worth 2ms
        if (j >= 0) 
            sum += b.charAt(j--) - '0'; 
        sb.insert(0, Integer.toString(sum % 2));
        carry = sum >= 2? 1 : 0;
    }
    if (carry > 0)
        sb.insert(0, "1");
    return sb.toString();
}