"Missing Operating system_ " After installing Yosemite

Please post the output of sudo gpt -vv -r show /dev/disk0 (you are missing a "/" before disk0).

1. Very suspicious that the gap between GPT#3 and GPT#4 is almost the same size as Windows. Did you have another 40GB partition that you have "lost"?

2. Please post the output of sudo dd if=/dev/rdisk0s4 count=1 2>/dev/null | hexdump -C (this looks for a NTFS header).

Yes, but it requires some work. If you want to please download...

1. Testdisk - http://www.cgsecurity.org/wiki/TestDisk this to look for the deleted NTFS header.

2. GPT Fdisk - http://sourceforge.net/projects/gptfdisk/ - this is to fix partitions after Testdisk has found the correct partition header.

If you have a 500GB disk, 419 for OS X and 40GB for Windows, where is the other ~31GB data. It looks like that is where the NTFS header is sitting.

1. Click on Create.

Avoid using left and right arrows (which usually change partition status). Please see http://www.cgsecurity.org/wiki/TestDisk_Step_By_Step.

You are looking for "familiar" Windows files using "P: List Files" in every partition which is MS Data (Microsoft Data). You will select the EFI partition type (because OS X uses EFI/GPT).

Please use /dev/rdisk0. Till it stays broken, my work is not done. 😉

Yes.

Please pick EFI.

Yes, please. Please post the list of partitions you see for recording purposes. Save the images that you are posting, if steps need to retraced.